TW490656B - Method and system for on-line blind source separation - Google Patents

Abstract

A method and apparatus is disclosed for performing blind source separation using convolutive signal decorrelation. For a first embodiment, the method accumulates a length of input signal (mixed signal) that comprises a plurality of independent signals from independent signal sources. The invention then divides the length of input signal into a plurality of T-length periods (windows) and performs a discrete Fourier transform (DFT) on the signal within each T-length period. Thereafter, estimated cross-correlation values are computed using a plurality of the averaged DFT values. A total number of K cross-correlation values are computed, where each of the K values is averaged over N of the T-length periods. Using the cross-correlation values, a gradient descent process computes the coefficients of a FIR filter that will effectively separate the source signals within the input signal. A second embodiment of the invention is directed to on-line processing of the input signal - I.e., processing the signal as soon as it arrives with no storage of the signal data. In particular, an on-line gradient algorithm is provided for application to non-stationary signals and having an adaptive step size in the frequency domain based on second derivatives of the cost function. The on-line separation methodology of this embodiment is characterized as multiple adaptive decorrelation.

Description

490656 五、發明說明（1) 本發明為0 9 / 1 9 1，2 1 7標題為"使用多去相關方法之疊積 遮蔽信號源分離"的接續申請案，該案申請曰期為1 9 9 8年 11月1 2號。 本案為1999年9月1日申請之臨時申請案6〇/151，838的延 續，在此省略其說明 。 發明領域 本發明之發明領域係有關於信號處理，尤其是用於執行 線上遮蔽信號源分離的方法及裝置。 發明背景 在習知技術的語音處理中，必需某些環境以分離不同疊 積及混合信號的混合，在此基本上這些信號來自多個來源 ’而不必具有這些信號的先前知識。此將結合信號分離為 不同的架構分量信號的方法稱為遮蔽信號分離（BSS)，且 習知技術中熟知多種不同的B S S技術。使用這些技術以分 離由語音信號同時產生的來源信號，即多說話者，聲陣， 等所產生者，且該信號供應在疊積介質中。BSS技術可使 用在多麥克風，在多頻道通訊，多頻道辨識及等化，聲陣 之到達方向估計（D 0 A )，用於聲訊及被動聲納之束成形及 在不同的生物信號中找出獨立的來源信號，如EEG，MEG等 〇 大部份的BSS演算法試著由找出大略轉換前向頻道的多 路徑有限脈衝響應（FIR)而反轉一多路徑聲訊環境。但是 丄一完全的轉換必需相當長的FIR濾波器，尤其是在長回 曰及回響的室’其中大部份，幾乎所有現在的演算法均告490656 V. Description of the invention (1) The present invention is a continuation application entitled 0 9/1 9 1, 2 1 7 entitled " Multiple decorrelation method for superposition of masked signal source separation ", the application date of this case is November 12, 1998. This case is an extension of the provisional application 60 / 151,838 filed on September 1, 1999, and its description is omitted here. FIELD OF THE INVENTION The field of the invention relates to signal processing, and more particularly, to a method and apparatus for performing separation of an on-line shielding signal source. BACKGROUND OF THE INVENTION In the speech processing of the prior art, certain environments are necessary to separate the mixture of different overlays and mixed signals, where basically these signals come from multiple sources' without having prior knowledge of these signals. This method of separating a combined signal into different architectural component signals is called a masked signal separation (BSS), and a variety of different B S S techniques are well known in the art. These techniques are used to separate the source signals, i.e. multi-speaker, acoustic array, etc., generated simultaneously from the speech signal, and the signals are supplied in a stacked medium. BSS technology can be used in multi-microphone, multi-channel communication, multi-channel identification and equalization, estimation of the direction of arrival of the sound array (D 0 A), used for beam forming of acoustic and passive sonar and finding in different biological signals Independent source signals, such as EEG, MEG, etc. Most BSS algorithms try to invert a multi-path audio environment by finding the multi-path finite impulse response (FIR) of the roughly converted forward channel. However, a complete conversion requires a fairly long FIR filter, especially in most of the long echoes and reverberation rooms. Almost all current algorithms report

490656 五、發明說明（2) ' -- 失敗。另外，由於移動來源，移動感測器，而改變前向頻 道，或改變環境必需一種環境，其可充份且快速地轉換， 以維持一準確的頻道反轉。 習知技術之用於寬頻帶信號之疊積混合的遮蔽來源信號 為兩種型式的BSS演算法，其為（1)對角化一第二階統計之 一估計的演算法’及（2)經由疊積高階統計，辨識統計獨 立信號的演算法。類型的演算法由對角度第二階統計，且 具有可有效配置之簡單結構的去相關信號。[可參見例如 ’E· Weinstein， M· Feder, and Α· V· Oppenheim，” 由 去相關進行的多頻道”，IEEE Trans. Speech Audio Processing, vol. 1, no. 4, pp. 405-413, Apr. 1993; S· VanGerven及D· 由對稱可適性去 相關達成的信號分離：穩定，收歛，及唯一”，\^EE Trans. Signal Processing, vol. 43, no. 7, 1602- 1612 頁，1995 年七月；K·—c· Yen and γ· zhao ，"使用 adf之共頻道分離的改進：低複雜度，快速收歛，且一般 化n ’ in Proc· ICASSP 98， Seattle， WA， 1998， 1025-1 0 28頁；M. Kawamoto，n用於疊積非靜態信號的遮蔽分離 方法” ，Neurocomputing， vol. 22， no·卜3， 157 —171 頁 ’1998 年；s. Van Gerven and D· Van Compemolle ，π 由 輸出去声關達成之對稱可適性去雜訊器中的信號分離”， 參見fVoc. ICASSP 92， 1 9 9 2，vol. IV， 22 1 -224 頁。]但 疋 這些不保證收欽到正確的解，如同單一的去相關不是 一得到獨立模型的充分條件一般。而是，實際上必需考量490656 V. Description of Invention (2) '-Failure. In addition, changing the forward channel or changing the environment due to moving the source, moving the sensor requires an environment that can be fully and quickly switched to maintain an accurate channel reversal. The masking source signal used for the superimposed mixing of wideband signals in conventional techniques is two types of BSS algorithms, which are (1) an algorithm for diagonalization and one estimation of second-order statistics' and (2) An algorithm for identifying statistically independent signals through convolutional higher-order statistics. The type of algorithm consists of the second-order statistics of angles and has a decorrelation signal with a simple structure that can be efficiently configured. [See, for example, 'E. Weinstein, M. Feder, and A. Oppenheim, "Multichannel by decorrelation", IEEE Trans. Speech Audio Processing, vol. 1, no. 4, pp. 405-413 , Apr. 1993; S. VanGerven and D. Signal separation achieved by symmetrically adaptive decorrelation: stable, convergent, and unique ", ^ EE Trans. Signal Processing, vol. 43, no. 7, 1602- 1612 , July 1995; K · c · Yen and γ · zhao, " Improvement of the use of adf common channel separation: low complexity, fast convergence, and generalization n 'in Proc · ICASSP 98, Seattle, WA, 1998, 1025-1 0 p. 28; M. Kawamoto, n. Occlusion separation method for superimposed non-static signals ", Neurocomputing, vol. 22, no · bu 3, pp. 157-171 '1998; s. Van Gerven and D. Van Compemolle, π Signal separation in a symmetric adaptive denoiser achieved by output denoising ”, see fVoc. ICASSP 92, 1 9 9 2, vol. IV, 22 1-224.] But疋 These do not guarantee the correct solution, just as a single decorrelation is not sufficient to obtain an independent model. Conditions in general. Rather, in fact necessary to consider

490656 五、發明說明（3) 高階統計之靜態信號，可應用直接量測或高階統計的最適 化，[參見例如D· Yel 1 in及E· Wei nstei.n，，，多頻道信號 分離··方法及分析 ”，IEEE Trans. Signal Processing， vol. 44， no· 1， 106-118 頁，1996 年；Η·—L· N. Thi a η d C · J u 11 e η，π用於疊積混合結構的遮蔽來源”，490656 V. Description of the invention (3) Static signals of higher-order statistics can be optimized by direct measurement or higher-order statistics. [See, for example, D · Yel 1 in and E · Wei nstei.n ,,, Multi-channel signal separation ·· Methods and Analysis ", IEEE Trans. Signal Processing, vol. 44, no. 1, pp. 106-118, 1996; Η · —L · N. Thi a η d C · Ju 11 e η, π is used for stacking Shadow source of product hybrid structure ",

Signal Processing， vol. 45， no· 2, 209-229 頁，1995 年；S. Shamsunder and G· Giannakis，n 多頻道遮蔽信 號分離及重建"，LKEE Trans. Speech Audio Processing, vol· 5， no· 6, 515-528 頁，Nov· 1997]， 或者是間接假設信號之累積密度函數（cdf)的形狀。[請參 見例如，R· Lambert and A· Be 1 1 ，’’在多頻道環境中的 多語音遮蔽分離"，在Proc. ICASSP 97， 1 9 9 7年，423- 426 頁；S· Amari，S. C. Douglas, A· Cichocki, and A. A· Yang，n使用中性梯度的多頻道遮蔽去相關” i η Proc. 1st IE^ Workshop on Signal Processing App.Signal Processing, vol. 45, no · 2, pp. 209-229, 1995; S. Shamsunder and G · Giannakis, n Multi-channel masked signal separation and reconstruction ", LKEE Trans. Speech Audio Processing, vol · 5, no · Pages 515-528, Nov 1997], or the shape of the cumulative density function (cdf) of the indirectly assumed signal. [See, for example, R. Lambert and A. Be 1 1, "Multi-speech masking separation in a multi-channel environment", in Proc. ICASSP 97, 1997, pp. 423-426; S. Amari , SC Douglas, A. Cichocki, and A. A. Yang, n Multi-channel masking with neutral gradient for decorrelation "i η Proc. 1st IE ^ Workshop on Signal Processing App.

Wireless Comm·， 1997年，101-l〇4 頁；t. Lee， AWireless Comm, 1997, pp. 101-104; t. Lee, A

Bel 1，and R· Lambert，n延遲及疊積源遮蔽分離”，in Proc. Neural Information Processing Systems 96 1 9 9 7 ]。前面的方法相當複雜及難以配置，而後面的方法 當cdf的假設不精確時則失敗。 / 熟知一種線上BSS演算法的限制體，一般用於單去相關 及a間接高階方法，而且，與非線上部份具有相同的限制'Bel 1, and R. Lambert, Separation of n-Delay and Convolutional Source Shadowing ", in Proc. Neural Information Processing Systems 96 1 9 9 7]. The previous method is quite complicated and difficult to configure, while the latter method does not assume the cdf assumption. It fails when it is accurate. / Familiar with the restriction body of an online BSS algorithm is generally used for single decorrelation and a indirect high-order method, and it has the same restrictions as the offline part. '

[參見e.g·，E. Weinstein, Μ·…Feder，and A. V[See e.g., E. Weinstein, M ... Feder, and A. V

Oppenheim，”由去相關導致的多頻道信號分離” ，IMeOppenheim, "Multichannel Signal Separation Due to Decorrelation", IMe

490656 五、發明說明（4)490656 V. Description of Invention (4)

Trans. Speech Audi o Processing, vol. 1，η0. 4, 405-413 頁，1993 年四月；S. Van Gerveη and D· VanTrans. Speech Audi o Processing, vol. 1, η0. 4, pages 405-413, April 1993; S. Van Gerveη and D. Van

Compemo 1 1 e，n由對稱可寧性去相關達到的信號分離：穩 定，收斂及唯一性π，ΐβΕ Trans. Signal Processing， vol. 43， no· 7， 1 6 0 2- 1 6 1 2 頁，1 995 年七月；Κ· 一C. Yen and Y. Zhao，n使用ADF在共頻道分離的改進：低複雜度 ，快速收斂及一般化n，in Proc. ICASSP 98，Seattle， WA， 1998， 1025-1028 頁；K — C Yen and Y. Zhao，"可適 性共頻道語音分離及辨識π，Ι、Ρ：Ε Trans. Signal Processing, vol· 7， no. 2 ， 1999 年三月；S· Amari， C. S· Douglas, A· Cichocki，and Η· H. Yang，n 使用 中性梯度方法之用於遮蔽去疊積的新線上可適性學習演算 法n ， iη Pr〇c· 1th IFAC Symposium on SystemCompemo 1 1 e, n Signal separation achieved by symmetric negativity decorrelation: stability, convergence and uniqueness π, ΐβΕ Trans. Signal Processing, vol. 43, no · 7, 1 6 0 2- 1 6 1 2 , July 1 995; K. Y. C. Yen and Y. Zhao, n Improved common channel separation using ADF: low complexity, fast convergence and generalization, in Proc. ICASSP 98, Seattle, WA, 1998 , 1025-1028; K — C Yen and Y. Zhao, " Suitable co-channel speech separation and identification π, I, P: EI Trans. Signal Processing, vol · 7, no. 2, March 1999; S. Amari, C. Douglas, A. Cichocki, and Η H. Yang, n A new online adaptive learning algorithm n, iη Pr〇c · 1th, which uses the neutral gradient method for masking deconvolution IFAC Symposium on System

Identification, Kitakyushu City ，日本，1997 年七月 ，vol· 3，ρρ· 1057-1062; Ρ· Smaragdis，"在頻域中疊 積混成結構的遮蔽分離”，Neurocomputing，vol· 22， pp. 2 1 - 3 4， 1 9 9 8 ]。已提出信號去相關演算法以支援在非 靜態信號上的操作[參見e· g.，M· Kawamoto，π用於疊積 非靜態信號的遮蔽分離方法” ’ NeurocomPut丨nS，νο 1 · 22， no. ；1 -3， 157-171 頁，1 9 98 年；Τ· Ngo and Ν·Identification, Kitakyushu City, Japan, July 1997, vol · 3, ρ ·· 1057-1062; ρ · Smaragdis, " Shadow separation of superimposed and mixed structures in the frequency domain ", Neurocomputing, vol. 22, pp. 2 1-3 4, 1 9 9 8]. Signal decorrelation algorithms have been proposed to support operation on non-static signals [see e · g., M · Kawamoto, π masking separation method for superimposed non-static signals "" NeurocomPut 丨 nS, νο 1 · 22, no .; pp. 1-3, 157-171, 1989; TT · Ngo and Ν ·

Bhadkamkar，"使用第二階統計方法由實際上的精緻裝置 進行的聲訊之可適性遮蔽分離’’ ，i η ’99，LoubatonBhadkamkar, " Suitable masking separation of sound using practically sophisticated devices using second-order statistical methods ' ', i η ' 99, Loubaton

Cardoso，Jutten，Ed.，1 9 9 9，,2 5 7-2 6 0 頁；Η· Sahlin and H. Broman，n真實世界信號的分離"’SignalCardoso, Jutten, Ed., 199, 9, 2 5 7-2 6 0; Η · Sahlin and H. Broman, n Separation of Real World Signals " ’Signal

第9頁 490656 五、發明說明（5)Page 9 490656 V. Description of the invention (5)

Processing， ν〇1· 64， 1〇3一1〇4 頁 基本的準則，考量該數據只可以進一 a ]。BSS方法： a ’必需要有詳細可準確且快诘拥y 關的遮蔽信號源分離延伸。 、執仃疊積信號去相 發明相n 習知技術之方法及裝置的缺點再於 „周期中，經由同時對角化第二二，在頻域上的多 #號去相關執行遮蔽信號源分離。尤二、θ计，而使用疊積 中本發明累加一包含獨立信號源之=人在第一貫施例 度（分段）。然後本發明中將該輸入信ς二的輸入信號之長 Τ線上調整（窗口），且在Τ線上調整丄=、、曰長，分離為多個 散傅立葉轉換（DFT)。此後，本發明曾此合^號處執行離 ’其為T長度期間除以N之平均值計5 互相關功率頻譜 互相關功率頻譜而在輸入信號内右I昇將由同時去相關Κ 波器係數。 有政分離信號源的？以濾 為了達到上述目的，在濾波器係 下降處理只包含某些值，即時域濟；：日:域值中限制梯度 在任何日寺間以〈〈丁内，該/在2 ^係數賴”限制 問題已解決，且計算用於F ^ ?皮長哭〜周：二為° ’即排列 八/愿/皮态係數的唯一解， 使用這些係數產生的濾波器可有效地分離來源信號。 對於不貫際累積輸入信號長度，以依據第一實施例方法 處理的環境，本發明的第二實施例中用於解決輸入信號的 線上處理，即只要信號到達即即以處理，而不儲存信號數 據。尤其是’提供-線上梯度演算法以應用在非靜態信號Processing, ν〇1 · 64, 103-104, basic rules, considering that the data can only be advanced by a]. BSS method: a ′ must have a detailed and accurate shield signal source that can be quickly and easily separated and extended. The disadvantages of the method and device of performing superphase signal dephasing and inventing phase-n-known techniques are again in the cycle, by simultaneously diagonalizing the second two, and performing multi- # decorrelation in the frequency domain to perform mask signal source separation. In particular, the θ meter, and using the superposition product in the present invention, accumulating one including an independent signal source = one person in the first embodiment (segmentation). Then in the present invention, the input signal is divided into two input signal lengths. Adjust (window) on the T line, and adjust 丄 = ,, and length on the T line, and separate them into multiple scattered Fourier transforms (DFT). Thereafter, the present invention performs the division by the number 'T' which is the length of T divided by The average value of N is 5 cross-correlation power spectrum. The cross-correlation power spectrum and the right I liter in the input signal will be correlated by the K-wave filter coefficients at the same time. To separate the signal source? In order to achieve the above purpose, the filter system drops. The processing contains only certain values, and the real-time domain is limited; the limit of the gradient in any day is limited to << within Ding, the / in 2 ^ coefficient Lai "limit problem has been solved, and the calculation is used for F ^? Skin long cry ~ week: two for ° 'that is arranged eight / wish / skin state The number of unique solution, the filter produced using these coefficients can be efficiently separated source signals. For the environment in which the length of the input signal is discontinuously accumulated to be processed according to the method of the first embodiment, the second embodiment of the present invention is used to solve the on-line processing of the input signal, that is, the signal is processed as soon as it arrives without storing the signal. data. Especially the ‘Provide-Online Gradient Algorithm to apply to non-static signals

第10頁 五、發明說明（ti) 中’而且基於成本函數 適應的步級尺寸。此實施 ~ &amp;从刀’在頻域中具有〜 適性去相關（mad)。 也$之線上分離方法的特徵為多可 一般，本發明的任何一者 一般用電腦系統上儲存的二2 2 Z以錯存在储存介質且在 下文詳細說明中的硬體。軟釭序配置。但是，也可以是 可以在如用於從不同信號 處理器系統的聲音辨識系 關6唬中在如一信號 聲音辨識可以使用在多明的應用，使得； 源。為了響應聲訊，該聲立 而5周整干擾雜音 電腦文字。 曰辨硪處理器可產生電腦命令； 1^·^簡單說明 由下文中的說明可更進一牛 ” 閱讀時並請參考附圖。 V 了解本發明之特徵及優點， 圖1為本發明實施例的流程圖； 圖2為本發明另一實施 ρ,ο . ^ , 員W例的流程圖； 圖3為本發明一實施例 圖； 座生之濾波器係數的流程頻域 圖4為本發明實施例產 及 生之濾波器係數的流程時域圖； 圖5為用於執行本發明之 月之叙體配置的系統。 本發明方法之一項重要 _ 行辨識，該非靜態可用於=理念為應用非靜態信號進 、相關在多次中之BSS環境下的 49〇6M&gt; 估計來源，g户 應用在多在此夕次中，其中一次具有不同的相關性。 測可在第一I您信號中的互相關計算，一不同的互相關量 非靜態中，=^定’而非第二及往後的次數中決定。在此 法在一暫聍1f源環境中，依據本發明方法之分離的演算 此將於^ = 57離的多互相關上操作以同時對其進行珍斷。 中，從整個Ϊ加以說明本發明之一實施例。在第一實施例 演算法用於：ΐ中先計算所有的互相關。然後一梯度下降 逛ί濾波)1算最佳的診斷渡波器，隨後可使用此濾波器 。一線上梯声ί = 例中，改變互相關的單一進入估計 相關。馬上二审:决算法用於更新濾波器以診斷現在的互 改變ds為非…濾波器作用在進入的信號中。Page 10 5. In the description of the invention (ti) ', and based on the cost function, the step size is adapted. This implementation ~ & slave &apos; has ~ adaptive decorrelation (mad) in the frequency domain. The characteristic of the online separation method is that it is generally possible. In general, any of the present invention generally uses hardware stored in a computer system and stored in a storage medium and described in detail below. Soft sequence configuration. However, it can also be used in a signal such as a sound recognition system from a different signal processor system. Sound recognition can be used in Doming applications such that the source. In response to the sound, the sound immediately interfered with noise and computer text for 5 weeks. The processor can generate computer commands; 1 ^ · ^ Brief description can be further improved from the description below "Please refer to the drawings when reading. V Understand the features and advantages of the present invention, Figure 1 is an embodiment of the present invention Figure 2 is a flowchart of another example of the implementation of the present invention; Figure 3 is a diagram of an embodiment of the present invention; Block filter process frequency domain Figure 4 is the present invention The time-domain diagram of the filter coefficients produced and produced in the embodiment; Figure 5 is a system for performing the narrative configuration of the month of the present invention. An important _ method of the present invention is row identification, which is non-static can be used = concept is The application of non-static signals is used to estimate the source of 4906M in the BSS environment. It is used in many cases, and one of them has a different correlation. It can be measured at the first time. In the cross-correlation calculation, a different cross-correlation quantity is not static, and is determined by the second and subsequent times. In this method, the separation according to the method of the present invention in a temporary environment of 1f source The calculation of this will operate on the multiple cross-correlation of ^ = 57 In the first embodiment, an embodiment of the present invention is described. In the first embodiment, the algorithm is used to calculate all cross-correlation in the first. Then a gradient descent filter is used. This filter can be used for the best diagnostic wave filter. The ladder sound on the line ί = In the example, the cross-correlation single entry estimation correlation is changed. The second trial is now: the algorithm is used to update the filter to diagnose the current cross-change ds as Non ... filters act on incoming signals.

，其已在 ^⑴= [Sl(t)，···，則]T 禾感測器係數I；?；；些⑴，ΎΟΜ表 ，目與來源信號相同。在日士、：即感測器的 (稱為一向前模式）：下文表不疊積雜訊的數^ ⑴ = [Sl (t), ···,] T and sensor coefficients I;? ;; ⑴, ΎΜΜ table, the same as the source signal. In Japan, the sensor's (called a forward mode):

F X(() = Σ j(x〇s(i - τ) + η(ί) ^ ^ ^ ^ ^ ^ a % f 1；^^ m ϋ· ^ ^ }t； 0 知信號的估計值二;侧#係數’且最後決定未FX (() = Σ j (x〇s (i-τ) + η (ί) ^ ^ ^ ^ ^ ^ a% f 1; ^^ m ϋ · ^ ^} t; 0 The estimated value of the known signal is two; Side #factor 'and finally decided not

第12頁 適當選擇長度Q 2 J ί :某些狀況下’多路徑通道可廊用 w(”而可反轉。響應CFIR)的多路徑濾波哭應用 、_ 式表示反轉模式(稱為向後模 490656Select the appropriate length Q 2 J on page 12: In some cases, the multi-path channel can be reversed with w (". Respond to CFIR). Multi-path filtering application. Mod 490656

(2) ，0 = |&gt;(τ)χ(卜 τ) ^力c明的方法由經由假設非靜態來源係數，且使用最小平 # 法估什W，及信號和雜訊而最適化估計方程式2中反 轉杈式中之參數W。 K 說明。 號$ 的貫施例為一使用多離散傅立葉轉換之非線上信 步H 在下产中以圖1說明本發明。請參考附圖，在 號剖狀炎輸入疊積（混合）信號，且在步驟101中，將該信 包;一為包含，入信號x(t)之τ樣本的多個窗口。該方法 於具命用於各囱口坟七）的離散傅立葉轉換（DFT)值，即對 又為τ之樣本之各窗口的一數值。 工力率tΓ102巾’本發明的方法使用dft值以累加K互相關 如 目關，其中各[頻譜在長度為了之樣本的Ν個窗口上 八十均 0 且S ϋ非靜態信號而言，互相關估計將與絕對時間相關， lot著—估計分段（一ΝΤ周期）到下一分段而改變。在步驟 4中計算該互相關估計。 (3) 其中 χ(ΐ + ηΤ, ν) = FFT X{t + ηΤ) X(r) = [^(r)-x(^4-r-l)] 在 此p )為在包含τ樣本之一窗口内輸入信號的FFT 因(2), 0 = | &gt; (τ) χ (bu τ) The method is optimized by estimating non-static source coefficients and using the least squares method to estimate W, and the signal and noise to optimize the estimation. The parameter W in Equation 2 is inverted. K description. The implementation example of $ is an offline step H using multiple discrete Fourier transforms. The present invention will be described with reference to FIG. 1 in the production. Please refer to the accompanying drawings, and input a superimposed (mixed) signal at No. 2 phlebitis, and in step 101, the packet; one is a plurality of windows containing τ samples of the input signal x (t). This method is applied to the discrete Fourier transform (DFT) value of each epoch, that is, a value for each window of the sample that is also τ. The power rate tΓ102 is used. The method of the present invention uses the dft value to accumulate K cross-correlation, where each [spectrum in the N windows of a sample of length eighty are zero and S ϋ for non-static signals, the mutual The correlation estimate will be correlated with the absolute time. The estimated segment (one NT period) changes to the next segment. This cross-correlation estimate is calculated in step 4. (3) where χ (ΐ + ηΤ, ν) = FFT X (t + ηΤ) X (r) = [^ (r) -x (^ 4-rl)] where p) is one of the samples containing τ FFT factor of input signal in window

第13頁 490656 五、發明說明（9) 此，在步驟1 0 4中，該程床祖 . ^ ^ 柱序對於各時間及各頻率^計算該 矩陣，且然後加總各矩陳八曰 σ祀|早刀夏内所有的矩陣分量。步驟 及k=0到Κ迭 106 ’ 108，110 及112 在步驟1〇4 中，η = 〇 到Ν， 代（iterate)計算該相關估計’以產生κ頻譜 然後式（3 )可以簡化成為： (4) 足 V) = 乂 (V)八』(“ V) (v)十八&quot;(，，v) 如果N夠大’ As(t，2；)及An(t，^ )可由於信號的被模形化 ，為一對角矩矩陣。對於不同的時間中，式4為線性獨立 ’需要限制(t，ζ；)隨著時間?文變，即信號為非靜態者 使用式4的互相關估計，本發明使用互功率頻譜計算來 源信號，其滿足下式： 八= π(ν)(βλ·(ί,ν) 一八( 5 ) 為了對於各時間周期得到獨立的狀況，一般選擇時間周 期為具有心（tk，〉）的不重疊估計時間，即_^ = 1ίΤΝ。但是^ 果信號的改變夠快，則必需使用重疊估計時間。而且，^ 然一般窗口 T為序列方式者，但是各窗口必需互相關， 得各DFT值從信號資訊中得到，也包含在一窗口中。在另 一聲信號處理系統中，基於信號記錄的室内之聲音，、琴 =定的T。例如，具有許多反射路徑的大空間内必9需長^ 窗二T，使得本發明可處理大量的信號資訊，以達:^源 ^號分離的目的。N的值一般由處理之數據量決定。美本Page 13 490656 V. Description of the invention (9) Therefore, in step 104, the Cheng ancestor. ^ ^ Column order calculates the matrix for each time and frequency ^, and then sums the moments Chen Ba Yue σ Say | All the matrix components in the early knife summer. Steps and k = 0 to κ 106, 108, 110, and 112. In step 104, n = 0 to N, iteratively calculate the correlation estimate 'to generate a kappa spectrum and then equation (3) can be simplified to: (4) sufficient V) = 乂 (V) eight "(" V) (v) eighteen &quot; (,, v) if N is large enough 'As (t, 2;) and An (t, ^) can be The signal is modeled as a pair of angular moment matrices. For different times, Equation 4 is linearly independent. 'Needs to limit (t, ζ;) over time? The text changes, ie the signal is non-static. The cross-correlation estimation of the present invention uses the cross-power spectrum to calculate the source signal, which satisfies the following formula: eight = π (ν) (βλ · (ί, ν) one eight (5) In order to obtain an independent status for each time period, generally The time period is selected as the non-overlapping estimation time with heart (tk,>), that is, _ ^ = 1ίΝΝ. However, if the signal changes fast enough, it is necessary to use the overlapping estimation time. Moreover, ^, the general window T is a sequence However, each window must be cross-correlated, and each DFT value is obtained from the signal information and is also included in a window. In another acoustic signal processing system Based on signal recording of indoor sound, Qin = fixed T. For example, a large space with many reflection paths must be long ^ window two T, so that the present invention can process a large amount of signal information to achieve: ^ source ^ The purpose of number separation. The value of N is generally determined by the amount of data processed.

490656 五、發明說明（10) 上.=，Τ,24樣本，且K = 5。 示明泣的法計算多路徑通道W (即多維F 1 R滤波器的標 其見際上滿足用於K估計周期如2到5之用於處理聲 二广b的估°十抑周☆期之式5。此程序在步驟1 1 4，1 1 6，1 1 8中執 =(一濾、波器參數估計程序124)，且使用下式之最小平方 法表示： ' =ar 多 mini； D耶，4 ^Τλ，，Αλ v«vl i (6) v 其中490656 V. Description of the invention (10). =, T, 24 samples, and K = 5. The explicit method is used to calculate the multi-path channel W (i.e., the target of the multi-dimensional F 1 R filter meets the estimation for the K estimation period such as 2 to 5 for processing the sound b and b). Equation 5. This procedure is performed in steps 1 1 4, 1 1 6, 1 1 8 = (a filter, wave device parameter estimation procedure 124), and expressed using the least square method of the following formula: '= ar multi mini; D Yeah, 4 ^ Τλ, Aλ v «vl i (6) v where

五(毛 v) = r(v)(4 (/：，V) 一 Λ,从 V)) (v) — Λ“々，v) 為了簡化起見，在式6中使用簡短的命名法，在此 As(k, .)^As(tk, ，且 Λ尸、（tl， v)，…，\(tk， η ，且一相同的簡化符號使用在An(t，ζ；)及匕（七，^ )中。 為了處理參數W ’使用梯度下降程序1 2 4 (包含步驟1 1 4， ，，118，及12。）’且物的選代值使得成：；=為 最小。在步驟1 1 6中，更新W值為Wnew = WQld- // \7we，其中 E為梯度級距值’且v為係數常數，其控制更新的尺寸Five (Mao v) = r (v) (4 (/ :, V)-Λ, from V)) (v) — Λ "々, v) For simplicity, use the short nomenclature in Equation 6, Here As (k,.) ^ As (tk,, and Λ corpse, (tl, v), ..., \ (tk, η), and an identical simplified symbol is used in An (t, ζ;) and dagger ( Seven, ^). In order to process the parameter W 'use the gradient descent program 1 2 4 (including steps 1 14, 4, 118, and 12.)' and the alternative values of the objects are made as follows: = is the smallest. In step In 1 1 6, the updated W value is Wnew = WQld- // \ 7we, where E is the gradient level value 'and v is the coefficient constant, which controls the size of the update

尤其是，梯度下降程序決定梯度值如下。In particular, the gradient descent program determines the gradient value as follows.

5E κ = Z^v)^(v)5/y(fc,v) 4 1 (7)、 dE —ττ--= dA](k) :-cfiag{E(k，V)) (8)- SE Ίκ^)ζ =-diag{ W11 {v)E{ky v) W{v)) (9) V 第15頁 490656 五、發明說明（11) B^yV)^kx (*,ν)-ΛΜ(/:,ν) (10) 令式8等於0，該程序可值參數As(k，^ )，而夂 y5E κ = Z ^ v) ^ (v) 5 / y (fc, v) 4 1 (7), dE —ττ-= dA] (k): -cfiag (E (k, V)) (8) -SE Ίκ ^) ζ = -diag {W11 {v) E {ky v) W (v)) (9) V Page 15 490656 V. Description of the invention (11) B ^ yV) ^ kx (*, ν) -ΛM (/ :, ν) (10) Let Eq. 8 be equal to 0. This program can take parameters As (k, ^), and 夂 y

Ar (k，y )及w ( i；)應用梯度下降規則計算，/之的 的程序計算的Λ (k，)及w( ^)，確定Wi 心用新通過 的值W“)不同，即⑶收歛。）“W“)的新值與舊 注意’式6包含在時域中對於濾波器尺 對於該限制，似乎不同的頻率^ =丨，···，了 :、限制。 題。但是值W( υ )限制這些渡波器在不相^的問 響應。有效的方法為該程序產生在¥( 〇 &amp;有時間 係數的參數隨著Qdsdx參數（W r )參數化。每 S χ濾波器 中，在a些頻域的數值上執行FFT以將w( 拖 結果，即w( r)。在時域中，任何在時 =換成為 現在W值設定為〇，且在Q以下的所有數值均予以間中出 ϊ=。的時域值使用一反FFT轉換回頻域。將在Ϊ域Ϊ ::二：，所有時間。化’則該頻率的頻率響應平整，而 使付在决疋在各頻率中的唯一解。 ，3圖^示頻/Λ應讓及3州及圖4為對應之時域響細4A 古3〇4B。使用步驟124的梯度下降程序找出係數的 ΪΪ二Γ:使用迭代方式決定?的正確值。-當式7的梯 :S'數作用二：Ϊ坦化時’ &amp;步驟1 22中’將計算的濾波 。期κΐτ Λ^ 1。使用FIR攄波器以在長度的時 間周，月KNT中的輸出（混合）信號X⑴的樣本渡波。在步驟Ar (k, y) and w (i;) apply gradient descent rule calculation, and the program calculates Λ (k,) and w (^) to determine that the Wi center uses the newly passed value W "), that is, (3) Convergence.) The new value of the "W") and the old note 'Equation 6 contains the frequency in the time domain. For this limit, the frequency seems to be different. ^ = 丨, ..., limit. Problem. But The value W (υ) limits the response of these ferrules to inconsistent questions. An effective method is to generate a parameter with time coefficients in Q (〇 &) along with the Qdsdx parameter (W r). Each S χ filter In the processor, perform FFT on some values in the frequency domain to drag w (the result, that is w (r). In the time domain, any time == to now all W values set to 0, and all below Q The values are given out in time. Ϊ =. The time domain value is converted back to the frequency domain using an inverse FFT. It will be in the Ϊ domain Ϊ :: 2 :: all time. If the 化 'is used, the frequency response of the frequency is flattened, and the decision is made. The only solution of 疋 in each frequency. 3, ^ shows the frequency / Λ should let 3 states and Figure 4 correspond to the time domain response 4A ancient 30B. Use the gradient descent program of step 124 to find the system The second value of the number Γ: Use the iterative method to determine the correct value of?.-When the ladder of Eq. 7: S 'number works two: Ϊtanning' &amp; the filtering to be calculated in step 1 22. Period κΐτ Λ ^ 1 . Use a FIR chirped wave to sample the wave of the output (mixed) signal X⑴ in the month KNT for a long period of time. At step

第16頁 490656 — —'-— 五、發明說明（12) 6中5亥F1R濾波器產生混合信號的去相關分量信號。铁 後在步‘ 1 2 8中的程序中得到該處理中‘之下一 κ n τ樣本 t然後進行步驟100，以濾波下一KNT樣本。 ： 去除珂一OT樣本。 中 η· 多去相關實 段(應至用小上h實施例的非線上多去相關方法’將整個信號分 相μ數中）分為不同的部份（1(估計周期），而***互 使‘；：二f €，該操作該實施例中的分離演算法以同時 多〜 ’相關對角度。隨著該實施例，該基本點必兩 段：嶋該演算法中，重疊不可能2 ^才间T進行互相關的量測。 應用（包V語大音H ^為有意義的限制。對於許多的BSS 將相當得大，為百〜 -甚至表示多頻率語音數據的檔案 不實際，尤其是在古^ ^大小。儲存此大小的數據檔相當 自多來源的頻率作:。因此，在此提供一種方法以來 ，些數據，不儲存數。據進行線上處理，即是說即時處理 G相關之優點，而二：將於下文中加以說明實現分離 f。 吊要儲存輸入數據之線上多去相關 D同f知技術實施 的梯度 下降方法只是本 3梯度下降演算法，：：目關演算法，此實施例的演算 解？化，料則為跨時間：此:寅异法以使得尤其是的準則 使得成本函數最小化从f ^目關的去相關[但是，須了 發明較佳 11 第17頁 490656 五、發明說明（13) 實施例之一在本發明中也可以使用其他熟知的 適方法達到本發明的目的]。在本發明方‘法的操作M數最 作梯度下降演算法以使得以分離濾波器定義的成’操 小化，以因此建立該濾波器的參數。 ㈡數最 操作本發明的去相關演算法以提供互相關矩陣的 計，即當新的數據組進入時，用於習知技術數據组^動估 關估計值被更新，以成為用於信號數據的現在互相關互相 用該移動估計值以計算濾波器參數最適準則的複雜梯^使 其中該複雜梯度用於一梯度下降演算法，此係對每—二， 進行梯度步驟，而不是在更新前，加總全部的梯度。别入 在下一節中說明本發明去相關演算法，在說明=^ 據本發明方法之該演算法的應用在功能上以本發明依 的流程圖說明，如圖2中所示者。 汽％例 在本發明方法的操作中，將多個輸入信號分為一 窗口分段。將窗口分段輸入本發明的流程圖（步驟2〇〇爭的 在當輸入各窗口分段組時，纟窗口的信號。 立葉轉換（DFT)轉換為頻域（步驟2〇1)。然後在 1政傳 ’使用窗口信號分量的DFT轉換以計算估計的互相關〇二： 由即在信號分段中每頻率分量計算互相關陣 ，程4 ’對應各互相關矩陣的梯度 ：-梯 中決定。然後使用這些梯户以佑摅士八t 多個信號輸出中包含，境，且；發：：：：：；： 法在各個輸入及輸出之間提供一不同的濾波器。因此^ 田Page 16 490656 — —'-— V. Description of the Invention (12) The 5F1R filter in 6 produces a decorrelated signal of the mixed signal. Then, in the program in step ′ 1 2 8, the next κ n τ sample t in the process is obtained, and then step 100 is performed to filter the next KNT sample. : Remove Ke-OT samples. The middle η · de-correlation real section (the off-line multi-correlation method of the Xiaoshang h embodiment should be used to 'separate the whole signal into μ's) is divided into different parts (1 (estimate period), and the mutual Let ';: two f €, the operation of the separation algorithm in this embodiment is simultaneously more ~' correlation pair angle. With this embodiment, the basic point must be two paragraphs: 重叠 In the algorithm, overlap is impossible 2 ^ Between T is a cross-correlation measurement. Application (including V language big sound H ^ is a meaningful limit. For many BSS will be quite large, a hundred ~-even the file representing multi-frequency speech data is not practical, especially It is in the ancient size. Storing data files of this size is quite frequent from multiple sources. Therefore, since a method is provided here, some data are not stored. Data is processed online, which means that G-related processing is performed in real time. The advantages, and two: will be described below to achieve separation f. The de-correlation on the line to store the input data D The gradient descent method implemented by the same technology is only the 3 gradient descent algorithm: , The calculation of this embodiment Decomposition, it is expected to span time: this: the difference method to minimize the cost function from the correlation in particular to minimize the cost function [but, the invention is better 11 page 17 490656 5. Invention Explanation (13) One of the embodiments in the present invention may also use other well-known suitable methods to achieve the purpose of the present invention.] In the method of the present invention, the operation M number is used as the gradient descent algorithm to define the separation filter. The size of the filter is reduced to thereby establish the parameters of the filter. The maximum number is to operate the decorrelation algorithm of the present invention to provide a cross-correlation matrix, which is used to learn technical data when a new data set enters. The group estimation value is updated to become a complex ladder for the current cross-correlation of the signal data, and the motion estimation value is used to calculate a filter parameter optimal criterion. The complex gradient is used in a gradient descent algorithm. This is to perform the gradient step for every two, instead of summing all the gradients before updating. Do not enter in the next section to describe the decorrelation algorithm of the present invention, and to explain = ^ the algorithm according to the method of the present invention The application of the function is illustrated by the flowchart according to the present invention, as shown in Fig. 2. In the operation of the method of the present invention, multiple input signals are divided into a window segment. The window segment input The flowchart of the present invention (step 200) is the signal of the window when each window segment group is input. The Transform (DFT) is converted to the frequency domain (step 201). Then it is used in 1 political mission. DFT conversion of the window signal components to calculate the estimated cross-correlation 02: By calculating the cross-correlation matrix for each frequency component in the signal segment, the process 4 'corresponds to the gradient of each cross-correlation matrix: -determined in ladders. Then use these ladders The user ’s multiple signal outputs include the environment, and the ::::::;: method provides a different filter between each input and output. Therefore ^ Tian

第18頁 4y〇6i)6 五、發明說明（14) 去=演算法對於遽波器的矩陣發 只際上，該濾波器參數值w 波益係數組。 際上在分離出需要的信號時減少/不^需的係數，其實 較佳實施例中，在步驟2 0 5中-由皮=效率。因此，在 時轉換為時域，而去除這此不必兩由^域W值使用反DFT暫 時間比〇大的時間中顯示的一w值（等Vy糸數/然後，任何在 而且低於q之範圍内全部的數改fm定為〇 ’ 值使用DFT轉換回頻域。經由將=。然後限制的時域 間内的濾波器響應〇化 滹波二中對於戶:：：於9之時 在各頻率中的唯—解可決皮时的頻率響應平整，使得 。= 數ί新的移動估計作業中唯-解可決定 用的渡波器係數。將現在的濾波器作 =步驟2。7)，以提供'犧號的去相關。 ^日守’在步W08中’本發明的程序回到輸入步驟中，而 輸入下一窗口信號分段。 B· 去相随演算法的偏離 (1)基本演算法 =上所述，可使得最適化濾波器係數⑺而回復非靜態來 源信號，使得估計的來源$(t)在不同的時間中具有對角第 二階統計： ▽Λτ :E[S(〇S&quot;(卜τ)] =人々，τ) … (13) ν 在此八=伽gaA#：)，.·.人(ί，τ)])表示在時間七時來源信號的自相 關，這些自相關必需從數據中予以估計。此準則決定έ(ίPage 18 4y〇6i) 6 V. Explanation of the invention (14) The == algorithm is used for the matrix transmission of the wave filter. In fact, the filter parameter value is the wave gain coefficient group. Actually, the required / reduced coefficients are reduced when the required signals are separated. In a preferred embodiment, in step 205-from the skin = efficiency. Therefore, the time is converted to the time domain, and this need not be removed. It is not necessary to use a value of w displayed in the time when the DFT time is greater than 0 (such as Vy 糸 number / then, any All the numbers in the range are changed to fm and set to 0. The value is converted back to the frequency domain using DFT. By setting =. Then the filter response in the time domain is limited. The frequency response when the unique solution in each frequency can be determined is flat, so that == the number of wavelet coefficients can be determined by the unique solution in the new motion estimation operation. Use the current filter as step 2. 7) To provide 'correlation of sacrifices'. ^ Rishou 'in step W08' The program of the present invention returns to the input step, and the next window signal segment is input. B. Deviation of the decoherent algorithm (1) Basic algorithm = As described above, it can optimize the filter coefficient ⑺ and restore the non-static source signal, so that the estimated source $ (t) has an opposite effect at different times. Angular second-order statistics: ▽ Λτ: E [S (〇S &quot; (卜 τ)] = person 々, τ)… (13) ν Here eight = gagaA # :), .. person (ί, τ) ]) Indicates the autocorrelation of the source signal at 7 o'clock. These autocorrelation must be estimated from the data. This guideline determines

第19頁 490656Page 19 490656

五、發明說明（15) 最好為一原始信號s(t)的交換及疊積型式。在 相關實施例中，如上所述者，估計多次中的;二 且同時在頻域中對角化。 一 h、、充汁， 對於本發明實施例的線上例子而言，結束 φ .. ^ . , T且ί要在日ΤΓ域 甲進仃用於發展濾波器參數的成本函數，且然後該演管法 轉換成為頻域以產生更有效且快速轉換的線上更g 2^ 使用在時間t時的樣本平均以得到期望值，即 、、V. Description of the invention (15) It is best to use an exchange and superposition type of the original signal s (t). In a related embodiment, as described above, is estimated multiple times; and at the same time diagonalized in the frequency domain. For the online example in the embodiment of the present invention, end φ .. ^., T and T to be used to develop a cost function for the filter parameters in the Japanese ΓΓ domain, and then the performance The tube method is converted into the frequency domain to produce a more efficient and fast conversion on the line. G 2 ^ Use the sample average at time t to get the expected value, that is,

Etf Ct)] = Σ r· f (t+ ri)。然後可使用一分離 蚪&amp;几， Μ疋義同時 (14) V (15) ν (1 6 ) 7 j (W) = {t, \v) = J]||j(t, w)||2 ^ Λ =ΣI印⑽&quot;(卜τ)] 一入〆/，τ )『 =Σ Σ^^ + τ,)§/ί(/-τ4-τ,)~Λί(ί,τ)| χ· 在此Fr〇beniUs模（1101^)為μ丨丨、Tr(JJii)。使用者 :予演算法而㈣(W)達到最小化以搜尋分離濾：二 /、疋/在對於每一 t之各輸入取額外函數的梯度1 “，w) 相對於在更新前加總全部的梯度）[注意對於ς ; 。因此，口 1 適估计值為E[i(〇r(i叫]的對角开夸1 ^此，、品要對應W的梯度。此複雜的梯声角凡素] 列式子， 巾度方法導致下 dj (r, W) 、 石的十 τ.)〇 + τ’-τ) —人儿 τ) χΣ^ + τη-τ)χ//(/+τΜ~/)Etf Ct)] = Σ r · f (t + ri). Then we can use a separation unit 几, Μ 疋 simultaneously (14) V (15) ν (1 6) 7 j (W) = {t, \ v) = J] || j (t, w) | | 2 ^ Λ = ΣI 印 ⑽ &quot; (卜 τ)] Once entered 〆 /, τ) 『= Σ Σ ^^ + τ,) § / ί (/-τ4-τ,) ~ Λί (ί, τ) | χ. Here, the FrobeneUs module (1101 ^) is μ 丨, Tr (JJii). User: Pre-algorithm and ㈣ (W) is minimized to search for separation filters: 2 /, 疋 / take the gradient of the extra function 1 ”for each input of t, w) relative to summing all before updating (Note that for ς;. Therefore, the appropriate estimate of mouth 1 is E [i (〇r (i 叫) 's diagonally exaggerated 1 ^ here, and the product should correspond to the gradient of W. This complex ladder angle Fansu] column formula, the degree method leads to the following dj (r, W), Shi Shi τ.) 〇 + τ'-τ) —human τ) χΣ ^ + τη-τ) χ // (/ + τΜ ~ /)

第20頁 490656 五、發明說明（16) +Σ Σ沁+τ’—人Page 20 490656 V. Description of the invention (16) + Σ Σ 沁 + τ’—person

T V r' J ,&gt;&lt;2^(/ + τ&quot;)ί&quot;(/ + τ&quot;—r—/) τ&quot; 為了簡化此式子，可顯示在r上第一及第二加總可相等 。在梯度程序中，使用者可以選擇在時間t以外的時間中 ，將不同的梯度項作用在這些加總中。在該增項後，可以 以第二加總中的t - r取代t，其而且使用在時間t ’二t - r的 梯度更新中的加總值。另外，正及負值的r加總。假設為 對稱者，則可以在第二加總中改變r的符號。建議在這些 轉換後，對角矩陣的As (t，I* )仍沒有改變，至少在準靜 態的近似中沒有改變。隨著//的步級大小，對於1 ag 1的 時間t該所得到的濾波器預定更新為 W(/) = -2μγ(^s(/ 4- t})sH (/ + τ'^τ) ~ Λ, (ί,τ) ( 1 ?)TV r 'J, &gt; &lt; 2 ^ (/ + τ &quot;) ί &quot; (/ + τ &quot; —r— /) τ &quot; In order to simplify this formula, the first and second summation on r can be displayed. equal. In the gradient program, the user can choose to apply different gradient terms to these totals at times other than time t. After this addition, t may be replaced by t-r in the second summation, which also uses the summation value in the gradient update at time t '2 t-r. In addition, r for positive and negative values is added up. Assuming symmetry, the sign of r can be changed in the second summation. It is suggested that after these transformations, the As (t, I *) of the diagonal matrix remains unchanged, at least in the quasi-static approximation. With the step size of //, the obtained filter is scheduled to be updated to W (/) = -2μγ (^ s (/ 4- t)) sH (/ + τ '^ τ ) ~ Λ, (ί, τ) (1?)

7 V τ' J V r 在r ’及r n的加總表示平均運算，而在r上的加總源自 式1 3中的相關。感測器信號之估計的互相關可表示成The sum of 7 V τ 'J V r at r ′ and r n represents the averaging operation, and the sum at r is derived from the correlation in Equation 13. The estimated cross-correlation of the sensor signals can be expressed as

Ax(r，T)=E[i(r)V(r-〇], (18) v 經由將式2***式1 7中，而且使用式1 8的關係，則對於時 間t可對於濾波器參數更新得到一式如下 △rW = -2/iJ(0 * w +1(0 (19)、 with J(〇 = W * R K(t) ^ - Ax (〇 在上式的更新表不式中，以*表不豐積，而以星號☆表不相Ax (r, T) = E [i (r) V (r-〇], (18) v By inserting Equation 2 into Equation 17 and using the relationship of Equation 18, for time t can be used for the filter The parameter update is obtained as follows: △ rW = -2 / iJ (0 * w +1 (0 (19), with J (〇 = W * RK (t) ^-Ax (〇 * Means no accumulation, but asterisks ☆

490656 五、發明說明（π) 關運异，且，略時間延遲。在得到此更一 估計的互相關在對應一濾波器長度的日士 ρ 、示式中，假設 ，即 ’ θ尺寸中改變有限490656 V. Description of the Invention (π) Different operations are different, and there is a slight time delay. In obtaining this more estimated cross-correlation in the Japanese formula ρ corresponding to the length of a filter, it is assumed that the change in the size of θ is limited

Κχ(ί,ττ)«Κχ(^ + /,τ) f〇rO&lt;/&lt;Q (2)頻域轉換 在信號處理的技術中，熟知的方式 非時域中，以增加計算演算法的效率:=頻域中操作，而 據組可以轉換為頻域以進行數據處理 此頻域信號數 在BSS互相關中，考量基本±使 。方=尤其是使用 ，其基本上以疊積為計算方式，使/ 信號數據 時域上有效。 彳口在頻域中的疊積比在 ^匕’此將於下文中加以說明基本時域梯度渖 上頻域配置。在該頻域配置的發展中，一項方:=试，丨、; 算的成本且改進梯度更新的收歛性能。 ^ 计 拖^ ^在式1 9中疊積計算過於昂貴，所以將梯度表示法轉 換=在Τ頻率單元中的頻域。如果假設與頻率分量比較下 ^使H、的滤、波，即Q«T，則疊積因素近似。因此，圖19 複*梯度似近規則的良好近似轉換為頻域 Δ,\ν(ω) = 2μ&lt;Ι(γιω)\ν(ω)灸水ω) ( 2 0 ) ν with J(i^) = W(c〇)R;c(/?c〇)\V^((U)^^(/)6)) 在此W( ω )表示考量中之信號頻率分量的濾波器參數，而 示互相關的移動似近，其分別為w( Γ)之τ點的 月、立葉轉換，及Rx (t，I* ) ; t表示同時估計之時間。Κχ (ί, ττ) «Κχ (^ + /, τ) f〇rO &lt; / &Q; (2) Frequency domain conversion In the signal processing technology, the well-known method is not in the time domain in order to increase the computational algorithm. Efficiency: = operation in the frequency domain, and the data group can be converted into the frequency domain for data processing. The number of signals in the frequency domain is considered in the BSS cross-correlation. Square = especially using, which basically uses the superposition as the calculation method to make / signal data valid in the time domain. The superposition ratio of the gate in the frequency domain is described in the following. The basic time domain gradient 渖 is configured in the frequency domain. In the development of this frequency domain configuration, one term: = trial, 丨,; calculation cost and improve the convergence performance of gradient update. ^ Calculate drag ^ ^ The superposition calculation in Equation 19 is too expensive, so the gradient representation is converted = the frequency domain in the T frequency unit. If it is assumed that the filter and wave of H and Q are compared with the frequency component, that is, Q «T, the superposition factor is approximate. Therefore, the good approximation of the complex * gradient-like-near-rule in Figure 19 is converted to the frequency domain Δ, \ ν (ω) = 2μ &lt; Ι (γιω) \ ν (ω) moxibustion waterω) (2 0) ν with J (i ^ ) = W (c〇) R; c (/? C〇) \ V ^ ((U) ^^ (/) 6)) Here W (ω) represents the filter parameter of the frequency component of the signal under consideration, and It shows that the cross-correlation movements are close, which are the moon, T-leaf transformations at τ points of w (Γ), and Rx (t, I *); t represents the time of simultaneous estimation.

490656 五、發明說明（18) ΐ度：U此表示對應ff之實部及虛部之部二的數： δ 。在此式子中，對於學習速率以之複雜/ 則為Λω = 2μ^。 /数ω的更新規 (3 ) 功率的正規化 在本發明此實施例的另一效應中，最好一 的梯度表*，一方法可以改進本發明去相關二；：：階 性能。一適當的Newton-Raphson中更新要二^ 、 斂 陳的妬陆 又^而要的Hessian矩 -二在此例子中正破反Hessia_乎相當困難。 可得到有效的梯度更新，其中係數並沒有、在此入例子中 不了解時域中濾波器大小的限制，則近似的果 數去’如式2°中所示者。對於不同的頻率將此參 當的“性Ϊ，在單頻率中W(W)的數個元素可具有相 因此，對於认 例子中，HeSSian的對角似近相當差。 非一項ρ妊定的頻率修改矩陣元素w(〇)的梯度方向並 但是對方式。在較佳實施例中，可應用原始梯度， 新表示式為同的頻率對於應用正規化因素h(t，ω )。此更 Λ d) (ί,ω) 了中#為一固定之學習常數，h為級距可適化之加權因數490656 V. Description of the invention (18) ΐ Degree: U This represents the number corresponding to the real and imaginary parts of ff: δ. In this formula, the learning rate is complicated / Λω = 2μ ^. (3) Normalization of power In another effect of this embodiment of the present invention, a gradient table of * is preferred, and a method can improve the decorrelation of the present invention; 2: order performance. A proper Newton-Raphson update requires two ^, Chen's jealous Lu, and two required Hessian moments-two In this example, it is quite difficult to break the reverse of Hessia_. An effective gradient update can be obtained, in which the coefficients are not available. In this example, the limit of the filter size in the time domain is not known, and the approximated result is to be shown in Equation 2 °. For different frequencies, this parameter is "existent." In a single frequency, several elements of W (W) may have similar phases. Therefore, in the example, the diagonal of HeSSian seems to be quite close. Non-term The direction of the gradient of the matrix element w (〇) is modified in the same manner. In the preferred embodiment, the original gradient can be applied, and the new expression is the same frequency for applying the normalization factor h (t, ω). Λ d) (ί, ω) 了 中 # is a fixed learning constant, h is a weighting factor that can be adapted

第23頁 490656 五、發明說明（19) -適當的步驟大小正規化因素可應用下法決定 ^值的平方成本中，J(z&gt;azz*(在複數平面上）。適去的 第一階梯度步驟等於构/δ2(92”·1(9^/5ζ*二z 。在、 函數中的感測式子為^=2((WRx)h(wr為。苴勃 與輸入i無關。最好，對〃於戶^有的函數使用相同大3小的級 ^表=·’可使用S j的加總。該級距步驟正規化的因素Page 23 490656 V. Description of the invention (19)-Appropriate step size normalization factor can be determined by the following method. In the squared cost of J ^, J (z &gt; azz * (on the complex plane). Suitable first step The degree step is equal to the construction / δ2 (92 ”· 1 (9 ^ / 5ζ * two z. The sensing formula in the function is ^ = 2 ((WRx) h (wr is. Coherence has nothing to do with the input i. Most Well, for some functions that are used by households, use the same large and small levels. Table = · 'You can use the sum of S j. Factors for the regularization of this step

地武Ml2 (22) V 功率正規化。本發明基本上可決定使 Ί二…法的此級距大小的適用性，所 相s fe疋，且得到更正的收歛。 更新、·Ό果 ,(4) 皮器係教 濾波為參數值w可白合总 波器效率的不了^/貝^上在分離需要信號時減少濾 更新計算中，因此’在較佳實施例中，在各 ®將頻域（W( ω))值（传用 頻域，而去除不需要的㈣：：使用反DFT)暫時轉換為 I&quot; &gt; Q &lt; &lt; T之外± ' 因此限制濾、波器的解為在 執行反DFT，以轉換 士數值，且在這些頻域數值上 _的時間中出現的任广定V。在時域中。在大於時 。將大於Q之頻域 f由此日宁域值轉換為頻域 中的遽響應0化’濾波器的頻率響應Diwu Ml2 (22) V power is normalized. The present invention can basically determine the applicability of this step size of the Ί2 ... method, so s fe 疋, and obtain a correct convergence. Update, · Fruit, (4) The leather system teaches the filtering as the parameter value w, which can not combine the efficiency of the total wave filter. ^ / ^ ^ In the filter update calculation when the signal is separated, so 'in the preferred embodiment In each ®, the frequency domain (W (ω)) value (passes the frequency domain and removes unwanted ㈣ :: using inverse DFT) is temporarily converted to I &quot; &gt; Q &lt; &lt; T outside ± ' Therefore, the solution of the filter and the wave filter is limited to any Guangding V that occurs during the time when the inverse DFT is performed to convert the ± value, and the _ is in these frequency domain values. In the time domain. When greater than. The frequency domain f greater than Q is converted from this value to the frequency response of the 遽 response in the frequency domain.

第24頁 490656 五、發明說明（20) 的解 平整化，使得各濾波器中可決定唯 (5)圭i目關演算生^的操作 如在圖2流程中所示纟，本發明 塊處理程序。該本發明以窗口限法配置可方 號，即[士⑴，…，x1(t小U對於 轉換成為^域信 *χ-(t ω) 〇 , ^ A#^ ^ ^ 關，即$ f f ,、、！？「/ X T汁异估计的互相 中，：本，二，(“)以“)]。在-線上演4 τ基本上以過去的指數窗口平均 /去 在頻域中觀察的互相關，此為 、^ #作。對於 {，❽)=(1 - }〇άχ(ί，ω) +沖，(〇〇\ 在此Τ表示依據作§# 士日日 ）ν 間t中，⑹切所 广”儀選擇的忘記因素。在時 步驟。上气 ，應默x(t，ω)的現在估計計算梯产 乂私。當在頻域中計算更新時， 1 τ ^ #度 的步驟可得到數攄的τ二&quot;“亥化5虎，則丁樣本 度及估叶」t :塊。這些數據方塊可使用在梯 多的梯度=即但：時:二在進^ 新。-妒，乂的：A 内 方式必需更多次的更 率分量且的時框速率^中。使用者必需計算2丁頻Page 24, 490656 5. The solution of the invention description (20) is flattened, so that the operations of determining the (5) Guimeiguan calculus operator in each filter can be determined as shown in the flowchart of Figure 2. program. The present invention configures the square number using the window limit method, that is, [Shi, ..., x1 (t small U for conversion into ^ domain information * χ- (t ω) 〇, ^ A # ^ ^ ^ off, that is, $ ff, ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-, and -4. Related, this is, ^ # 作. For {， ❽) = (1-} 〇άχ (ί, ω) + 冲, (〇〇 \ In this T means according to § # 士 日 日) ν Room t, The factor of forgetting the choice of the instrument ”. In the current step. The gas should be calculated by the current estimate of x (t, ω). When the calculation is updated in the frequency domain, 1 τ ^ #degrees Steps can get the number of τ 2 "" Haihua 5 tiger, then the sample degree and estimation of leaves "t: blocks. These data blocks can be used in the gradient of the multi-step = = Dan: Hour: 2 in the new ^. -Jealous, jealous: the method in A must have more rate components and the time frame rate ^. The user must calculate 2 times

Kx(t , Γ ’ 2T/r ’ 3T/r ’ ···中更新W( ω )及 二ω)。傳統的重疊及節省方式對應ρ 來用方於ΓΛ本㈣BSS方法之非線上或線上實施例之 信號源提供將八i統。ΐ糸統包含一疊積的信號526，此 ’、’、、71為分置信號的信號，且包含一電腦系統 490656Kx (t, Γ '2T / r' 3T / r '... W (ω) and two ω) are updated. The traditional overlapping and saving method corresponds to ρ, and is used in the signal source of the non-online or online embodiment of the ΓΛ 本 ㈣BSS method. The system includes a superimposed signal 526, where ′, ′, and 71 are signals of discrete signals and include a computer system 490656

5 08，此系統執行本發明多去相關程序524。來源526可包 含豐積#號的任何來源，但是圖示中包含一感測器陣列 5 0 2及一信號處理器5 〇 4。感測器陣列包含一或多個傳感器 502A，502B，5 0 2C，如麥克風。此傳感器耦合到信號處^ 态5 0 4以執行信號的數位化。數位信號耦合電腦系統5 〇 8， 以分離信號且更進一步處理該信號。 電腦系統508包含中央處理單元（Cpu) 514，一記憶體 522 ’支援電路516，及輸入/輸出（I/O)介面5 20。該電腦 系統5 0 8 —般經I/O介面52〇耦合顯示器512及不同的輸入裝 置5 1 0 ’如滑鼠或鍵盤。一般支援電路包含熟知的電路， 如快取記憶體，電源，時脈電路，通訊匯流排等。記憶體 522可包含隨機存取記憶體（RAM)，唯隨記憶體（R〇M)，磁 碟’卡帶’等，或某些記憶體裝置的結合。本發明配置如 儲存在圮憶體5 2 2中，而且由CPU 5 1 4執行的多去相關程序 524_\以處理來自信號源526的信號。因此，電腦系統5〇8 t二般用的電腦系統，但在執行程序524時即為一特定之 電腦/系統。圖中顯示該一般其他的電腦系統為平台。熟習 本技術者應了解本發明使用如特用IC (ASIC)，數位信號 處理（DSP)積體電路，或其他的硬體電路或裝置以配置在 ^舍明的硬體中，因此，可以軟，硬體或其結合體配置5 08, this system executes the multi-correlation program 524 of the present invention. The source 526 may include any source of the Fengji # sign, but the illustration includes a sensor array 502 and a signal processor 504. The sensor array contains one or more sensors 502A, 502B, 50 2C, such as a microphone. This sensor is coupled to a signal state 504 to perform digitization of the signal. The digital signal is coupled to a computer system 508 to separate the signal and further process the signal. The computer system 508 includes a central processing unit (Cpu) 514, a memory 522 'supporting circuit 516, and an input / output (I / O) interface 520. The computer system 508 is generally coupled to the display 512 and various input devices 5 1 0 ′ such as a mouse or a keyboard via an I / O interface 52. The general support circuits include well-known circuits, such as cache memory, power supply, clock circuit, communication bus, etc. The memory 522 may include a random access memory (RAM), a random access memory (ROM), a magnetic disk 'cassette', etc., or a combination of some memory devices. The present invention is configured as a multi-correlation program 524_ \ stored in the memory 5 2 2 and executed by the CPU 5 1 4 to process signals from the signal source 526. Therefore, the computer system 508 is a general computer system, but it is a specific computer / system when the program 524 is executed. The figure shows that other general computer systems are platforms. Those skilled in the art should understand that the present invention uses special IC (ASIC), digital signal processing (DSP) integrated circuit, or other hardware circuits or devices to be configured in the hardware, so it can be soft , Hardware or its combination configuration

=^ &amp;腦系統5 0 8也包含一語音辨識處理器5 1 8，如語 =f =路卡，或語音辨識軟韓，用於處理分量信號者， …、發明從一疊積信號中得到者。因此，具有數種語音= ^ &amp; The brain system 5 0 8 also includes a speech recognition processor 5 1 8 such as language = f = Luca, or speech recognition software Han, for processing component signals, ..., invented from a superposition signal The winner. So with several voices

490656 五、發明說明（22) =景Λ音的人會議室可應用多麥克風5 02如以監視。麥克 人的成的語音，如果使用語音辨識系統轉換各 為'?腦信號或電腦命令則，該合成的語音信號 ，並數位…耗合到電腦；二心由 Ί ΐ相關程序524 ’分離合成的信號成為要素作號分量 :丄分量中，可簡單地去除背景雜。音'沒有 二θ的要素/刀量耦合語音辨識處理器518以處理分量 =成”腦文書或電腦指♦。依此方式，電腦系統5〇8 在執仃夕去相關程序524時會執行信號處理或決定語 識處理器5 1 8的條件。 ★雖然文中已應較佳實施例說明本發明，但嫺熟本技術者 需了解可對上述實施例加以更改及變更， 二 的精神及觀點。 侷離本發明 因此，對於上述基本上實施例的所有改變，修 發明的精神及觀點之内。 / ~在本 α490656 V. Description of the invention (22) = Jing Layin's conference room can use multiple microphones 502 such as surveillance. If the speech of the microphone is converted into a '? Brain signal or a computer command using a speech recognition system, the synthesized speech signal is digitally consumed by the computer; the two hearts are separated and synthesized by the Ί ΐ related program 524' The signal becomes the element numbering component: in the unitary component, the background noise can be simply removed. There is no two-theta element / knife volume coupled speech recognition processor 518 to process the component = into a brain instrument or a computer finger. In this way, the computer system 508 will execute a signal when it executes the relevant program 524 Process or determine the conditions of the speech processor 5 1 8. ★ Although the present invention has been described in terms of preferred embodiments, those skilled in the art need to understand that the above embodiments can be modified and altered, and the spirit and perspective of the second. From the present invention, therefore, for all the changes of the above-mentioned basic embodiments, it is within the spirit and perspective of the invention. / ~ 在 本 α

IIIIII

Claims (1)

490656 六、申請專利範圍 J · 一種用於將多個混合信號分離A $ &amp; ’包含下列步驟： “方法 (a )產生對應該混合信號之一輸入分段的頻率分量 個離散傅立葉轉換（DFT)值； ’ (b )使用DFT值更新互相關估計矩陣； (:)使用成本函數最小化處理’對於多個用於 :響，FIR)的多個遽波器係數，使用該互相關估計= 异一更新值； (g)使用具有該更新之濾波器係數的FIR J的信號’以將該混合信號分離為—或多個分量 (e)對於該混合信號之連續的輸入分段’以迭代 (iterate)方式重複步驟（a)，（b)，（c)及㈠）。 ^2為如中請專利範圍第i項之方法，其中步驟⑷尚包含步 (c 1 )將該更新濾波器係數從頻域轉換為時域； (c2) i比Γ預定的時間Q還要長的時間巾，將具有不為Π 之任何濾波态係數〇化’其中9小於一輸入分段長产了，因 此產生一組限制時域濾波器係數；以及 又 口 的時域遽波器係數從時 (如申晴專利範圍第丨項之苴勹A飞 化處理為一梯度下降處理。 八^成本函數最小 4 ·如申5青專利範圍第1項 新值的計算尚包含A y \ / ，/、中該濾波器係數更 3基於一正規化因素之更新級距大小的適490656 VI. Patent Application Range J · A method for separating multiple mixed signals A $ &amp; 'contains the following steps: "Method (a) generates discrete Fourier transforms (DFT) of frequency components corresponding to one of the input segments of the mixed signal ) Value; ((b) Update cross-correlation estimation matrix using DFT value; (:) Use cost function minimization process' For multiple wavelet coefficients used for: FIR, use this cross-correlation estimate = Heterogeneous update values; (g) use the signal of FIR J with the updated filter coefficients 'to separate the mixed signal into-or multiple components (e) continuous input segments for the mixed signal' to iterate (iterate), repeat steps (a), (b), (c), and ㈠). ^ 2 is the method of item i in the patent scope, where step ⑷ still includes step (c 1) to update the filter The coefficients are converted from the frequency domain to the time domain; (c2) i is a time towel longer than the predetermined time Q of Γ, and will have any filter state coefficients other than Π, where 9 is less than an input segment. , Which results in a set of limited time-domain filter coefficients; and The time-domain wavelet coefficients are from time (such as the 苴 勹 A flyover process of the first item in the Shen Qing patent range to a gradient descent process. The minimum cost function is 4 The calculation still includes A y \ /, where the filter coefficients are more appropriate based on the update step size of a normalization factor. 第28頁 六、申請專利範圍 應0 :用於將多個混合信號分離成為多個分量信 '5· 置，包含· -一々旦旧肌《V 用於產生對應該混合信號之八a 離散傅立葉轉換（βί?τ)值的裝置·刀奴的頻率分量之多個 f : DF丁值更新互相關一矩陣的機構； 一成本函數最小化處理器， 在一有限脈衝響應（FiR)濾坡哭 相闕估計值對於使用 更新值；以及 扣的夕個濾波器係數計算一 一具有該更新濾波器係數的Fir k號分離使用一或多個分〜波杰，以將該混合的 (如申請專利範圍第5項之W “ 化處理器包含： 、置，其中該成本函數最小 一第一轉換器，用 時域； ^新濾波“數從頻域轉換為 在比—預定的時間Q還要 ^慮波器係數0化之裝置，勺^間中’將具有不為〇之任 因^生一組限制時域濾波器於：輪入分段長度τ， 弟—轉換器，用於 f 轉換回頻域。 的，、波器係數從時域 /.如申請專利範圍第5項之袭置，复“ 4值的叶算更進— 〃、中5亥濾波器俜數f 大小。 3基於正規化因f ϋ廡s 數更 J 京適應更新級距的 货·一福白.A _ 長式的電腦可讀取的記錄媒質— 田 一 490656 六、申請專利範圍 際上用電腦糸統上執行時，導致該一般用電腦系統成為特 定目的的電腦熟習本技術者，其執行一用於將多個混合信 號分離為多個分量信號的方法，包含下列步驟： (a) 產生對應該混合信號之—輸入分段的頻率分量的多 個離散傅立葉轉換（DFT)值； (b) 使用DFT值更新互相關估計矩陣； (c) 使用成本函數最小化處理，對於多個用於_有限脈 衝響應（FIR)的多個攄波器係數，使用該互相關 算一更新值； (d) 使用具有該更新之濾波器係數的nR濾波器濾波該混 合的信號，以將該混合信號分離為一或多個分量信號丨以 及 (e) 對於垓此合化嬈之連續的輸入分段，以迭代 (1〇teratel 方式重複步驟（a)，（b)，（c)及（d)。 其 由丰t,申Λ專利範圍第8項之電腦可讀取的記錄媒質 中步l^(c)尚包含步驟為·· 、 (?) =更新濾'波器係數從頻域轉換為時域； (c2)二比一預定的時_還要長 之任何濾波器係數〇化，苴中〇 /、有不為〇 此妄斗,^ T Q小於一輸入分段長户T 此產生一組限制時域濾波器係數；以 〜，因 (C3)將該調整的時域濾波器係數 1、0如申士主皇刹f m 、数仗守域皁&quot;T換為猸 上L如甲σ月專利乾圍第8項之勺肩域。 1…“- 电月自可頊取的記錄媒質， 素之Page 28 6. The scope of the patent application shall be 0: used to separate multiple mixed signals into multiple component signals, including the “5” set, including--one old muscle "V is used to generate eight a discrete Fourier corresponding to the mixed signal A device that converts (βί? Τ) values. Multiple f of the frequency components of the knife slave: a mechanism that updates the cross-correlation of a matrix of DF values; a cost function minimization processor that filters at a finite impulse response (FiR) filter slope The relative estimated value is used for the updated value; and the calculated filter coefficients are used to calculate the Fir k number with the updated filter coefficients. One or more points are used to separate the mixed (such as applying for a patent The W processor in the range of item 5 includes: 、 and 置, where the cost function is the smallest first converter, using the time domain; ^ new filtering "number is converted from the frequency domain to be more than-a predetermined time Q ^ In the device with the wave filter coefficient of 0, there will be a set of time-limiting filters that are not zero. In turn, the segment length τ, the brother-to-converter, is used to convert f In the frequency domain, the wave filter coefficients are from the time domain. The application of the fifth item in the scope of the patent application, the "four-valued leaf calculation is more advanced — 〃, 5, 亥, 亥, filter 俜 number f size. 3 Based on the normalization factor f ϋ 庑 s number is more J Beijing adapt to update the level Yifubai.A _ Long computer-readable recording medium — Tianyi 490656 6. When the scope of patent application is implemented on a computer system, this general computer system has become a computer cookbook for a specific purpose. A technician executes a method for separating a plurality of mixed signals into a plurality of component signals, including the following steps: (a) generating a plurality of discrete Fourier transforms (DFT) corresponding to the frequency components of the mixed input-input segment ) Values; (b) use DFT values to update the cross-correlation estimation matrix; (c) use the cost function minimization process, and use the cross-correlation calculation for multiple waverifier coefficients for _finite impulse response (FIR) An updated value; (d) filtering the mixed signal using an nR filter with the updated filter coefficients to separate the mixed signal into one or more component signals; and (e) for the combined one Continuous loss Segmentation, repeating steps (a), (b), (c), and (d) in an iterative (10teratel manner) step by step of a computer-readable recording medium in the scope of patent application No. 8 l ^ (c) still includes the steps as ..., (?) = update filter 'wave filter coefficients are converted from frequency domain to time domain; (c2) any filter coefficients that are longer than a predetermined time_苴, 〇 /, there is no 〇 this delusion, ^ TQ is less than an input segmented long household T This results in a set of limited time-domain filter coefficients; with ~, because (C3) the adjusted time-domain filtering The coefficients 1, 0, such as Shen Shi's main emperor brake, fm, and the number of battlefields, "T" are replaced by the shoulder area of the 8th item in the patent, which is the same as that in the patent. 1… "-Dianyue's self-extractable recording medium,