JPH01136407A - Hilbert transformation device - Google Patents
Hilbert transformation deviceInfo
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- JPH01136407A JPH01136407A JP29408187A JP29408187A JPH01136407A JP H01136407 A JPH01136407 A JP H01136407A JP 29408187 A JP29408187 A JP 29408187A JP 29408187 A JP29408187 A JP 29408187A JP H01136407 A JPH01136407 A JP H01136407A
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- 230000009466 transformation Effects 0.000 title abstract 5
- 238000005070 sampling Methods 0.000 claims description 2
- 238000000034 method Methods 0.000 abstract description 6
- 230000000295 complement effect Effects 0.000 abstract description 2
- 125000002015 acyclic group Chemical group 0.000 description 6
- 238000010586 diagram Methods 0.000 description 5
- 238000012545 processing Methods 0.000 description 3
- 230000003111 delayed effect Effects 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 238000003491 array Methods 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
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Abstract
Description
【発明の詳細な説明】
〔産業上の利用分野〕
本発明は通信、特に伝送分野で用いられるヒルベルト変
換器に係り、特に構成ハード量の増大を生ずることなく
、振幅および位相誤差を小さくすることが可能なヒルベ
ルト変換器に関する。[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a Hilbert converter used in communications, particularly in the transmission field, and in particular, to reduce amplitude and phase errors without increasing the amount of hardware. Regarding Hilbert transformers capable of
［従来の技術〕
ヒルベルト変換器は信号（周波数帯域制限された信号、
あるいは解析信号）の実数部と虚数部（実数部に対して
位相が９０°遅れた信号）とを相互に変換する作用をも
つ。〔詳細な説明はたとえばプレンティス・ホール社刊
、オッペンハイム他著、“ディジタル シグナル プロ
セシング（Ａ、Ｖ、Ｏｐｐｅｎｈｓｉｍ、 Ｒ，Ｗ、５
ｃｈａｔａｒ″Ｄｉｇｉｔａｌ ＳｉｇｎａｌＰｒｏｃ
ｅｓｓｉｎｇ’ Ｐｒｅｎｔｉｃｓ−Ｈａｌｌ、 Ｉｎ
ｃ、） １９７５ 。[Prior art] The Hilbert transformer converts signals (frequency band limited signals,
Alternatively, it has the function of mutually converting the real part of the analytic signal and the imaginary part (a signal whose phase is delayed by 90 degrees with respect to the real part). [For a detailed explanation, see, for example, Digital Signal Processing (A, V, Oppenhsim, R, W, 5, published by Prentice Hall, Oppenheim et al.
chatar”Digital SignalProc
essing'Prentics-Hall, In
c,) 1975.
（伊達訳“ディジタル信号処理”コロナ社、 １９７８
）〕従来、このヒルベルト変換器を設計する手法として
は、理想ヒルベルト変換器のインパルス応答を有限項近
似し、非巡回形フィルタで実現する方法（たとえば前掲
書下巻Ｐ、２２）、あるいは全域通過フィルタを用いて
９０°位相分波器を作製する方法（たとえば電子通信学
会編著“ディジタル信号処理の応用”コロナ社１９８１
年５月発行、Ｐ、１０５）が知られている。(Date translation “Digital Signal Processing” Corona Publishing, 1978
)] Conventionally, methods for designing this Hilbert transformer include a method of approximating the impulse response of an ideal Hilbert transformer with a finite term and realizing it with an acyclic filter (for example, Ibid., Vol. 2, P. 22), or an all-pass filter. A method for producing a 90° phase demultiplexer using
Published in May, P. 105) is known.
上記従来技術の非巡回形フィルタによりヒルベルト変換
器はヒルベルト変換器のインパルス応答を有限項近似し
て実現される。位相特性（同相出力（実数部）と直交出
力（虚数部））は９０”になるがインパルス応答が項数
ｎに対して１ ／ ｎで収束するために、収束が遅く、
振幅特性を良好にするには非常に多くの項数をとる必要
がある。−方、全域通過フィルタで９０’移相器を実現
する方法では、振幅特性は１となって正確であるが、位
相特性は近似によっているため、これも、正確な９０’
移相器を実現するには次数の高い全域通過フィルタを用
いねばならず、やはり構成ハード量が大きくなるという
問題があった０本発明の目的は従来のヒルベルト変換器
の欠点、すなわち、精度のよいヒルベルト変換器を実現
しようとする構成ハード量が大きくなる欠点を除き、少
ないハード量で高精度なヒルベルト変換器を実現するこ
とにある。The Hilbert transformer is realized by approximating the impulse response of the Hilbert transformer by a finite term using the acyclic filter of the prior art. The phase characteristics (in-phase output (real part) and quadrature output (imaginary part)) are 90", but since the impulse response converges at 1/n for the number of terms, the convergence is slow.
In order to improve the amplitude characteristics, it is necessary to use a very large number of terms. - On the other hand, in the method of realizing a 90' phase shifter using an all-pass filter, the amplitude characteristic is 1 and is accurate, but the phase characteristic is based on approximation, so this also has an accurate 90' phase shifter.
In order to realize a phase shifter, a high-order all-pass filter must be used, which also has the problem of increasing the amount of hardware involved.The purpose of the present invention is to solve the drawbacks of conventional Hilbert transformers, namely The object of the present invention is to realize a high-precision Hilbert converter with a small amount of hardware, while eliminating the drawback that the amount of hardware required to realize a good Hilbert converter is large.
上記目的は従来技術の二つの方法を組合せ、両者の相補
的な特徴を補い合うことで実現される。The above object is achieved by combining two methods of the prior art and complementing each other with their complementary features.
すなわち、同一の入力信号を非巡回形フィルタ（Ｆ Ｉ
Ｒ）によるヒルベルト変換器と全域通過フィルタ（Ａ
ＰＦ）によるヒルベルト変換器に同時に入力する。ＦＩ
Ｒの出力は位相特性は正確であるが、振幅特性が正しく
ない。一方ＡＰＦの出力は振幅特性は正確であるが位相
特性は誤差を含んでいる。そこで、ＡＰＦ出力がら振幅
値を計算する。すなわち同相出力の２乗と直交出力の２
乗を加算し、平方根をとったものを計算する。同様にＦ
ＩＲ出力の振幅値を計算し、両者の振幅比を求メチ・コ
レをＩ” Ｉ Ｒ出力の同相、直交出力に掛けた値を出
力とする。すなわちＦ Ｉ Ｒの出力振幅を、ＡＰＦ出
力で補正することにより、正しいヒルベルト変換出力が
得られる。In other words, the same input signal is passed through an acyclic filter (FI
Hilbert transformer with R) and all-pass filter (A
PF) is simultaneously input to the Hilbert transformer. FI
The output of R has accurate phase characteristics but incorrect amplitude characteristics. On the other hand, although the amplitude characteristics of the output of the APF are accurate, the phase characteristics include errors. Therefore, the amplitude value is calculated from the APF output. In other words, the square of the in-phase output and the square of the quadrature output
Calculate by adding the powers and taking the square root. Similarly F
Calculate the amplitude value of the IR output, and find the amplitude ratio of both. Multiply the in-phase and quadrature output of the I"IR output by the value of the in-phase and quadrature output.In other words, the output amplitude of the FI R is calculated by the APF output. By correcting, a correct Hilbert transform output can be obtained.
以上の構成が目的どおり作動するためにはＦＩＲとＡＰ
Ｆの出力がほぼ同じ時点の出力波形である必要がある。In order for the above configuration to work as intended, FIR and AP
It is necessary that the outputs of F have output waveforms at approximately the same point in time.
ＡＰＦの遅延時間は１次のＡＰＦでは１サンプル遅延、
２次のＡＰＦの場合は２サンプル遅延に等しい、一方、
ＦＩＲの遅延時間は遅延素子列の入力端から中点までの
遅延時間に等しい０両者の出力時点を合せるには、ＡＰ
Ｆへの入力信号を、ＦＩＲの遅延素子列の中点からＡＰ
Ｆの遅延時間分、入力側へ逆のぼった遅延素子の出力か
ら取り出せばよい、こうすることによってＦＩＲからは
位相の正確な出力が、ＡＰＦからは振幅の正確な出力が
得られる０両者の出力はほぼ同時刻の出力であるので、
ＦＩＲ出力の振幅をＡＰＦ出力で補正してやればよい。The delay time of APF is 1 sample delay in first-order APF,
For a second order APF it is equal to 2 sample delay, while
The delay time of FIR is equal to the delay time from the input end to the midpoint of the delay element array.To align both output points, AP
The input signal to F is input from the midpoint of the delay element array of FIR to AP
The delay time of F can be extracted from the output of the delay element that flows backwards to the input side.By doing this, you can obtain an accurate phase output from the FIR and an accurate output of the amplitude from the APF. are the outputs at almost the same time, so
The amplitude of the FIR output may be corrected by the APF output.
このとき、へＰＦ出力の直交出力と同相出力の位相は９
０”から若干ずれているが、そのずれを５°以下にする
ことは容易にできる。したがって位相誤差を振幅誤差に
換算すると、 １−−ｓｉｎ５゜＝０．９６で、４％
（０，３ｄ Ｂ）以下となる。ちなみに、４％以下の振
幅誤差をＦＴＲで実現するには５０段以上の遅延素子が
必要となる。At this time, the phase of the orthogonal output and the in-phase output of the PF output is 9
Although it deviates slightly from 0", it is easy to reduce the deviation to 5 degrees or less. Therefore, when converting the phase error into an amplitude error, 1--sin 5 degrees = 0.96, which is 4%.
(0.3dB) or less. Incidentally, in order to achieve an amplitude error of 4% or less using FTR, 50 stages or more of delay elements are required.
本発明の一実施例を図面を用いて説明する。第１図にお
いて１は非巡回形フィルタ（ＦＩＲ）、２、′３は全域
通過フィルタ（ＡＰＦ）、４，５゜７．８，１２．１３
は掛算器、６，９は加算器、１０は除算器、１１は平方
根演算器である。入力信号ｘｔｎはＦＩＲＩに入力され
、同相出力Ｒ１と直交出力ＸＺが出力される。An embodiment of the present invention will be described with reference to the drawings. In Figure 1, 1 is an acyclic filter (FIR), 2, '3 is an all-pass filter (APF), 4,5°7.8, 12.13
is a multiplier, 6 and 9 are adders, 10 is a divider, and 11 is a square root calculator. The input signal xtn is input to FIRI, and an in-phase output R1 and a quadrature output XZ are output.
ＦＩＲＩの詳細構成図を第３図に示す。第３図において
、３０１〜３０ｚｎは遅延素子、３１１〜３１．÷１は
係数掛算器、３２は加算器である。第３図はヒルベルト
変換器のインパルス応答を有限項で近似し、非巡回形フ
ィルタで構成したものである。前掲書（伊達訳゛′ディ
ジタル信号処理″下巻Ｐ、２２）によれば９０°移相器
のインパルス応答ｈ （ｎ）は
で与えられる。すなわち中点（ｎ＝ｏ）から数えπ Ｎ
の値をとる。）第３図の係数す、（ｉ＝１〜ｍ＋１）は
で与えられる。ただしｍは奇数である。A detailed configuration diagram of FIRI is shown in FIG. In FIG. 3, 301-30zn are delay elements, 311-31. ÷1 is a coefficient multiplier, and 32 is an adder. FIG. 3 shows an approximation of the impulse response of a Hilbert transformer using finite terms, which is constructed using an acyclic filter. According to the above-mentioned book (translated by Date, "Digital Signal Processing", Vol. 2, P. 22), the impulse response h (n) of a 90° phase shifter is given by: i.e., the value of π N counted from the midpoint (n=o). ) The coefficients (i=1 to m+1) in FIG. 3 are given by, where m is an odd number.
第３図に示すＦＩＲ形のヒルベルト変換器では同相出力
Ｒ１が遅延素子列の中点（遅延素子３０゜の出力）から
得られ、直交出力Ｉｔが加算器３２の出力として得られ
る。これらは、遅延素子列３０１〜３０．によって遅延
されているのでｍＴだけ入力信号より遅れている。（Ｔ
は遅延素子１個の遅延時間＝Ｆ４Ｒフィルタの動作標本
周期）−方、第１図のＡＰＦ形ヒルベルト変換器の出力
の遅延時間は、これと異なる。そこで二つの出力波形が
同時刻のものとなるようにＡＰＦの入力にはＦＩＲの入
力を遅らせたものを用いる。したがって、第３図の遅延
素子列の中点より入力端子側にＡＰＦの遅延時間だけ逆
のぼった遅延素子からの信号Ｘａ を取り出し、ＡＰＦ
ｔ、ＡＰＦｚの入力とする。In the FIR type Hilbert transformer shown in FIG. 3, the in-phase output R1 is obtained from the midpoint of the delay element array (the output of the delay element 30°), and the orthogonal output It is obtained as the output of the adder 32. These are delay element arrays 301-30. Since the input signal is delayed by mT, it lags behind the input signal by mT. (T
(Delay time of one delay element=Operation sampling period of F4R filter) - The delay time of the output of the APF type Hilbert transformer shown in FIG. 1 is different from this. Therefore, the input of the FIR is used as the input of the APF so that the two output waveforms are at the same time. Therefore, by taking out the signal Xa from the delay element which has been reversely extended by the delay time of the APF from the midpoint of the delay element row in Fig. 3 to the input terminal side,
t and APFz input.
第４図にＡＰＦ２．３の具体的回路例を示す。FIG. 4 shows a specific circuit example of APF2.3.
第４図において、４１．４２は遅延素子、４３゜４５は
加算器、４４は係数掛算器である。入力信号をＸ、出力
信号をｙとすると、第４図の動作はｙ＝ｂ（ｚ−工ｙ−
ｘ）＋ｚ−”ｘで表わされる。（ここでｚ−１は１サン
プル遅延演算子である。したがって伝達関数は
で与えられる。（３）式にｚ二〇′ＩＩＴ （ω：角周
波数ＪＴ＝動作標本周期）を代入して絶対値を求めると
、ωに関わらず常に１となり、（３）式は１次７１次の
全域通過フィルタとなっていることがわかる。第１図の
ＡＰＦｘ、ｘはこの１次／１次ＡＰＦをいくつか縦続に
接続して、Ａ Ｐ Ｆ １とＡ Ｐ Ｆ ２の出力位相
差がある周波数帯域にわたってほぼ９０”となるように
設計したものである。したがって同相出力Ｒ２と直交出
力Ｉ２は振幅特性は正確であるが位相差は近似的に９０
″となるにすぎない。In FIG. 4, 41, 42 are delay elements, 43.degree. and 45 are adders, and 44 is a coefficient multiplier. When the input signal is X and the output signal is y, the operation in Figure 4 is y=b(z-work y-
x)+z-"x (where z-1 is a one-sample delay operator. Therefore, the transfer function is given by When the absolute value is obtained by substituting the operating sample period), it is always 1 regardless of ω, and it can be seen that equation (3) is a first-order 71st-order all-pass filter.APFx, x in Fig. 1 is designed by connecting several of these primary/primary APFs in cascade so that the output phase difference between A P F 1 and A P F 2 is approximately 90" over a certain frequency band. Therefore, the in-phase The amplitude characteristics of the output R2 and the orthogonal output I2 are accurate, but the phase difference is approximately 90
”.
一方、ＦＩＲ形ヒルベルト変換器では位相差は正確に９
０”となるが、有限項近似しているため振幅は正しくな
い。そこで、振幅の正しいＡＰＦ出力の振幅値で１位相
は正しいが振幅の正しくないＦＩＲ出力の振幅値を補正
することにより正しいヒルベルト変換出力ＲおよびＩが
得られる。これを実行するには掛算器４，５と加算器６
によりＡＰ Ｆ出力１７）電力Ｐｚ”＝Ｒｚ”＋ Ｉｚ
”を求め、同様に掛算器７，８と加算器９によりＦＩＲ
出力の電力Ｐ １２＝ Ｒｔ２＋ Ｉ １”を求める。On the other hand, in the FIR type Hilbert transformer, the phase difference is exactly 9
0", but the amplitude is incorrect because it is approximated by a finite term. Therefore, by correcting the amplitude value of the FIR output, which has the correct amplitude but the correct amplitude, with the amplitude value of the APF output, which has the correct amplitude, the correct Hilbert The conversion outputs R and I are obtained.To perform this, multipliers 4, 5 and adder 6 are used.
AP F output 17) Power Pz”=Rz”+Iz
” and similarly calculate the FIR using multipliers 7 and 8 and adder 9.
Calculate the output power P12=Rt2+I1''.
除算器１０および平めで、これを掛算１２，１３により
ＦＩＲの同相出力Ｒ１，直交出カニ１に掛けることによ
り振幅補正された出力ＲおよびＩが得られる。Amplitude-corrected outputs R and I are obtained by multiplying the in-phase output R1 of the FIR and the orthogonal output crab 1 by the divider 10 and the square output by the multipliers 12 and 13.
振幅補正の原理を第２図のベクトル図でさらに詳しく説
明する。ＦＩＲ出力Ｒ１，Ｉｆは位相は正確に９０°で
ある・が振幅Ｐｉは正しい値でない。The principle of amplitude correction will be explained in more detail using the vector diagram in FIG. The phase of the FIR output R1, If is exactly 90°, but the amplitude Pi is not a correct value.
他方ＡＰＦ出力Ｒ，Ｉ２は位相は正しくなく、同相軸よ
りθ工、直交軸より０２位相ずれしている。On the other hand, the phases of the APF outputs R and I2 are incorrect, and are out of phase by θ from the in-phase axis and by 02 from the orthogonal axis.
しかし、出力振幅Ｐ２は正確である。Ｐ２は次式によっ
て求められる。However, the output amplitude P2 is accurate. P2 is determined by the following equation.
（４）式で０２−０１は位相誤差であり５″以内になる
ようにＡＰＦを設計することは容易である。したがって
５ｉｎ（θ２−０１）の項を省略してＰ２ ＝＝１．０
４ で４％以下である。こうして求めたＰ２によりＦＩ
Ｒの振幅Ｐ１を補正することにより正しい出力Ｒおよび
工を求めることができる。In equation (4), 02-01 is the phase error, and it is easy to design the APF so that it is within 5". Therefore, by omitting the term 5in (θ2-01), P2 = = 1.0
4 is less than 4%. Based on P2 obtained in this way, FI
By correcting the amplitude P1 of R, the correct output R and power can be obtained.
本発明によれば従来の方法に較べて少ないハード量で振
幅特性９位相特性共に高精度なヒルベルト変換器が得ら
れる。According to the present invention, a Hilbert transformer with high accuracy in both amplitude characteristics and phase characteristics can be obtained with less hardware than conventional methods.
第１図は本発明の一実施例の構成を示すブロック図、第
２図は第１図の原理を説明するベクトル図、第３図は第
１図の構成要素の非巡回形フィルタの詳細構成を示すブ
ロック図、第４図は第１図の構成要素の全域通過フィル
タの詳細構成を示すブロック図である。FIG. 1 is a block diagram showing the configuration of an embodiment of the present invention, FIG. 2 is a vector diagram explaining the principle of FIG. 1, and FIG. 3 is a detailed configuration of an acyclic filter as a component of FIG. 1. FIG. 4 is a block diagram showing the detailed configuration of the all-pass filter, which is a component of FIG. 1.
Claims (1)
素子を偶数個縦続に接続して、前記入力信号を前記遅延
素子列の片端に入力し、前記遅延素子列の中点から出力
した信号を同相出力とし、前記中点から、入力端から遠
ざかる方向に奇数（Ｎ）番目ごとに信号を取り出して、
各々、係数２／πＮ（πは円周率）を掛けた信号と、前
記中点から入力端に近づく方向奇数（Ｎ）番目ごとに信
号を取り出して各々、係数−２／πＮを掛けた信号との
総和を直交出力として出力する第１のヒルベルト変換器
と、出力信号の位相差がある周波数範囲にわたつて概略
９０°となるように設定した第１および第２の全域通過
フィルタを用いて構成した第２のヒルベルト変換とを設
け、前記遅延素子列の中点から前記第２のヒルベルト変
換器の遅延時間に等しい遅延段数だけ入力端子側に逆の
ぼつた遅延素子出力から取り出した信号を前記第２のヒ
ルベルト変換器の入力信号とし、前記第１および第２の
ヒルベルト変換器の出力振幅の比を求め、該出力振幅比
を第１のヒルベルト変換器出力に掛けて振幅値を補正し
、該補正した信号を同相および直交出力とすることを特
徴とするヒルベルト変換器。1. An even number of delay elements with a delay time equal to the sampling period of input signal data are connected in series, the input signal is input to one end of the delay element array, and the signal output from the midpoint of the delay element array is The in-phase output is taken out from the midpoint to every odd number (N)th signal in the direction away from the input end,
A signal multiplied by a coefficient 2/πN (π is pi), and a signal obtained by extracting signals every odd number (N) in the direction approaching the input end from the midpoint and multiplying each by a coefficient -2/πN. using a first Hilbert transformer that outputs the sum of A second Hilbert transform configured as shown in FIG. As an input signal of the second Hilbert converter, calculate the ratio of output amplitudes of the first and second Hilbert converters, and correct the amplitude value by multiplying the output amplitude ratio of the first Hilbert converter. , A Hilbert transformer characterized in that the corrected signal is output as in-phase and quadrature output.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP29408187A JPH01136407A (en) | 1987-11-24 | 1987-11-24 | Hilbert transformation device |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP29408187A JPH01136407A (en) | 1987-11-24 | 1987-11-24 | Hilbert transformation device |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| JPH01136407A true JPH01136407A (en) | 1989-05-29 |
Family
ID=17803040
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP29408187A Pending JPH01136407A (en) | 1987-11-24 | 1987-11-24 | Hilbert transformation device |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH01136407A (en) |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH01157611A (en) * | 1987-12-15 | 1989-06-20 | Kyocera Corp | Hilbert converter |
| JPH01175312A (en) * | 1987-12-28 | 1989-07-11 | Kyocera Corp | Hilbert transformer |
| US5394475A (en) * | 1991-11-13 | 1995-02-28 | Ribic; Zlatan | Method for shifting the frequency of signals |
| US5633937A (en) * | 1991-11-13 | 1997-05-27 | Viennatone Ag | Method for processing signals |
| TWI426394B (en) * | 2011-03-03 | 2014-02-11 | 私立中原大學 | Empirical Mode Decomposition Operation Device and Its Envelope Line Operation Circuit |
-
1987
- 1987-11-24 JP JP29408187A patent/JPH01136407A/en active Pending
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH01157611A (en) * | 1987-12-15 | 1989-06-20 | Kyocera Corp | Hilbert converter |
| JPH01175312A (en) * | 1987-12-28 | 1989-07-11 | Kyocera Corp | Hilbert transformer |
| US5394475A (en) * | 1991-11-13 | 1995-02-28 | Ribic; Zlatan | Method for shifting the frequency of signals |
| US5633937A (en) * | 1991-11-13 | 1997-05-27 | Viennatone Ag | Method for processing signals |
| TWI426394B (en) * | 2011-03-03 | 2014-02-11 | 私立中原大學 | Empirical Mode Decomposition Operation Device and Its Envelope Line Operation Circuit |
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