CN111289106B - Spectral noise reduction method based on digital filtering - Google Patents
Spectral noise reduction method based on digital filtering Download PDFInfo
- Publication number
- CN111289106B CN111289106B CN202010224295.6A CN202010224295A CN111289106B CN 111289106 B CN111289106 B CN 111289106B CN 202010224295 A CN202010224295 A CN 202010224295A CN 111289106 B CN111289106 B CN 111289106B
- Authority
- CN
- China
- Prior art keywords
- filtering
- noise reduction
- signal
- spectral
- frequency
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000001914 filtration Methods 0.000 title claims abstract description 84
- 230000003595 spectral effect Effects 0.000 title claims abstract description 36
- 230000009467 reduction Effects 0.000 title claims abstract description 34
- 238000000034 method Methods 0.000 title claims abstract description 33
- 238000012546 transfer Methods 0.000 claims abstract description 27
- 238000005316 response function Methods 0.000 claims abstract description 26
- 230000000694 effects Effects 0.000 claims abstract description 15
- 230000001131 transforming effect Effects 0.000 claims abstract description 5
- 238000001228 spectrum Methods 0.000 claims description 12
- 238000011156 evaluation Methods 0.000 claims description 7
- 108010076504 Protein Sorting Signals Proteins 0.000 claims description 5
- 238000005259 measurement Methods 0.000 claims description 4
- 230000008030 elimination Effects 0.000 claims description 2
- 238000003379 elimination reaction Methods 0.000 claims description 2
- 230000000052 comparative effect Effects 0.000 description 9
- 238000009826 distribution Methods 0.000 description 7
- 238000013461 design Methods 0.000 description 6
- HEFNNWSXXWATRW-UHFFFAOYSA-N Ibuprofen Chemical compound CC(C)CC1=CC=C(C(C)C(O)=O)C=C1 HEFNNWSXXWATRW-UHFFFAOYSA-N 0.000 description 5
- 229960001680 ibuprofen Drugs 0.000 description 5
- 238000010586 diagram Methods 0.000 description 4
- 238000005457 optimization Methods 0.000 description 4
- 238000001069 Raman spectroscopy Methods 0.000 description 3
- 238000001237 Raman spectrum Methods 0.000 description 3
- 230000008901 benefit Effects 0.000 description 3
- 230000010354 integration Effects 0.000 description 3
- 238000012545 processing Methods 0.000 description 3
- 230000005284 excitation Effects 0.000 description 2
- 238000009499 grossing Methods 0.000 description 2
- 230000009466 transformation Effects 0.000 description 2
- 230000003321 amplification Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000003199 nucleic acid amplification method Methods 0.000 description 1
- 230000004044 response Effects 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 230000005236 sound signal Effects 0.000 description 1
- 238000009827 uniform distribution Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
- G01J3/28—Investigating the spectrum
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
- G01J3/02—Details
- G01J3/0297—Constructional arrangements for removing other types of optical noise or for performing calibration
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
- G01J3/28—Investigating the spectrum
- G01J2003/283—Investigating the spectrum computer-interfaced
- G01J2003/2843—Processing for eliminating interfering spectra
Landscapes
- Physics & Mathematics (AREA)
- Spectroscopy & Molecular Physics (AREA)
- General Physics & Mathematics (AREA)
- Image Processing (AREA)
Abstract
The invention discloses a spectral noise reduction method based on digital filtering, which comprises the following steps of 1, selecting a spectral signal S to be subjected to noise reduction; step 2, designing a frequency-amplitude response function PF of the spectral signal S to be denoised; step 3, transforming the frequency-amplitude response function PF to obtain a corresponding filtering convolution transfer function H; step 4, calculating the convolution Y of the spectral signal S to be denoised and the convolution transfer function H; step 5, intercepting data from the beginning of Y to the length equal to S, namely the result after noise reduction of S; and 6, selecting parameters Wr and Wp with optimal filtering effect to obtain a corresponding optimal filtering convolution transfer function H, and then obtaining an optimal noise reduction result. Data points obtained by the method are more compact and uniform, the end point is not truncated, and the length of a data sequence can be selected according to the precision requirement; and the method has no polynomial order limitation, no lattice phenomenon under the high-order condition and more precise result.
Description
Technical Field
The invention relates to the field of spectrum instruments, in particular to a spectrum noise reduction method based on digital filtering.
Background
Data smoothing and noise reduction has become an important means of improving instrument performance and increasing precision in modern instrument design and manufacture. Smoothing noise reduction, which is essentially low-pass filtering that filters out high frequency components in the signal, is the key to the choice and design of the filter. Compared with other applied filters, the purpose of the filter adopted by the spectrometer is to reduce noise and filter white noise outside a real signal, on one hand, the intensity of the filtered noise is as high as possible, and on the other hand, the loss of the real signal is as low as possible. A reasonable and efficient filter is of great importance to the performance of an instrument, the performance and the cost of the instrument are directly related in a spectrum instrument, the hardware quality is controlled, a digital filter which is targeted to a spectrum signal can be simply, reasonably and flexibly provided on the software level, and the digital filter has important significance for improving the cost performance of equipment, so that instrument users and manufacturers all provide strong requirements for designing and selecting the digital filter.
Most spectrometers include filtering and noise reduction functions in hardware, software, and hardware and software integration. In the design of an FIR filter commonly used in the field of signal processing, because a plurality of parameters need to be set, the difficulty is large in actual spectrum application, and the IIR filter has the limitation of difficult design. At present, the commonly accepted application effect is polynomial fitting-least square optimization filtering represented by an S-G filter, and compared with simple Gaussian filtering and moving window filtering, the method has better signal fidelity performance. Polynomial fitting-optimization is actually a simplified FIR filter, and has inherent disadvantages, namely, firstly, rigid parameter setting, including two parameters, the order of the polynomial and the fitting window width are difficult to accurately adapt to specific spectral characteristics; secondly, the problems of polynomial fitting precision and overfitting are solved, the adopted polynomial with lower order has better stability, but higher precision is difficult to obtain, and the higher precision needs higher polynomial order, which can cause the problems of stability damage and overfitting; thirdly, the method defined by S-G reaches the limit of polynomial optimization, and the performance is difficult to further improve.
Compared with other types of signals, such as audio signals and video signals, the spectral signal processing has higher certainty, relatively fixed frequency range and low requirements on phase and time lag, and is more beneficial to adopting simplified FIR thought processing, which is also the reason that S-G filtering is widely accepted. The S-G filtering adopts polynomial fitting signals, a convolution function is obtained through least square optimization, and due to the Runge phenomenon, polynomial orders are selected to be higher, uncertainty is larger, and therefore improvement of the accuracy of a polynomial method is limited.
The spectrum peak appearance accords with Voigt distribution, the frequency domain amplitude response after Fourier change also basically accords with Voigt distribution or approximately accords with Gaussian distribution, and white noise has the characteristic of uniform distribution on the frequency domain. The invention proposes that the frequency-amplitude distribution can be directly designed according to the difference between the two. And performing Fourier inverse transformation on the designed frequency-amplitude distribution to obtain a function which can be used as a convolution transfer function of FIR filtering, and calculating the convolution of the noise-reduced signal and the convolution transfer function to obtain the noise-reduced signal.
Disclosure of Invention
In order to solve the above problems, the present invention provides a spectral noise reduction method based on digital filtering.
The invention discloses a spectral noise reduction method based on digital filtering, which is realized by the following steps:
the invention provides a spectral noise reduction method based on digital filtering, which comprises the following steps:
step 1, selecting a spectral signal S to be denoised;
step 3, transforming the frequency-amplitude response function PF to obtain a corresponding filtering convolution transfer function H;
and 5, intercepting data from the beginning of the Y to the length equal to that of the S, namely the noise-reduced result of the S.
Further, the frequency-amplitude response function PF comprises two part parameters: wr and Wp;
wherein Wr represents the band stop width of the spectral signal S to be noise reduced; wp represents the bandpass width of the spectral signal S to be noise reduced.
Further, the filtering convolution transfer function H in the step 3 is obtained by subjecting the response function PF to inverse Fourier transform to obtain PF N Taking PF N The left half of the real part, HL, is divided by its sum (HL), which in turn yields the filter convolution transfer function H.
Further, the method further comprises a step 6 of selecting parameters Wr and Wp with optimal filtering effects through the evaluation indexes, obtaining a corresponding optimal filtering convolution transfer function H according to the optimal parameters, and obtaining an optimal noise reduction result according to the optimal filtering convolution transfer function H.
Further, the frequency-amplitude response function PF is designed according to the following method:
a. generating a half-peak width by Wr, normalizing the peak height and taking the peak width as a band elimination part;
b. generating Wp sequence points equal to 1 as a band pass part;
c. and splicing the band-stop part and the band-pass part into a frequency-amplitude response function PF.
Further, the splicing means that the band-pass part and the band-stop part are connected end to be spliced into a frequency-amplitude response function PF, that is: in the former stage of Wr portion, wp 1s are added to form an array PF.
Further, the evaluation index is a residual mean square error-kurtosis ratio (VFR) value, and Wr and Wp corresponding to the maximum value of the residual mean square error-kurtosis ratio (VFR) value are the optimal Wr and Wp.
Further, the residual value mean square error-kurtosis ratio (VFR) value is obtained by the following steps:
step i, selecting a filtering algorithm, and carrying out treatment on the original measurement signal x b Performing smooth noise reduction to obtain an output signal x a ；
Step ii, finding x b And x a The residual value x of (c);
step iii, calculating the mean square error-kurtosis ratio VFR of the residual value x;
and v, adjusting the filtering parameters and calculating the VFRs corresponding to different parameters.
Further, the mean square error-kurtosis ratio VFR is calculated according to the following formula:
wherein σ is mean square error, and g is kurtosis ratio.
Further, the mean square error is calculated using the following formula:
the kurtosis ratio is calculated using the following formula:
in the above formula: the signal sequence contains n data singles, and the residual sequence x is the signal x before filtering b And the filtered signal x a Respectively calculating variance sigma according to the variance and kurtosis formulas 2 And g.
Compared with the prior art, the invention has the following advantages:
1) The method can directly design frequency-amplitude distribution, the designed frequency-amplitude distribution is subjected to Fourier inverse transformation to obtain a function which can be used as a convolution transfer function of FIR filtering, and the convolution of a noise-reduced signal and the convolution transfer function is calculated to obtain a noise-reduced signal;
2) The data points obtained by the method are more compact and uniform, the end point is not truncated, and the length of the data sequence can be selected according to the precision requirement;
3) The method has no polynomial order limitation, no dragon lattice phenomenon under the high-order condition and more precise result.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
FIG. 1 is a Raman spectrum simulated with Voigt peaks;
FIG. 2 is a graph of the S-G filter convolution function of comparative example 1;
FIG. 3 is a schematic diagram of the frequency-amplitude response function design of example 1 of the present invention;
FIG. 4 is a schematic diagram of the convolution generating transfer function H according to embodiment 1 of the present invention;
FIG. 5 is a schematic diagram of convolution Y in embodiment 1 of the present invention;
FIG. 6 shows the filtering result of embodiment 1 of the present invention;
FIG. 7 is a graph of a convolution function in embodiment 1 of the present invention;
fig. 8 is a graph comparing the results of ibuprofen original true signal, comparative example 1S-G filtering and example 2 filtering based on a sequence of data points, 8 (a) being the overall case, 8 (b) being the case of sharp peaks, and 8 (c) being the case of high frequency filtering of flat portions. (ii) a
Figure 9 is a graph comparing the results of ibuprofen original true signal based on raman shift, comparative example 1S-G filtering and example 2 filtering.
Detailed Description
The following description is given for illustrative embodiments of the invention and other advantages and benefits of the invention will become apparent to those skilled in the art from the disclosure herein.
The invention provides a spectrum noise reduction method based on digital filtering, which comprises the following steps:
step 1, selecting a spectral signal S to be denoised;
step 3, transforming the frequency-amplitude response function PF to obtain a corresponding filtering convolution transfer function H;
and 5, intercepting data from the beginning of the Y to the length equal to that of the S, namely the noise-reduced result of the S.
Further, the frequency-amplitude response function PF comprises two part parameters: wr and Wp;
wherein Wr represents the band stop width of the spectral signal S to be noise reduced; wp denotes the band pass width of the spectral signal S to be noise reduced.
Further, the filtering convolution transfer function H in step 3 is obtained by subjecting the response function PF to inverse Fourier transform to obtain PF N Taking PF N The left half of the real part, HL, is divided by its sum (HL), which in turn yields the filter convolution transfer function H.
Further, the method further comprises a step 6 of selecting parameters Wr and Wp with optimal filtering effects through the evaluation indexes, obtaining a corresponding optimal filtering convolution transfer function H according to the optimal parameters, and obtaining an optimal noise reduction result according to the optimal filtering convolution transfer function H.
Further, the frequency-amplitude response function PF is designed according to the following method:
a. generating a half-Gaussian peak by Wr, normalizing the peak height and taking the peak height as a band stop part;
b. generating Wp sequence points equal to 1 as a band pass part;
c. and splicing the band-stop part and the band-pass part into a frequency-amplitude response function PF.
Further, the evaluation index is a residual mean square error-kurtosis ratio (VFR) value, and Wr and Wp corresponding to the maximum value of the residual mean square error-kurtosis ratio (VFR) value are the optimal Wr and Wp.
Further, the residual value mean square error-kurtosis ratio (VFR) value is obtained by the following steps:
step i, selecting a filtering algorithm and carrying out filtering on the original measurement signal x b Performing smooth noise reduction to obtain an output signal x a ；
Step ii, finding x b And x a The residual value x of (d);
step iii, calculating the mean square error-kurtosis ratio VFR of the residual value x;
and v, adjusting the filtering parameters, and calculating the VFRs corresponding to different parameters.
Further, the mean square error-kurtosis ratio VFR is calculated according to the following formula:
where σ is the mean square error and g is the kurtosis ratio.
Further, the mean square error is calculated using the following formula:
the kurtosis ratio is calculated using the following formula:
in the above formula: the signal sequence contains n data singles, and the residual sequence x is the signal x before filtering b And the filtered signal x a Respectively calculating the variance sigma according to the variance and kurtosis formulas 2 And g.
Comparative example 1:
the raman spectrum was simulated with the Voigt peak and then white noise at 2% variance intensity was added to generate a simulated spectral signal containing noise. Referring to FIG. 1, FIG. 1a, FIG. 1b, and FIG. 1c respectively show a noise-free signal S 0 An added noise signal N and an analog spectrum S after the addition of noise.
And (3) adopting S-G filtering to obtain a residual error between the noise-containing signal and a filtering result, and then calculating a correlation coefficient between the residual error and the added noise, wherein the better the correlation is, the better the noise filtering effect is. When the parameters are selected to be order 6 and window width 59, the optimal correlation coefficient is 0.9512, and the convolution function of the S-G filter is as shown in fig. 2.
Comparative example 2
The raman spectrometer was used to collect the true signal of ibuprofen (532 nm excitation, 2048 pixel array spectrometer, integration time 5S), and S-G filtering had the best effect with parameters of 9 order and window width 17.
Example 1:
to illustrate the effect of the filter of the present embodiment, the present embodiment uses the same simulation data as in comparative example 1, i.e., a raman spectrum is simulated using a Voigt peak, and then white noise of 2% variance intensity is added to generate a simulated spectrum signal containing noise. Referring to FIG. 1, wherein a, b, and c are noise-free signals S 0 The noise signal N is added, and the simulated spectrum S after noise is added.
The frequency-amplitude response function contains two parts of parameters: a bandstop width Wr and a bandpass width Wp. (defined by a Gaussian peak hypothesis, wr is the width of a Gaussian peak, if other peak types such as Voigt peak are adopted, wr is a parameter related to three peak types, and the Gaussian function can meet most requirements due to simple and accurate comprehensive consideration);
a. generating a half-Gaussian peak by Wr, normalizing the peak height and taking the peak height as a band stop part;
b. generating Wp sequence points equal to 1 as a band pass part;
c. and connecting the band-pass part and the band-stop part end to form a frequency-amplitude response function PF by splicing, namely: in the former stage of Wr portion, wp 1s are added to form an array PF, as shown in FIG. 3.
Defining Wp and Wr as 100, performing inverse Fourier transform on the response function according to the input signal sequence length of 5000, and obtaining PF of 5000 sequence data points N The solid portion is shown in fig. 4 (a). The left half HL of FIG. 4 (a) is cut, as in FIG. 4 (b). Dividing HL by PF N The sum (HL) as convolution transfer function H, as shown in fig. 4 (c), contains data points that are compact and uniform, has good continuity, and facilitates precise numerical operation.
The convolution Y of S and H was calculated as shown in fig. 5.
The first 5000 data of Y are truncated and output as the result of filtering, as shown in fig. 6.
The optimal filter effect parameters of this embodiment, wp =130 and Wr =89, the noise-and-residual correlation coefficient is 0.9526, as shown in fig. 7, fig. 7 is a convolution function diagram of the filter of this embodiment, it can be seen that the data points of this embodiment are dense and uniform, and the end point is not truncated, and the data sequence length can be selected according to the precision requirement. And the polynomial order limit is avoided, and the dragon lattice phenomenon appearing under the high-order condition does not exist, so that the result is more precise.
Example 2
In order to illustrate the effect of the filter in this embodiment, the same signal as that in comparative example 2, that is, the true signal (532 nm excitation, 2048 pixel array spectrometer, integration time 5S) of ibuprofen is collected by using a raman spectrometer as the spectral signal S to be denoised in this embodiment.
The other steps were the same as in example 1.
The filter of the present embodiment has the best filtering effect at Wp =550 and Wr =650, evaluated by the residual mean square error-kurtosis ratio VFR value.
The evaluation indexes used in the embodiment 1 and the embodiment 2 are residual mean square error-kurtosis ratio (VFR) values, the Wr and the Wp corresponding to the VFR values are found out according to the maximum value of the VFR values, the Wr and the Wp are optimal, and the noise reduction result obtained by using the optimal Wr and Wp parameters is the optimal noise reduction result;
the method comprises the following steps of obtaining a residual value mean square error-kurtosis ratio (VFR) value by the following steps:
step i, selecting the filtering algorithm of the invention, and carrying out the filtering algorithm on the original measurement signal x b Performing smooth noise reduction to obtain an output signal x a ；
Step ii, finding x b And x a The residual value x of (d);
step iii, calculating the mean square error-kurtosis ratio VFR of the residual value x;
v, adjusting the filtering parameters Wr and Wp, calculating VFRs corresponding to different parameters, and finding out Wr and Wp corresponding to the maximum value of the VFR;
the mean square error-kurtosis ratio VFR is calculated according to the following formula:
wherein sigma is mean square error, g is kurtosis ratio;
wherein, the mean square error is calculated by adopting the following formula:
the kurtosis ratio is calculated using the following formula:
in the above formula: the signal sequence contains n data singles, and the residual sequence x is the signal x before filtering b And the filtered signal x a Respectively calculating variance sigma according to the variance and kurtosis formulas 2 And g.
Filtering noise reduction result
1. Comparative example 1 and example 1
As shown in fig. 8, fig. 8 is a comparison of the results of the original real signal, S-G filtering and embodiment 1 filtering of the present invention. Fig. 8 (a) shows the entire case, (b) shows the case of a sharp peak, and (c) shows the case of high-frequency filtering of a flat portion. It can be seen that the overall S-G and the filtering mode of embodiment 1 of the present invention have good effects, and in the local amplification effect, embodiment 1 of the present invention has less distortion on the sharp high-frequency peak, and the high-frequency component in the flat portion is filtered more thoroughly, and the curve is smoother.
The filtering effect of embodiment 1 of the invention is superior to the S-G filtering of the prior art.
2. Comparative example 2 and example 2:
figure 9 is a comparison of the results of the original real signal of ibuprofen, S-G filtering and the filter of the present invention. (a) is the overall effect; (b) Is the detail of the peak top, the distortion of the filter of this embodiment is less than S-G; (c) In the case of the peak bottom, it can be seen that the filtering method of embodiment 2 filters the high frequency signal to a slightly better degree than S-G, and the result is smoother.
Claims (10)
1. A spectral noise reduction method based on digital filtering is characterized by comprising the following steps:
step 1, selecting a spectral signal S to be denoised;
step 2, designing a frequency-amplitude response function PF of the spectral signal S to be denoised;
step 3, transforming the frequency-amplitude response function PF to obtain a corresponding filtering convolution transfer function H;
step 4, calculating the convolution Y of the spectrum signal S to be denoised and the filtering convolution transfer function H;
and 5, intercepting data from the start of Y to the length equal to that of S, namely the noise-reduced result of S.
2. A method for spectral noise reduction based on digital filtering according to claim 1, wherein said frequency-amplitude response function PF comprises two parameters: wr and Wp;
wherein Wr represents the band stop width of the spectral signal S to be noise reduced; wp denotes the band pass width of the spectral signal S to be noise reduced.
3. A method for spectral noise reduction based on digital filtering according to claim 2, wherein said filtering convolution transfer function H of step 3 is obtained by inverse fourier transforming said response function PF to obtain PF N Taking PF N The left half of the real part, HL, is divided by its sum (HL), which in turn yields the filtering convolution transfer function H.
4. The spectral noise reduction method based on digital filtering according to claim 3, further comprising step 6, selecting parameters Wr and Wp with optimal filtering effect through evaluation indexes, obtaining a corresponding optimal filtering convolution transfer function H according to the optimal parameters, and obtaining an optimal noise reduction result according to the optimal filtering convolution transfer function H.
5. A method for spectral noise reduction based on digital filtering according to any of claims 1 to 4, characterized in that the frequency-amplitude response function PF is designed according to the following method:
a. generating a half-peak width by Wr, normalizing the peak height and taking the peak width as a band elimination part;
b. generating Wp sequence points equal to 1 as a band pass part;
c. and splicing the band-stop part and the band-pass part into a frequency-amplitude response function PF.
6. The spectral noise reduction method based on digital filtering according to claim 5, wherein the splicing is performed by splicing the band-pass part and the band-stop part end to form a frequency-amplitude response function PF, that is: the front part of the Wr part is added with Wp 1s to form an array PF.
7. The spectral noise reduction method based on digital filtering according to claim 4, wherein the evaluation index is a residual mean square error-kurtosis ratio VFR, and Wr and Wp corresponding to the maximum value of the residual mean square error-kurtosis ratio VFR are the optimal Wr and Wp.
8. A method of spectral noise reduction based on digital filtering according to claim 7, characterized in that the residual mean square error-kurtosis ratio VFR is obtained by:
step i, selecting a filtering algorithm, and carrying out treatment on the original measurement signal x b Performing smooth noise reduction to obtain an output signal x a ；
Step ii, finding x b And x a The residual value x of (d);
step iii, calculating the mean square error-kurtosis ratio VFR of the residual value x;
and v, adjusting the filtering parameters and calculating the VFRs corresponding to different parameters.
9. A method of spectral noise reduction based on digital filtering according to claim 8, characterized in that the residual mean square error-kurtosis ratio VFR is calculated according to the following formula:
where σ is the mean square error and g is the kurtosis ratio.
10. A method for spectral noise reduction based on digital filtering according to claim 9, wherein the mean square error is calculated using the following formula:
the kurtosis ratio is calculated using the following formula:
in the above formula: the signal sequence contains n data singles, and the residual sequence x is the signal x before filtering b And the filtered signal x a Respectively calculating the variance sigma according to the variance and kurtosis formulas 2 And g.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010224295.6A CN111289106B (en) | 2020-03-26 | 2020-03-26 | Spectral noise reduction method based on digital filtering |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010224295.6A CN111289106B (en) | 2020-03-26 | 2020-03-26 | Spectral noise reduction method based on digital filtering |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111289106A CN111289106A (en) | 2020-06-16 |
| CN111289106B true CN111289106B (en) | 2022-11-11 |
Family
ID=71026028
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010224295.6A Active CN111289106B (en) | 2020-03-26 | 2020-03-26 | Spectral noise reduction method based on digital filtering |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111289106B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111256819B (en) * | 2020-02-20 | 2022-09-09 | 苏州沓来软件科技有限公司 | Noise reduction method of spectrum instrument |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106462957A (en) * | 2016-05-19 | 2017-02-22 | 深圳大学 | Method and system for removing stripe noise in infrared image |
| CN106644075A (en) * | 2016-11-17 | 2017-05-10 | 天津津航技术物理研究所 | Efficient de-noising method for Fourier spectrograph |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8688759B2 (en) * | 2006-06-16 | 2014-04-01 | Bae Systems Information And Electronic Systems Integration Inc. | Efficient detection algorithm system for a broad class of signals using higher-order statistics in time as well as frequency domains |
-
2020
- 2020-03-26 CN CN202010224295.6A patent/CN111289106B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106462957A (en) * | 2016-05-19 | 2017-02-22 | 深圳大学 | Method and system for removing stripe noise in infrared image |
| CN106644075A (en) * | 2016-11-17 | 2017-05-10 | 天津津航技术物理研究所 | Efficient de-noising method for Fourier spectrograph |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111289106A (en) | 2020-06-16 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CA2659158A1 (en) | Device and method for processing a real subband signal for reducing aliasing effects | |
| CN114970602A (en) | Signal denoising method and system based on improved empirical mode decomposition and wavelet threshold function | |
| CN111289106B (en) | Spectral noise reduction method based on digital filtering | |
| Kumar et al. | A closed form design method for the two-channel quadrature mirror filter banks | |
| CN106644075A (en) | Efficient de-noising method for Fourier spectrograph | |
| van Waterschoot et al. | A pole-zero placement technique for designing second-order IIR parametric equalizer filters | |
| CN109724693B (en) | Fusion spectrum denoising method based on stationary wavelet | |
| CN108168697B (en) | Spectrometer noise reduction and wavelength calibration method | |
| Turulin et al. | Analysis of controlled digital recursive high-pass filters structures with infinite non-negative impulse response | |
| CN109460614B (en) | Signal time-frequency decomposition method based on instantaneous bandwidth | |
| CN112332809B (en) | Fractional order elliptic filter design method for amplitude unattenuated balanced phase | |
| CN111207830B (en) | Low-distortion spectral noise reduction filtering method | |
| CN114331926B (en) | Two-channel graph filter bank coefficient design optimization method based on element changing idea | |
| CN107315713B (en) | One-dimensional signal denoising and enhancing method based on non-local similarity | |
| CN113630104B (en) | Filter bank frequency selectivity error alternation optimization design method of graph filter | |
| Anurag et al. | An efficient iterative method for nearly perfect reconstruction non-uniform filter bank | |
| CN118249784A (en) | Full-adaptive filtering and arbitrary order calculus data processing method based on multiple region extraction | |
| Weiss et al. | Noise and digital signal processing | |
| CN117056671B (en) | EMD-based Raman spectrum noise reduction method | |
| CN112687277B (en) | Method and device for determining voice formant, electronic equipment and readable storage medium | |
| CN116388729B (en) | Prototype filter based on DFT filter bank structure and design method | |
| CN113472350A (en) | Continuous adjusting and optimizing method for analog-to-digital conversion precision | |
| CN118378018A (en) | Method for extracting weak signal by combining mixing and fractional Fourier transform | |
| JP4214391B2 (en) | How to design a digital filter | |
| Pankaj et al. | Design of Auto Adaptive IIR Filter Using P th Optimization Algorithm and Artificial Neural Network Technique |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| TR01 | Transfer of patent right |
Effective date of registration: 20230505 Address after: Floor 3, No. 2, Lane 455, Zhuting Road, Yexie Town, Songjiang District, Shanghai, 201600 Patentee after: Shanghai Ruhai Instrument Equipment Co.,Ltd. Address before: 545006 268 East Ring Road, Central District, Liuzhou, the Guangxi Zhuang Autonomous Region Patentee before: GUANGXI University OF SCIENCE AND TECHNOLOGY |
|
| TR01 | Transfer of patent right |