A mismatched system static correction filter design method based on frequency domain weighting

Abstract

The application discloses a mismatched system static correction filter design method based on frequency domain weighting, which comprises the following steps: collecting analog signals and reference signals of a single-peak to-be-corrected system output respectively, and adjusting the obtained two groups of periodical data in the time dimension; dividing the two groups of adjusted data according to the periodical law, and performing periodical accumulation on the obtained data to obtain to-be-corrected data and reference data; solving the frequency spectrum of the to-be-corrected data and the reference data, and the difference frequency spectrum of the two, to obtain an effective frequency spectrum; solving the amplitude and phase curves of the effective frequency spectrum, and performing peak elimination processing and correction processing on the two curves respectively; reconstructing the expected response of the whole frequency domain by using the corrected amplitude and phase curves; and solving the optimal weight value of the target correction filter by using the expected response of the whole frequency domain based on a least square frequency domain equalization algorithm. The method can enhance the stability of the static correction filter for system mismatch correction, and improve the correction effect.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a design method for a static correction filter for a mismatched system based on frequency domain weighting. Background Technology

[0002] With the rapid advancement of electronic technology, digital signal processing technology has penetrated deeply into people's production and daily lives, encompassing radar, communication, computers, and many other fields. A crucial foundation for these technologies is the ability of front-end equipment to accurately acquire and transmit analog signals. In practice, because the characteristics of the components within these devices are often nonlinear, mismatches can occur in the acquired or transmitted signals. Specifically, this manifests as distortions in the amplitude and phase characteristics of the signal, which can adversely affect subsequent signal processing and even lead to incorrect results.

[0003] Currently, there are two main types of algorithms for correcting mismatched systems: time-domain correction and frequency-domain correction. Frequency-domain correction algorithms, which use the desired spectral characteristics as the target when calculating weights, are more suitable for static correction of the system. Generally, static correction of mismatched systems is achieved using a weighted approach. When the amplitude and phase characteristics of the filter corresponding to the added weights cancel each other out with the system's inherent mismatch characteristics, the distorted signal can be corrected.

[0004] However, existing static correction algorithms for mismatch systems still have the following drawbacks:

[0005] First, since the reference signal for static weights comes from accurate devices such as oscilloscopes, although these devices usually do not have large mismatches, the sampling results of these devices are also affected by factors such as noise. Therefore, when only one set of oscilloscope signals and acquired signals are used as reference and target signals according to the principle of adaptive frequency domain equalization, the correction effect is limited and the advantage of using multiple sets of data when statically solving for weights cannot be taken advantage of.

[0006] Second, in practice, due to the existence of system noise and the special nature of the difference spectrum solution, when the signal spectrum is very small, the difference spectrum will fluctuate violently, and there will be spikes in the difference between the target signal and the reference signal. This will make the in-band difference spectrum unable to reflect the mismatch characteristics of the system well, and will lead to system instability.

[0007] Third, a large number of peak spikes often appear in the out-of-band spectrum. When the peak values ​​of the spikes are large, the weighting of the system will be greatly affected by the out-of-band components.

[0008] Fourth, the correction effect is limited because the difference between signals within and outside the bandwidth is only based on weighting. Summary of the Invention

[0009] To address the aforementioned problems in the prior art, this invention provides a design method for a static correction filter for a mismatched system based on frequency domain weighting.

[0010] The main idea of ​​this invention is: based on the characteristic that static weighting can use multiple sets of data, the data is accumulated and then processed to reduce the impact of noise; the signals within the bandwidth and signals outside the bandwidth are processed to a greater extent to obtain a spectrum that can more accurately reflect the system mismatch characteristics, thereby obtaining better weights.

[0011] The technical problem to be solved by this invention is achieved through the following technical solution:

[0012] A method for designing a static correction filter for a mismatched system based on frequency domain weighting, comprising:

[0013] Step 1: Acquire the analog signal and reference signal output by the single-peak system to be corrected at the same sampling rate, and adjust the two sets of periodic data in the time dimension to obtain two sets of adjusted data.

[0014] Step 2: Divide the two sets of adjusted data according to the periodic pattern, and accumulate the two clusters of data periodically to obtain the data to be corrected and the reference data.

[0015] Step 3: Solve for the spectra of the data to be corrected and the reference data respectively, and calculate the difference spectrum between the two; obtain the effective spectrum based on the difference spectrum;

[0016] Step 4: Solve for the amplitude and phase curves of the effective spectrum, and perform peak removal processing on the two curves respectively to obtain the amplitude and phase curves after peak removal.

[0017] Step 5: Correct the amplitude and phase curves after peak elimination using the least squares method to obtain the corrected amplitude and phase curves;

[0018] Step 6: Reconstruct the desired response in the entire frequency domain using the corrected amplitude and phase curves;

[0019] Step 7: The frequency domain equalization algorithm based on least squares uses the expected response of the entire frequency domain to solve for the optimal weights of the target correction filter, so as to obtain the expected correction filter spectrum and thus realize the design of the static correction filter for the mismatch system.

[0020] The beneficial effects of this invention are:

[0021] This invention first accumulates the initial signal to be corrected and the reference signal over multiple cycles, enhancing their representation of system mismatch characteristics, suppressing the influence of noise, and eliminating some spikes in the difference spectrum introduced by specific signals. Then, it discards the out-of-band difference spectrum and performs peak-shaving and correction on the amplitude and phase curves of the in-band difference spectrum, reducing the influence of signal specificity and noise on the trend of the difference curve, making the curve more representative of the overall system mismatch characteristics. Finally, it reconstructs the mismatch characteristic spectrum of the entire system using the corrected difference curve, thereby deriving the desired correction filter spectrum. Ultimately, this invention enables it to maintain good correction performance in high-noise environments where some traditional methods fail, enhancing the stability of the static correction filter for system mismatch correction.

[0022] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating a design method for a frequency-domain weighted static correction filter for a mismatched system provided in an embodiment of the present invention.

[0024] Figure 2 It shows the waveforms of the acquired signal and the reference signal under simulation conditions;

[0025] Figure 3 The amplitude-frequency response of the correction filter is obtained by traditional methods under simulation conditions;

[0026] Figure 4 The phase frequency characteristics of the correction filter obtained by traditional methods under simulation conditions;

[0027] Figure 5 The result is the correction of the filter obtained by the traditional method under simulation conditions;

[0028] Figure 6 The amplitude-frequency characteristic of the correction filter obtained by the method of this invention under simulation conditions;

[0029] Figure 7 The phase frequency characteristics of the correction filter obtained by the method of this invention under simulation conditions;

[0030] Figure 8 This is the correction result of the correction filter obtained by the method of this invention under simulation conditions. Detailed Implementation

[0031] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0032] Example 1

[0033] Please see Figure 1 , Figure 1 This is a flowchart illustrating a frequency-domain weighted static correction filter design method for mismatched systems provided in an embodiment of the present invention, which includes:

[0034] Step 1: Acquire the analog signal and reference signal output by the single-peak system to be corrected at the same sampling rate, and adjust the two sets of periodic data in the time dimension to obtain two sets of adjusted data.

[0035] In this embodiment, step 1 specifically includes:

[0036] (1a) Use an acquisition system at a sampling rate f s A set of periodic data D is obtained by acquiring an analog signal output from a periodic, single-peak system to be calibrated. x .

[0037] Among them, F band >0, f s >0 and f s >2F band F band For analog signal bandwidth; data D x The total length is N D The number of data points in each period is N. T N D and N T All are positive integers, and N D >2N T .

[0038] Correspondingly, at the same sampling rate f s The reference signal is acquired to obtain a set of periodic data D. y Its length is also N D .

[0039] In this embodiment, the reference signal can be generated using an accurate oscilloscope.

[0040] Understandably, the reference signal can be obtained not only through an oscilloscope, but also through any measurement that is considered accurate. For example, a more accurate acquisition device can be used for sampling, or the user can construct the desired reference signal based on their own experience.

[0041] (1b) respectively using data D x and D y The position of the first peak point is used as the index marker to obtain two sets of time-dimension adjusted data D. xq and D yq .

[0042] Specifically, let's assume data D x The first peak at p s Points, data Dy The first peak at q s One point. Remove data D x The front p s Data D was obtained from each point. xq Remove data D y The first q s Data D was obtained from each point. yq Among them, p s are positive integers and p s <N T +1, q s It is a positive integer and q s <N T +1.

[0043] Step 2: Divide the two sets of adjusted data according to the periodic pattern, and accumulate the two clusters of data periodically to obtain the data to be corrected and the reference data.

[0044] In this embodiment, step 2 specifically includes:

[0045] (2a) Take data D xq The former Z T Data for each period, in terms of period points N T The data was split to obtain a cluster of data D. xq1 D xq2 ,…, Its relationship with D xq The logical relationship is as follows:

[0046]

[0047] Its nth T Group data The nth q The data is

[0048] At the same time, take data D yq The former Z T Data from N periods T The data was split to obtain a cluster of data D. yq1 D yq2 ,…, Its relationship with D yq The logical relationship is as follows:

[0049]

[0050] Its nth T Group Data D yqnT The nth q The data is d yqnT (n q ).

[0051] Among them, Z T Z is a positive integer and T satisfy:

[0052]

[0053] n q =0,1,…,N T -1, n T =1,2,…,Z T .

[0054] (2b) Transfer data D xq1 D xq2 ,…, By performing periodic accumulation, the data X to be corrected is obtained. dj Its expression is:

[0055]

[0056] Its length is N T Its nth element is x dj (n), where n = 0, 1, ..., N T -1.

[0057] Simultaneously, data D yq1 D yq2 ,…, By accumulating data over a period of time, we can obtain reference data Y. ref Its expression is:

[0058]

[0059] Its length is N T Its nth element is y ref (n), where n = 0, 1, ..., N T -1.

[0060] This embodiment performs periodic accumulation of the input signal to be corrected and the reference signal over multiple cycles, which enhances its performance in representing the system mismatch characteristics and suppresses the influence of noise.

[0061] Step 3: Solve the spectra of the data to be corrected and the reference data respectively, and calculate the difference spectrum between the two; obtain the effective spectrum based on the difference spectrum.

[0062] In this embodiment, step 3 specifically includes:

[0063] (3a) Set the number of frequency domain observation points to N F And satisfy N F >N T ;

[0064] (3b) For the data to be corrected X dj Do N F The spectrum of the point is used to obtain the spectrum X of the data to be corrected. djf Its k-th element is represented as:

[0065]

[0066] Where, x dj (n) represents the data X to be corrected. dj The nth element, k = 0, 1, ..., N F -1;

[0067] Meanwhile, for the reference data Y ref Do N F The point spectrum is used to obtain the spectrum Y of the reference data. reff Its k-th element is represented as:

[0068]

[0069] Among them, y ref (n) represents the reference data Y ref The nth element;

[0070] (3c) Spectrum X based on the data to be corrected djf and the spectrum Y of the reference data reff Calculate the difference spectrum C diff ; wherein, the difference spectrum C diff The formula for calculating the k-th element is:

[0071]

[0072] Where k = 0, 1, ..., N F -1.

[0073] (3d) Determine the effective frequency range F fcs The effective frequency range F fcs Must meet:

[0074]

[0075] (3e) Based on the effective frequency range F fcs The formula for determining the number of points that should be retained is as follows:

[0076]

[0077] in, This represents rounding the numerical value up.

[0078] (3f) The difference spectrum C is obtained based on the number of points obtained in step (3e). diffPrincipal component screening is performed to obtain the effective spectrum C. diffuse , its kth use The elements are: ·

[0079] c diffuse (k use ) = c diff (k use )

[0080] Where, k use =0,1,…N Fuse -1.

[0081] Step 4: Solve for the amplitude and phase curves of the effective spectrum, and perform peak removal processing on the two curves respectively to obtain the amplitude and phase curves after peak removal processing.

[0082] In this embodiment, step 4 specifically includes:

[0083] (4a) Based on the effective spectrum C diffuse Calculate the amplitude-frequency curve C abs and phase curve C ang ;in,

[0084] The amplitude-frequency curve C abs The kth use Each element is represented as:

[0085] c abs (k use ) = c diffuse (k use )

[0086] Where, k use =0,1,…N Fuse -1.

[0087] The phase curve C ang The kth use Each element is represented as:

[0088] c ang (k use ) = angle(c diffuse (k use ))

[0089] Where angle(·) is the angle function, its expression is:

[0090]

[0091] In the formula, 0≤θ a <360, and meets the requirements

[0092]

[0093] In the formula, real(·) represents taking the real part of a complex number, and imag(·) represents taking the imaginary part of a complex number.

[0094] (4b) Set the window length to N wds Index parameter p map =0; take the amplitude-frequency curve C abs The first N wds Construct matrix C from points abswin Its expression is:

[0095] C abswin =[c abs (0),c abs (1),…,c abs (N wds )]

[0096] Where, matrix C abswin The nth win The element is c abswin (n win ).

[0097] Take the phase curve C ang The first N wds Construct matrix C from points angwin Its expression is:

[0098] C angwin =[c ang (0),c ang (1),…,c ang (N wds )]

[0099] Where, matrix C angwin The nth win The element is c angwin (n win ).

[0100] Define C absnpb and C angnpb It is the length N Fuse -N wds Two row vectors with +1. C absnpb The nth npb The element is c absnpb (n npb ), C angnpb The nth npb The element is c angnpb (n npb ). Where n npb =0,1,…,N Fuse -N wds .

[0101] (4c) Adjust matrix C abswin The positions of each element in the matrix are used to obtain matrix C. abswin ', whose elements satisfy:

[0102] c abswin '(0) <c abswin '(1)<… <c abswin '(N wds -1)

[0103] Adjustment matrix C angwin The positions of each element in the matrix are used to obtain matrix C. angwin ', whose elements satisfy:

[0104] c angwin '(0) <c angwin '(1)<… <c angwin '(N wds -1)

[0105] (4d) Based on matrix C abswin 'and matrix C angwin Construct matrix C respectively absnpb and C angnpb ;

[0106] Specifically, when N wds When it is an odd number, let

[0107]

[0108]

[0109] When N wds When it is even, let

[0110]

[0111]

[0112] (4e) Let p map =p map +1; if p is judged map ≤N Fuse -N wds Then update matrix C according to the following formula. abswin and C angwin , and return to step (4c);

[0113] C abswin =[c abs (p map ),c abs (p map +1),…,c abs (p map +Nwds )]

[0114] C angwin =[c ang (p map ),c ang (p map +1),…,c ang (p map +N wds )]

[0115] Otherwise, proceed to step (4f);

[0116] (4f) Based on matrix C absnpb Construct matrix C absnp This is used as the amplitude curve after peak removal; simultaneously, based on matrix C angnpb Construct matrix C angnp This is used as the phase curve after peak elimination processing.

[0117] Specifically, when N wds When it is an odd number:

[0118] Set the length to row vector S abss , its nth st The elements are

[0119] s abss (n st ) = c absnpb (0)

[0120] Set the length to row vector S abse , its nth st The elements are

[0121] s abse (n st ) = c absnpb (N Fuse -N wds )

[0122] Set the length to row vector S angs , its nth st The elements are

[0123] s angs (n st ) = c angnpb (0)

[0124] Set the length to row vector S ange , its nth st The elements are

[0125] sange (n st ) = c angnpb (N Fuse -N wds )

[0126] Among them, the nth st =0,1,…,

[0127] Construct row vector C based on the above vectors. absnp and C angnp Its expression is:

[0128] C absnp =[S abss C absnpb ,S abse ]

[0129] C angnp =[S angs C angnpb ,S ange ]

[0130] When N wds When it is even:

[0131] Set the length to row vector S absqs , its nth sqs The elements are

[0132] s absqs (n sqs ) = c absnpb (0)

[0133] Among them, the nth sqs =0,1,…,

[0134] Set the length to row vector S absqe , its nth sqm The elements are

[0135] s absqe (n sqm ) = c absnpb (N Fuse -N wds )

[0136] Where the nth sqm =0,1,…,

[0137] Set the length to row vector S angqs , its nth sqs The elements are

[0138] s angqs (n sqs ) = c angnpb (0)

[0139] Set the length to row vector S angqe , its nth sqm The elements are

[0140] s angqe (n sqm ) = c angnpb (N Fuse -N wds )

[0141] Construct row vector C based on the above vectors. absnp and C angnp Its expression is:

[0142] C absnp =[S absqs C absnpb ,S absqe ]

[0143] C angnp =[S angqs C angnpb ,S angqe ]

[0144] The C constructed above absnp This is the amplitude curve after peak reduction processing, and its k-th peak... use The element is c absnp (k use The C constructed above angnp This is the phase curve after peak elimination processing, and its k-th peak... use The element is c angnp (k use );k use =0,1,…N Fuse -1.

[0145] Step 5: Correct the amplitude and phase curves after peak elimination using the least squares method to obtain the corrected amplitude and phase curves.

[0146] In this embodiment, step 5 specifically includes:

[0147] (5a) Set the polynomial order L d L d The integers are positive integers, and 1 ≤ L. d <N Fuse ;

[0148] (5b) Using the least squares method as the criterion, the amplitude curves C after peak elimination are respectively...absnp and phase curve C angnp Polynomial fitting is performed to obtain the magnitude correction result C. absnh and phase correction result C angnh .

[0149] Among them, the magnitude correction result C absnh The kth use The element is c absnh (k use Phase correction result C angnh The kth use The element is c angnh (k use ), k use =0,1,…N Fuse -1.

[0150] This embodiment discards the out-of-band difference spectrum and performs peak removal and correction on the amplitude and phase curves of the in-band difference spectrum, reducing the influence of signal specificity and noise on the trend of the difference curve. This makes the curve more representative of the overall mismatch characteristics of the system.

[0151] Step 6: Reconstruct the desired response in the entire frequency domain using the corrected amplitude and phase curves.

[0152] In this embodiment, step 6 specifically includes:

[0153] (6a) The amplitude correction result C absnh and phase correction result C angnh Reconstruct the desired response vector C. tgt , its kth use Each element is represented as:

[0154]

[0155] Among them, c absnh (k use ) indicates the magnitude correction result C absnh The kth use The kth element use c elements angnh (k use ) represents the phase correction result C angnh The kth use One element;

[0156] (6b) Construct a length of row vector G S All of its values ​​are constants P. dw P dw It is a real number, and it needs to satisfy 0. <P dw <max(Cabsnh ), where max(·) is the maximum value of the orientation quantity;

[0157] (6c) Based on the desired response vector C tgt and row vector G S Construct vector C Zhlf Its expression is:

[0158] C Zhlf =[C tgt C Zhlf ]

[0159] Wherein, vector C Zhlf The kth hlf The element is c Zhlf (k hlf ), k hlf =1,2,…,

[0160] (6d) Construct a length of row vector C Fhlf , its kth hlf The value of the element is:

[0161]

[0162] Where conj(·) represents taking the conjugate of a complex number;

[0163] (6e) Based on the row vector C Fhlf and the vector C Zhlf Construct the desired response C in the entire frequency domain toll .

[0164] Specifically, when N F When the number is odd, the construction length is N. F row vectors

[0165] C toll =[C Fhlf ,P dw C Zhlf ,]

[0166] When N F When the number is even, the construction length is N. F row vectors

[0167] C toll =[C Fhlf C Zhlf ,]

[0168] The above C toll This is the expected response in the entire frequency domain, and its k-th element is c. toll (k).

[0169] Step 7: The frequency domain equalization algorithm based on least squares uses the expected response of the entire frequency domain to solve for the optimal weights of the target correction filter, so as to obtain the expected correction filter spectrum and thus realize the design of the static correction filter for the mismatch system.

[0170] In this embodiment, step 7 specifically includes:

[0171] (7a) Determine the number of target weights L of the correction system wt L wt It is a positive integer, and its value must satisfy:

[0172] 1 <L wt <N F

[0173] (7b) Construct a weighted diagonal matrix:

[0174]

[0175] Among them, w bf1 ,w bf2 ,…, The weights are the weighted values.

[0176] (7c) The optimal weights of the target correction filter are solved using the least squares algorithm for frequency domain correction. The calculation formula is as follows:

[0177] W opt =(W bf A ws ) + C toll T

[0178] Where, matrix A ws Let be a constant matrix, which can be written as

[0179]

[0180] In the formula (·) + This indicates finding the pseudo-inverse of a matrix, (·). T This indicates finding the transpose of a matrix.

[0181] The frequency-domain weighted static correction filter design method for mismatched systems provided in this embodiment first accumulates the initial signal to be corrected and the reference signal over multiple cycles, enhancing their representation of the system's mismatch characteristics, suppressing the influence of noise, and eliminating some glitches in the difference spectrum introduced by specific signals. Then, the out-of-band difference spectrum is discarded, and the amplitude and phase curves of the in-band difference spectrum are processed and corrected to reduce the influence of signal specificity and noise on the trend of the difference curve, making the curve more representative of the overall system mismatch characteristics. Finally, the mismatch characteristic spectrum of the entire system is reconstructed using the corrected difference curve, thereby deriving the desired correction filter spectrum. Ultimately, this invention enables the system to maintain good correction performance in high-noise environments where some traditional methods fail, enhancing the stability of the static correction filter for system mismatch correction.

[0182] Example 2

[0183] The beneficial effects of the present invention will be verified and explained through simulation experiments below.

[0184] 1. Simulation conditions

[0185] In this simulation experiment, we assume a mismatched data acquisition device in reality. The accumulated data yields one set of signals, denoted as the first set of data. Two more sets of data are also acquired, denoted as the second and third sets. Using an oscilloscope to acquire the same signal source, the data is accumulated, and the result is denoted as the reference signal Y. sto The waveform is obtained by plotting the reference signal and the signal acquired by the target device on the same graph, as shown below. Figure 2 As shown.

[0186] 2. Simulation Content

[0187] A set of data is selected from the data acquired by the oscilloscope as a reference signal, and another set of data is selected from the data acquired by the acquisition device as the signal to be corrected. Frequency domain correction is performed using the original method. The desired and actual amplitude and phase frequency characteristics of the correction filter are obtained as follows: Figure 3 and Figure 4 As shown. Using this correction filter for signal correction, the corrected results for three sets of signals are obtained as follows. Figure 5 As shown.

[0188] With Y sto Using signal 1 as a reference signal and signal 1 as the signal to be corrected, frequency domain correction processing is performed using the method of this invention to obtain the desired and actual characteristics of the amplitude and phase frequencies of the correction filter, as shown below. Figure 6 and Figure 7 As shown. Using this correction filter for signal correction, the corrected results for three sets of signals are obtained as follows. Figure 8 As shown.

[0189] If the average relative error of the correction result is defined as:

[0190]

[0191] Where x res (n) where y is the corrected result. sto (n) is the reference signal after the oscilloscope data is accumulated.

[0192] Define the improvement in correction performance of this invention compared to the original method.

[0193]

[0194] Where e o e represents the average relative error of the correction results obtained using the original technique. n The average relative error is the result of the correction using the present invention.

[0195] The correction effects of the present invention and the original method are compared, and the results are shown in Table 1 below.

[0196] Table 1 Comparison of correction effects between the present invention and the original method.

[0197] The original method's average relative error The average relative error of this invention Improvement in effectiveness (%) 0.0362 0.0175 51.67 0.0579 0.0336 41.99 0.0590 0.0351 40.52

[0198] 3. Results Analysis

[0199] contrast Figure 5 and Figure 8 The filtering results show that the frequency domain correction curve obtained by sampling the present invention is closer to the reference signal, i.e., the effect is better. Table 1 shows that the present invention provides a greater improvement in signal correction performance.

[0200] The reason for the difference in the above results is that the expected spectrum of the correction filter obtained by the traditional method is significantly different from the mismatch characteristics of the system, while the expected spectrum of the correction filter obtained by the method of this invention is more suitable for the mismatch characteristics of the system, thus obtaining more universal weight coefficients and achieving better correction results.

[0201] As can be seen from the above embodiments, the present invention has the following advantages compared with the prior art:

[0202] First, it enhances the stability of the static correction filter for system mismatch correction. Traditional methods utilize information across the entire frequency band for weight calculation, inevitably introducing noise into the system, leading to instability. This invention accumulates the initial signal to be corrected and the reference signal to suppress noise. Then, it divides the spectrum into in-bandwidth and out-of-bandwidth parts, employing various methods to correct the in-bandwidth difference spectrum and suppress unstable spikes. This allows the spectrum to more accurately reflect the system's point mismatch characteristics. The corrected spectrum is then used to solve for the weights, ultimately enabling this invention to maintain good performance and improved stability even in high-noise environments where traditional methods fail.

[0203] Secondly, it improves the performance of static correction filters in correcting system mismatches. Traditional methods use information across the entire frequency band for weight calculation, failing to suppress noise or correct abrupt changes in the spectrum. This results in the spectrum not effectively reflecting the system's distortion characteristics. This invention suppresses noise and eliminates glitches in the spectrum introduced by specific signals, allowing the spectrum to more accurately reflect the system's point mismatch characteristics. By using the corrected spectrum to calculate the weights, the resulting filter significantly improves its performance in correcting mismatched systems.

[0204] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A mismatched system static correction filter design method based on frequency domain weighting, characterized in that, Comprise: Step 1: collect the analog signals of single-peak value to-be-corrected system output and reference signals respectively at the same sampling rate, and adjust the two groups of periodic data obtained in the time dimension, and correspondingly obtain two groups of adjusted data; (1a) using a collection system to sample the analog signal at a sampling rate collecting a periodic single peak analog signal of the system to be corrected to obtain a set of periodic data at the same sampling rate collecting a reference signal to obtain a set of periodic data wherein, , is the analog signal bandwidth; (1b) respectively index the first peak position of data and to obtain two sets of time dimension adjusted data and ; Step 2: according to the periodic law, the two groups of adjusted data are divided, and the two groups of data obtained are respectively accumulated, and correspondingly the to-be-corrected data and the reference data are obtained; (2a) take data of the first periods of data, divide the data by period to obtain a cluster of data ; at the same time, take data of the first periods of data, divide the data by period to obtain a cluster of data ; wherein is a positive integer and satisfies: is the total length of the periodic data and is the total length of the periodic data is the number of data points per period is a positive integer and , is a positive integer and ; (2b) accumulating data to obtain the data to be corrected ; and simultaneously accumulating data to obtain the reference data ; Step 3: the frequency spectrum of the to-be-corrected data and the reference data is solved respectively, and the difference frequency spectrum of the two is calculated; the effective frequency spectrum is obtained based on the difference frequency spectrum; (3a) set the number of frequency domain observation points to , and satisfy ; (3b) For the data to be corrected Do The spectrum of the point is used to obtain the spectrum of the data to be corrected. , its first Each element is represented as: wherein, represents the first element of the data to be corrected to be corrected , ; At the same time, the reference data is pointed spectrum to get the spectrum of the reference data , the first element is expressed as: wherein represents the i-th element of the reference data th element of the reference data​ (3c) a spectrum of said data to be corrected and a spectrum of said reference data computing a difference spectrum ; wherein said difference spectrum the formula for the first element is: (3d) determining an effective frequency range ; the effective frequency range must satisfy: (3e) based on the effective frequency range The number of points to be retained is solved, and the calculation formula is: wherein represents the rounding up of the numerical value; (3f) obtaining a difference spectrum based on the number of points obtained in step (3e) performing principal component filtering to obtain an effective spectrum whose first element is: · wherein ; Step 4: the amplitude and phase curves of the effective frequency spectrum are solved, and the two curves are respectively peak-eliminated to obtain the amplitude and phase curves after peak-elimination processing; (4a) based on the effective spectrum the amplitude-frequency curve is calculated and the phase curve ; wherein, The amplitude-frequency curve The first element of the set is represented as: The phase curve The first element is represented as: wherein is the angle function; (4b) set the window length as , the index parameter ; take the first points of the amplitude-frequency curve to construct a matrix , and the expression is: Take the phase curve The former Construct a matrix from points Its expression is: (4c) adjustment matrix the position of each element of the matrix whose elements satisfy: adjustment matrix the position of each element of the matrix each element of which satisfies: (4d) based on the matrix and the matrix are constructed respectively and ; (4e) Let If it is determined then update the matrices and according to the following equations and return to step (4c); Otherwise, jump to step (4f); (4f) based on a matrix constructing a matrix as the amplitude curve after de-peak processing; simultaneously based on a matrix constructing a matrix as the phase curve after de-peak processing; Step 5: the amplitude and phase curves after peak-elimination processing are respectively modified based on the least square method to obtain the modified amplitude and phase curves; (5a) setting the polynomial order , is a positive integer, and ; (5b) The amplitude curves after peak elimination were processed using the least squares method. and phase curve Polynomial fitting is performed to obtain the corresponding amplitude correction results. and phase correction results ; Step 6: the expected response of the whole frequency domain is reconstructed by using the modified amplitude and phase curves; (6a) the amplitude correction result and the phase correction result are reconstructed to obtain a desired response vector whose first element is expressed as: wherein, denotes the amplitude correction result the first element of the first element denotes the phase correction result the first element; (6b) construct a row vector of length whose all values are taken as constant , , is a real number and needs to satisfy where is the maximum value of the orientation vector; (6c) constructing a response vector based on the desired response vector and row vectors constructing a vector whose expression is wherein the vector has a first element of , ; (6d) Construct a length of row vectors , its first The value of the element is: wherein denotes taking the conjugate of a complex number; (6e) constructing an expected response for the entire frequency domain based on the row vectors and the vectors ;​ Step 7: the optimal weight value of the target correction filter is solved by using the expected response of the whole frequency domain based on the least square frequency domain equalization algorithm, so as to obtain the expected correction filter spectrum, thereby realizing the design of the mismatch system static correction filter; (7a) determining a number of target weight values of the correction system , is a positive integer whose value needs to satisfy: (7b) construct a weight diagonal matrix: wherein is a weighted weight; (7c) the optimal weight value of the target correction filter is solved by using the least square method of frequency domain correction, and the calculation formula is as follows: where the matrix is a constant matrix, which can be written as wherein denotes the pseudo inverse of a matrix, denotes the transpose of a matrix.

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