A hybrid filter bank analog-to-digital converter based on allpass filter banks

Abstract

The application relates to a hybrid filter bank analog-to-digital converter based on an all-pass filter bank, which comprises an analog analysis filter bank, an all-pass filter bank, an analog-to-digital converter bank and a digital synthesis filter bank which are electrically connected in sequence, the analog analysis filter bank performs band division on an input signal and suppresses adjacent channel band overlap; the all-pass filter bank compensates for phase differences of channels so that the phase at the band boundary is zero; the analog-to-digital converter bank samples and holds analog signals of the channels and converts the analog signals into digital signals; and the digital synthesis filter bank synthesizes the digital signals of the channels converted by the analog-to-digital converter bank. By inserting the all-pass filter bank, the phase mismatch of the analog analysis filter bank is compensated for, the frequency response discontinuity of the digital synthesis filter bank is eliminated, and the spur-free dynamic range is improved, thereby solving the problem of the frequency response discontinuity of the synthesis filter in the hybrid filter bank analog-to-digital converter.

Description

Technical Field

[0001] This invention relates to the field of analog-to-digital converters, and in particular to a hybrid filter bank analog-to-digital converter based on an all-pass filter bank. Background Technology

[0002] Emerging communication technologies, such as cognitive radio and software-defined radio, have a strong demand for high-speed, high-resolution analog-to-digital converters (ADCs) to achieve wideband sampling. However, with current ADC manufacturing techniques, it is difficult to simultaneously produce a single ADC that is both high-speed and high-resolution. Frequency-interleaved ADCs (FIADCs), which segment the input signal in the frequency domain, have become a widely used architecture for ADCs in recent decades. Within the FIADC framework, a parallel sampling method called hybrid filter bank (HFB) has been developed to achieve a high overall sampling rate while maintaining high resolution by using multiple low-speed ADCs. The successful operation of HFB depends on proper synchronization between the analog analysis filter bank (AFB) and the digital synthesis filter bank (SFB), which are responsible for segmenting and reconstructing the input wideband spectrum, respectively.

[0003] In optimizing a hybrid filter bank (HFB), many studies suggest starting with an AFB using an easily implemented analog filter (such as a first- or second-order Butterworth filter) and then creating an SFB that matches the previously established AFB. The design process of an SFB can be roughly divided into the following steps: (1) calculating the frequency response of the ideal synthesized filter according to the perfect reconstruction (PR) equation; (2) approximating the frequency response of the ideal synthesized filter with a finite impulse response (FIR) filter.

[0004] In traditional designs, AFBs often employ analytical filters such as Butterworth filters, but these suffer from discontinuous frequency response in digital synthesized filters, specifically manifested as follows:

[0005] 1. The non-zero phase of the filter at the frequency band boundary (such as ±π / T) causes a jump in the frequency response of the synthesized filter, making it difficult to approximate the ideal characteristics with a short FIR filter;

[0006] 2. Existing oversampling techniques address discontinuity issues by adjusting the frequency band weights of the analysis filter, but this introduces ill-conditioned coefficient matrix, leading to increased reconstruction errors and requiring additional post-processing filtering correction.

[0007] Existing technological shortcomings:

[0008] 1. The discontinuity problem leads to high design complexity and large reconstruction error in the synthesis filter;

[0009] 2. Although oversampling and other solutions can alleviate the discontinuity problem, they require complex optimization or post-processing, which increases the design complexity of digital filters, increases system cost and power consumption, and introduces ill-conditioned matrices and leads to reconstruction errors. Summary of the Invention

[0010] The purpose of this invention is to overcome the shortcomings of the prior art and provide a hybrid filter bank analog-to-digital converter based on an all-pass filter bank, thereby solving the problem of discontinuous frequency response of the synthesized filter in the hybrid filter bank analog-to-digital converter.

[0011] The objective of this invention is achieved through the following technical solution:

[0012] A hybrid filter bank analog-to-digital converter (ADC) based on an all-pass filter bank includes an analog analysis filter bank, an all-pass filter bank, an analog-to-digital converter bank, and a digital synthesis filter bank connected in sequence.

[0013] The analog analysis filter bank performs frequency band segmentation on the input signal to suppress frequency band overlap between adjacent channels;

[0014] The all-pass filter bank compensates for the phase difference between each channel, so that the phase at the frequency band boundary is synchronized to zero;

[0015] The analog-to-digital converter group samples and holds the analog signals of each channel and converts them into digital signals;

[0016] The digital synthesis filter bank synthesizes the digital signals from each channel obtained by the analog-to-digital converter bank.

[0017] Furthermore, the hybrid filter bank analog-to-digital converter is a four-channel hybrid filter bank analog-to-digital converter.

[0018] Furthermore, the all-pass filter bank and the analog-to-digital converter bank are electrically connected by a frequency shifter between the all-pass filter and the analog-to-digital converter in the same channel.

[0019] Furthermore, the analog-to-digital converter group and the digital synthesis filter group are electrically connected to a frequency multiplier between the analog-to-digital converter and the digital synthesis filter in the same channel.

[0020] Furthermore, the analog analysis filter bank employs Butterworth filters.

[0021] Furthermore, the low-pass filter in the analog analysis filter bank is a 6th-order Butterworth filter;

[0022] The bandpass filter in the analog analysis filter bank is a 12th-order Butterworth filter.

[0023] Furthermore, the transfer functions of the all-pass filter bank in the four-channel hybrid filter bank analog-to-digital converter are as follows:

[0024] ;

[0025] In the formula, s is the transfer function factor.

[0026] Furthermore, the digital synthesis filter bank employs an FIR filter.

[0027] Furthermore, the digital synthesis filter bank is designed based on the weighted least squares method, and the coefficients are solved by matrix optimization to minimize reconstruction error and aliasing noise;

[0028] The optimization objective of the FIR filter is to satisfy the perfect reconstruction condition; the optimization objective function is:

[0029] ;

[0030] In the formula, a=1, d is the delay constant, j is the imaginary sign, Ω is the frequency, T is the sampling period, M is the number of channels, and p is the channel number ordinal.

[0031] Furthermore, the digital synthesis filter minimizes the aliasing error using the weighted least squares method, and the calculation formula is as follows:

[0032] ;

[0033] In the formula, These are frequency band weighting coefficients. Here is the system transfer function expression for the hybrid filter bank analog-to-digital converter. This is the objective function for optimizing the digital synthesis filter.

[0034] The beneficial effects of this invention are:

[0035] By inserting an all-pass filter bank, the phase mismatch of the analog analysis filter bank is compensated, the frequency response discontinuity of the digital synthesis filter bank is eliminated, and the spurious-free dynamic range (SFDR) is improved. This solves the problem of discontinuous frequency response of the synthesis filter in the hybrid filter bank analog-to-digital converter, and is suitable for high-resolution, wideband signal acquisition systems. Attached Figure Description

[0036] Figure 1 This is a diagram of a four-channel hybrid filter bank analog-to-digital converter architecture.

[0037] Figure 2 To simulate and analyze the amplitude-frequency response of the filter bank;

[0038] Figure 3The phase response comparison diagrams of the simulated filter bank are shown in (a) without APF; (b) with APF.

[0039] Figure 4 The above are comparison diagrams of the frequency response of digital synthesis filters: (a) no APF (with abrupt transitions); (b) with APF (continuous transitions).

[0040] Figure 5 The image shows a comparison of the reconstruction performance of the hybrid filter bank: (a) without APF (high distortion); (b) with APF (low distortion). Detailed Implementation

[0041] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0042] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0043] Example 1:

[0044] like Figures 1 to 5 As shown, a hybrid filter bank analog-to-digital converter (ADC) based on an all-pass filter bank is disclosed. The hybrid filter bank ADC includes an analog analysis filter bank, an all-pass filter bank, an ADC bank, and a digital synthesis filter bank connected in sequence.

[0045] The analog analysis filter bank performs frequency band segmentation on the input signal to suppress frequency band overlap between adjacent channels;

[0046] The all-pass filter bank compensates for the phase difference between each channel, so that the phase at the frequency band boundary is synchronized to zero;

[0047] The analog-to-digital converter group samples and holds the analog signals of each channel and converts them into digital signals;

[0048] The digital synthesis filter bank synthesizes the digital signals from each channel obtained by the analog-to-digital converter bank.

[0049] By inserting an all-pass filter bank, the phase mismatch of the analog analysis filter bank is compensated, the frequency response discontinuity of the digital synthesis filter bank is eliminated, and the spurious-free dynamic range (SFDR) is improved. This solves the problem of discontinuous frequency response of the synthesis filter in the hybrid filter bank analog-to-digital converter, and is suitable for high-resolution, wideband signal acquisition systems.

[0050] The digital synthesis filter bank is designed based on the weighted least squares method. The coefficients are solved by matrix optimization to minimize reconstruction error and aliasing noise.

[0051] The hybrid filter bank analog-to-digital converter is a four-channel hybrid filter bank analog-to-digital converter.

[0052] The all-pass filter bank and the analog-to-digital converter bank are electrically connected to a frequency shifter between the all-pass filter and the analog-to-digital converter in the same channel.

[0053] The analog-to-digital converter group and the digital synthesis filter group are electrically connected to a frequency multiplier between the analog-to-digital converter and the digital synthesis filter in the same channel.

[0054] I. About Analog Analysis Filter Bank (AFB):

[0055] The analog analysis filter bank uses Butterworth filters (such as 6th-order low-pass and 12th-order band-pass filters).

[0056] A Butterworth filter is used as the AFB to suppress the overlap of adjacent channel frequency bands and avoid passband ripple and non-constant group delay.

[0057] The transfer function expression of the Butterworth filter is:

[0058] ;

[0059] The low-pass filter (channel 0 in this embodiment) in the analog analysis filter bank is a 6th-order Butterworth filter;

[0060] In the transfer function of a 6th-order Butterworth filter, s = jΩ / Ω c j represents the imaginary number sign, Ω represents the frequency, and Ω c This is the cutoff frequency of the low-pass filter.

[0061] The bandpass filters in the analog analysis filter bank (channels 1 to 3 in this embodiment) are 12th-order Butterworth filters;

[0062] The transfer function factor s in the transfer function expression of a 12th-order Butterworth filter is:

[0063] ;

[0064] Among them, Ωm,2 Ω m,1 These are the upper and lower cutoff frequencies of the bandpass filter, respectively, and m is the number of channel sequences.

[0065] II. About the All-Pass Filter Bank (APF):

[0066] All-pass filter bank (APF): Inserted after the analog analysis filter bank (AFB), the phase difference of each channel is compensated by optimizing the APF parameters (such as 1st / 2nd order all-pass filter), so that the phase at the frequency band boundary (±π / T) is synchronized to zero;

[0067] The all-pass filter bank uses first-order or second-order all-pass filters.

[0068] The transfer functions of the all-pass filter bank in the four-channel hybrid filter bank analog-to-digital converter are as follows:

[0069] ;

[0070] In the formula, s is the transfer function factor.

[0071] After inserting the all-pass filter bank, the phase response of each channel is aligned to zero at the frequency band boundaries (±π / T), such as... Figure 3 As shown.

[0072] III. Regarding frequency shifters:

[0073] A frequency shifter translates the spectrum of an input signal along the frequency axis, thus shifting the signal frequency. It moves the signal frequency of the m-th channel to a specified upper and lower frequency limit Ω. m,1 Ω m,2 between.

[0074] IV. Regarding analog-to-digital converter groups:

[0075] Analog-to-digital converters (ADCs): After processing the analog signals from each channel's receiving port via AFB and APF, the signals are sampled and held, then converted into digital signals for further processing. Due to sampling frequency limitations, the sampling period of the ADC is four times the original signal period, T'=4T.

[0076] V. Regarding frequency multipliers:

[0077] Frequency multiplier (FM): Increases the original signal frequency by 4 times to offset the effect that the sampling period of the analog-to-digital converter group is 4 times the original signal period.

[0078] VI. Regarding digital synthesis filter banks (SFB):

[0079] The digital synthesis filter bank uses FIR filters.

[0080] Digital Synthesized Filter Bank (SFB): Based on the weighted least squares (WLS) method, FIR filters are designed and the coefficients are solved through matrix optimization to minimize reconstruction error and aliasing noise.

[0081] Design a digital synthesis filter bank (SFB) based on the weighted least squares method to minimize aliasing error and reconstruction distortion.

[0082] The digital synthesis filter is modeled as an Nth-order FIR filter, and its frequency response is:

[0083] ;

[0084] Among them, f m (n) represents the nth-order coefficient of the mth channel of the Nth-order FIR filter, and Ω represents the frequency. The system transfer function expression of the hybrid filter bank analog-to-digital converter is:

[0085] ;

[0086] Where M is the total number of channels, N is the total order of the FIR filter, T is the sampling period, p is the signal ordinal number, p=0 is the main signal, and p=1, 2...M-1 are the harmonic ordinal numbers. and Let be the transfer function of the m-th channel Butterworth filter and the all-pass filter. The sample-and-hold transfer function for each channel analog-to-digital converter. Let be the nth order coefficients of the m-th channel FIR filter.

[0087] Construct the transfer function matrix equation based on the system transfer function expression;

[0088] The optimization objective of the FIR filter is to satisfy the perfect reconstruction condition; the optimization objective function is:

[0089] ;

[0090] In the formula, a=1, d is the delay constant, j is the imaginary sign, Ω is the frequency, T is the sampling period, M is the number of channels, and p is the channel number ordinal.

[0091] Minimize aliasing error using weighted least squares:

[0092] ;

[0093] In the formula, These are frequency band weighting coefficients. Here is the system transfer function expression for the hybrid filter bank analog-to-digital converter. This is the objective function for optimizing the digital synthesis filter.

[0094] Solve for the coefficients using the MATLAB Optimization Toolbox.

[0095] The parameters of the all-pass filter bank are optimized using the least squares method, so that the frequency response of the digital synthesized filter is continuous at the frequency band boundaries.

[0096] The digital synthesis filters were designed for orders of 40, 60, 80, and 100. The spurious-free dynamic range (SFDR) increases with the filter order, and after inserting an all-pass filter bank, the SFDR increases from 20 dB to 60 dB at order 80 and from 42 dB to 94 dB at order 120.

[0097] This embodiment uses a four-channel hybrid filter bank ADC as its core, combining theoretical derivation, algorithm implementation, and engineering practice to construct a complete HFB ADC design system. The content covers the frequency domain segmentation principle of the analytical filter bank (AFB), the mathematical modeling of phase compensation for the all-pass filter bank (APF), the optimization algorithm improvement of the synthetic filter bank (SFB), and the key technical challenges in hardware implementation.

[0098] Figure 1 The diagram shows the AFB, APF, frequency multiplier, sample-and-hold, and SFB processes.

[0099] I. Analysis of the frequency domain segmentation and circuit implementation of the filter bank (AFB):

[0100] 1. Frequency band division strategy and order calculation:

[0101] Four-channel frequency band allocation ( Figure 2 (as shown)

[0102] Channel 0 (low pass): 0~π / 4, covers baseband signals;

[0103] Channel 1 (bandpass): π / 4~π / 2, corresponding to the first high frequency band;

[0104] Channel 2 (bandpass): π / 2~3π / 4, covering the mid-frequency region;

[0105] Channel 3 (bandpass): 3π / 4~π, corresponding to the highest frequency band.

[0106] Overlap suppression requirement: Adjacent channels attenuate by ≥20dB at the boundary frequency, calculated using the Butterworth filter order formula:

[0107] ;

[0108] Where Ap = 3dB (passband attenuation), As = 20dB (stopband attenuation), Ω s / Ω p=1.1 (the ratio of the boundary frequency to the cutoff frequency), the low-pass filter order n of channel 0 is calculated to be ≥5.8, so we take it as order 6; the band-pass filters of channels 1 to 3 need to suppress the upper and lower stopbands, so we take it as order 12 (twice the order of the low-pass filter).

[0109] 2. Frequency conversion of a bandpass filter:

[0110] A bandpass filter is obtained from a low-pass prototype (cutoff frequency Ωc) through a bilinear transform. The transform formula is as follows:

[0111] ;

[0112] Taking channel 1 as an example (Ω) m,1 =π / 4,Ω m,2 =π / 2), we calculate Ω0=0.354π≈1.11rad / s, BW=π / 4≈0.785rad / s, and substituting them, we get the transfer function of the 12th order bandpass filter.

[0113] 3. Analog circuit implementation:

[0114] A 6th-order low-pass filter: Utilizing a three-stage cascade of second-order Butterworth sections, with each component's parameters determined using a lookup table (e.g., first stage RC = 1 / Ω). c (When C=1μF, R=4kΩ).

[0115] 12th-order bandpass filter: It consists of six cascaded second-order bandpass sections, each of which adopts a multiple feedback (MFB) structure. The center frequency and bandwidth are controlled by adjusting the resistor and capacitor values.

[0116] II. Mathematical Modeling of Phase Compensation for All-Pass Filter Banks (APFs):

[0117] 1. Mathematical description of phase mismatch:

[0118] Let the phase response of the m-th channel of the analysis filter be Φ. m If (Ω) = -arg[Hm(jΩ)], then the ideal phase of the synthesized filter is a linear phase of -dΩ. Without an APF, the sum of the phases of each channel is:

[0119] ;

[0120] Where ΔΦ(Ω) is the phase mismatch error at the frequency band boundary Ω b ΔΦ(Ω) b If ) ≠ 0, it causes a jump in the frequency response of the synthesized filter.

[0121] 2. APF Phase Compensation Model:

[0122] After introducing the APF, the total phase response is:

[0123] ;

[0124] For the frequency band boundary Ω b ,Require:

[0125] ;

[0126] Since each channel is compensated independently, it simplifies to a single-channel constraint (assuming dΩ). b (This can be achieved through global latency compensation)

[0127] ; In the formula, Ω, the frequency band boundary b Phase compensation for the m-th channel.

[0128] 3. Simulation Verification: Phase Compensation Effect:

[0129] Comparison of phase compensation before and after for Channel 1 at Ω=π / 4:

[0130] Without APF: φ1(π / 4) = 0.48 rad, group delay = 25 cycles;

[0131] APF: φ1(π / 4)+φ ap,1 (π / 4) = 0.01 rad, group delay = 20.1 cycles (close to the target value);

[0132] The amplitude-frequency response of the all-pass filter is |Hap(jΩ)|=1±0.005dB, verifying its all-pass characteristics.

[0133] III. Design of Digital Synthesized Filter Bank (SFB):

[0134] 1. FIR filter specifications and structure:

[0135] Order selection: N=80, balancing hardware complexity and performance.

[0136] Design goals:

[0137] Distortion function Amplitude fluctuation <0.02dB, phase linearity error <0.1°.

[0138] aliasing functions Attenuation >60dB.

[0139] 2. Weighted Least Squares (WLS) Optimization Process:

[0140] Frequency sampling: 2000 frequency points are selected uniformly in the range of 0-2GHz.

[0141] Weight function settings:

[0142] ;

[0143] Matrix construction:

[0144] Constructing a matrix (4 channels × 80 levels), each element is In the formula For the m-th channel analog analysis filter bank AFB at frequency point The transfer function in the complex frequency domain at that point.

[0145] Ideal response vector , element is (Delayed by 20 sampling periods).

[0146] Solve the equation:

[0147] ;

[0148] Use MATLAB's lsqnonneg function to solve nonnegative constrained least squares problems.

[0149] 3. Further optimization of Sequential Quadratic Programming (SQP):

[0150] Objective function: Minimize the maximum aliasing error.

[0151] ;

[0152] Constraints:

[0153] Within the passband ;

[0154] -Absolute value of FIR coefficient (To prevent overflow).

[0155] Algorithm implementation:

[0156] Using MATLAB's `fmincon` function, with a maximum iteration count of 200, and the initial solution being the WLS result, the aliasing attenuation was improved to 65 dB after optimization.

[0157] IV. System Integration and Performance Testing:

[0158] 1. Hardware platform setup:

[0159] AFB and APF circuits: Employing a 0.18μm CMOS process, the AFB filter uses an OTA-C structure, and the APF is implemented using Gm-C. Channel 0 has an area of ​​0.12mm² and a power consumption of 25mW; channels 1-3 have an area of ​​0.18mm² and a power consumption of 35mW.

[0160] Sub-ADC and digital section: 4-channel 12-bit 250 MSPS SAR ADC, SNR=68dB.

[0161] An 80th-order FIR is implemented on an FPGA, and a symmetrical structure is used to reduce the number of multipliers to 40.

[0162] 2. Test Signals and Measurement Methods:

[0163] Input signal:

[0164] Single tone test: frequency sweep 0-2GHz, amplitude -1dBFS.

[0165] Multi-tone test: 5 equally spaced carriers (200MHz, 600MHz, 1100MHz, 1600MHz, 1900MHz).

[0166] Performance metrics:

[0167] SFDR: Calculates the ratio of maximum spurious component to signal power.

[0168] THD: Total power of the first 5 harmonics.

[0169] Reconstruction error: The mean square error (MSE) between the output and the ideal sampled signal.

[0170] 3. Test Results:

[0171] SFDR: Full frequency band under single-tone test ( Figure 5 (b) shows a 40 dB improvement over the scheme without APF insertion. Figure 5 (a) in the middle.

[0172] THD: Multi-tone test .

[0173] Reconstruction error: ,correspond .

[0174] ENOB (Effective Number of Bits) is a core metric for measuring the actual dynamic performance of an analog-to-digital converter (ADC) or digital oscilloscope.

[0175] Table 1 Test results of the effect of SFDR on FIR filter length

[0176]

[0177] This invention addresses the discontinuity in the frequency response of digital synthesized filters by inserting an all-pass filter bank after the analysis filter bank to compensate for phase mismatch. A Butterworth filter simplifies the analog design, and weighted least squares optimization of the synthesized filter coefficients further significantly improves the spurious-free dynamic range (SFDR). This invention eliminates the need for complex oversampling or post-processing, making it suitable for high-resolution, wideband signal acquisition systems. It offers advantages such as simple structure, high reconstruction accuracy, improved robustness, and enhanced flexibility.

[0178] Specifically:

[0179] 1. All-pass filter phase compensation: The phase mismatch of the analysis filter is eliminated by the APF, which solves the problem of discontinuity in the frequency response of the synthesized filter without the need for complex oversampling or post-processing;

[0180] 2. Weighted Least Squares Optimization: Digital FIR filter design based on matrix equations effectively suppresses aliasing noise and improves spurious-free dynamic range (SFDR).

[0181] 3. Low complexity implementation: By using Butterworth filters and low-order APF, the complexity of analog circuits is reduced. It is not sensitive to the tolerance of analog filters, is suitable for low-cost processes, and is applicable to integrated design.

[0182] 4. Enhanced flexibility: APF parameters can be dynamically adjusted to adapt to different frequency band divisions.

[0183] Compared with traditional oversampling techniques, it does not lead to an increase in reconstruction matrix error, does not require the high condition number matrix caused by oversampling, and reduces the computational load by more than 50%; it does not require an additional post-processing filtering correction system; and it has a significant improvement in spurious dynamic range (SFDR).

[0184] The embodiments described above are merely illustrative of specific implementations of the present invention, and while the descriptions are detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A hybrid filter bank analog-to-digital converter based on an all-pass filter bank, characterized in that: The hybrid filter bank analog-to-digital converter includes an analog analysis filter bank, an all-pass filter bank, an analog-to-digital converter bank, and a digital synthesis filter bank that are connected in sequence. The analog analysis filter bank performs frequency band segmentation on the input signal to suppress frequency band overlap between adjacent channels; The all-pass filter bank compensates for the phase difference between each channel, so that the phase at the frequency band boundary is synchronized to zero; The analog-to-digital converter group samples and holds the analog signals of each channel and converts them into digital signals; The digital synthesis filter bank synthesizes the digital signals from each channel obtained by the analog-to-digital converter bank; The hybrid filter bank analog-to-digital converter is a four-channel hybrid filter bank analog-to-digital converter; The transfer functions of the all-pass filter bank in the four-channel hybrid filter bank analog-to-digital converter are as follows: ； In the formula, s is the transfer function factor.

2. The hybrid filter bank analog-to-digital converter based on an all-pass filter bank according to claim 1, characterized in that: The all-pass filter bank and the analog-to-digital converter bank are electrically connected to a frequency shifter between the all-pass filter and the analog-to-digital converter in the same channel.

3. The hybrid filter bank analog-to-digital converter based on an all-pass filter bank according to claim 1, characterized in that: The analog-to-digital converter group and the digital synthesis filter group are electrically connected to a frequency multiplier between the analog-to-digital converter and the digital synthesis filter in the same channel.

4. The hybrid filter bank analog-to-digital converter based on an all-pass filter bank according to claim 1, characterized in that: The analog analysis filter bank uses Butterworth filters.

5. The hybrid filter bank analog-to-digital converter based on an all-pass filter bank according to claim 1, characterized in that: The low-pass filter in the analog analysis filter bank is a 6th-order Butterworth filter. The bandpass filter in the analog analysis filter bank is a 12th-order Butterworth filter.

6. The hybrid filter bank analog-to-digital converter based on an all-pass filter bank according to claim 1, characterized in that: The digital synthesis filter bank uses FIR filters.

7. The hybrid filter bank analog-to-digital converter based on an all-pass filter bank according to claim 6, characterized in that: The digital synthesis filter bank is designed based on the weighted least squares method, and the coefficients are solved by matrix optimization to minimize reconstruction error and aliasing noise. The optimization objective of the FIR filter is to satisfy the perfect reconstruction condition; the optimization objective function is: ； In the formula, a=1, d is the delay constant, j is the imaginary sign, Ω is the frequency, T is the sampling period, M is the number of channels, and p is the channel number ordinal.

8. The hybrid filter bank analog-to-digital converter based on an all-pass filter bank according to claim 7, characterized in that: The digital synthesis filter minimizes the aliasing error using the weighted least squares method, and the calculation formula is as follows: ； In the formula, These are frequency band weighting coefficients. Here is the system transfer function expression for the hybrid filter bank analog-to-digital converter. The objective function for optimizing the digital synthesis filter is denoted as .

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