TIADC time mismatch calculation method and system based on feed-forward structure

Abstract

The invention relates to the technical field of data processing, in particular to a TIADC time mismatch calculation method and system based on a feed-forward structure, and the method comprises the steps: calculating a first difference value between the output sequences of two adjacent sub-ADC channels in a TIADC in an actual condition and a second difference value between the output sequences of the two adjacent sub-ADC channels in an ideal condition; performing modulo operation on the first difference value and the second difference value to obtain a modulo function; processing the modulo function by adopting a moving average method to obtain a modulo function after moving average; and performing constant matrix operation according to the modulo function after moving average to obtain a time mismatch value. According to the calculation method, a derivative filter does not need to participate in operation in the calculation process, the increase of calculation resources is avoided, time mismatch calculation can be accurately carried out, the error convergence time can be effectively shortened by adopting a feedforward mode, frequency spectrum stray caused by time mismatch is weakened, and the accuracy of time mismatch calculation is improved. And the dynamic performance of the TIADC is improved while the calculation complexity is reduced.

Description

Technical Field

[0001] The present invention relates to a TIADC time mismatch calculation method and system based on a feedforward structure, belonging to the technical field of data processing. Background Art

[0002] With the development of high-speed data acquisition and processing technologies, a single ADC is difficult to meet the requirements of high-speed and high-precision sampling. To solve this problem, the time-interleaved analog-to-digital converter (TIADC) has become the best choice. The TIADC realizes a multiple-fold increase in the sampling rate by connecting multiple low-speed ADC modules in parallel. This architecture brings significant performance improvements to signal acquisition, enabling the TIADC to be implemented in many high-speed application scenarios. However, in a TIADC system, there are inconsistencies in the sampling clocks and analog front-ends between sub-ADCs, resulting in the following four main mismatches: offset mismatch, gain mismatch, time mismatch, and bandwidth mismatch. Among them, the time mismatch is the most difficult to calculate. The time mismatch, that is, the sampling clock offset, is caused by the small differences in the sampling times between sub-ADCs, especially having a significant impact in high-frequency signal processing. This error introduces frequency-related distortion in the output signal, greatly reducing the signal-to-noise ratio (SNR) and spurious-free dynamic range (SFDR) of the system.

[0003] The current frequency-domain-based time mismatch calculation methods require the frequency of the input signal to be known to extract the time mismatch information, and the FFT operation consumes more computing resources. The time-domain-based time mismatch calculation methods mostly adopt a feedback form and often require the participation of derivative filters, increasing the resource consumption and having the problem of too long error convergence time. Summary of the Invention

[0004] To solve the problem that the calculation of time mismatch in the prior art requires the participation of derivative filters, increases the resource consumption, and has too long an error convergence time, the present invention provides a TIADC time mismatch calculation method and system based on a feedforward structure.

[0005] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention includes a TIADC time mismatch calculation method based on a feedforward structure, and the method includes:

[0006] Calculating a first difference between the output sequences of two adjacent sub-ADC channels in a TIADC in an actual situation and a second difference between the output sequences in an ideal situation;

[0007] Performing a modulo operation on the first difference and the second difference to obtain a modulo function;

[0008] According to the output sequences of two adjacent sub-ADC channels in the actual situation and the output sequences in the ideal situation, the modulo function is processed by the moving average method to obtain the modulo function after moving average;

[0009] The time mismatch value is obtained by performing constant matrix operations according to the modulo function after moving average.

[0010] In some embodiments, calculating the first difference between the output sequences of two adjacent sub-ADC channels in the actual situation in the TIADC and the second difference between the output sequences in the ideal situation includes:

[0011] According to the formula: y m [k]≈x m [k]+δ m x′ m [k] to calculate the output sequence y of the sub-ADC channel in the actual situation m , then the first difference can be obtained as y m+1 -y m ;

[0012] where k is an integer and can take values... -1, 0, 1, 2..., x m is the output sequence of the sub-ADC channel in the ideal situation, δ m represents the time mismatch of the m-th sub-ADC channel, and x′ m is the derivative of the output sequence of the m-th channel sub-ADC;

[0013] The second difference of the output sequence of the sub-ADC channel in the ideal situation is x m+1 -x m .

[0014] In some embodiments, performing a modulo operation on the first difference and the second difference to obtain a modulo function includes:

[0015] According to the formula perform a modulo operation on the first difference and the second difference, and finally obtain the modulo function

[0016] where, T s is the sampling time interval when all channels of the TIADC are interleaved and the maximum sampling rate is reached.

[0017] In some embodiments, according to the output sequences of two adjacent sub-ADC channels in the actual situation and the output sequences in the ideal situation, processing the modulo function by the moving average method to obtain the modulo function after moving average includes:

[0018] According to the modulo function formula Using τ m Perform a moving average process on the modulo function to obtain the modulo function Γ after moving average m ≈1 + τ m+1 -τ m , 0 ≤ m ≤ M - 2;

[0019] where τ m is the normalized value of the timing deviation of the m-th channel relative to T s and M is the total number of sub-ADC channels of the TIADC.

[0020] In some embodiments, the obtaining the time mismatch value by performing a constant matrix operation according to the modulo function after moving average includes:

[0021] According to the formula: τ ≈ A T (AA T ) -1 (Γ - C) to calculate the time mismatch value τ;

[0022] where A is a constant matrix obtained by deleting the last row of matrix P, P is a constant matrix of MxM, C is a constant vector with all elements being 1, and Γ is a column vector containing the modulo function after moving average of all channels.

[0023] In a second aspect, a TIADC time mismatch calculation system based on a feedforward structure, the system includes:

[0024] A calculation unit, configured to calculate a first difference between output sequences of two adjacent sub-ADC channels in the TIADC under actual conditions and a second difference between output sequences under ideal conditions;

[0025] A modulo operation unit, configured to perform a modulo operation on the first difference and the second difference to obtain a modulo function;

[0026] A processing unit, configured to perform a moving average method on the modulo function according to the output sequences of the two adjacent sub-ADC channels under actual conditions and under ideal conditions to obtain a modulo function after moving average;

[0027] A matrix operation unit, configured to perform a constant matrix operation according to the modulo function after moving average to obtain a time mismatch value.

[0028] In some embodiments, the calculation unit is configured to calculate the output sequence y of the sub-ADC channel under actual conditions according to the formula: y m [k] ≈ x m [k] + δ m x′ m [k], then the first difference can be obtained as y m ​m+1 -y m ; The second difference of the output sequence of the sub-ADC channel under ideal conditions is x m+1 -x m ; where k is an integer and can take values... -1, 0, 1, 2..., x m is the output sequence of the sub-ADC channel under ideal conditions, and δ m represents the time mismatch of the m-th sub-ADC channel, and x′ m is the derivative of the output sequence of the m-th channel sub-ADC.

[0029] In some embodiments, the modulo operation unit is configured to perform a modulo operation on the first difference and the second difference according to the formula to finally obtain a modulo function where T s is the sampling time interval when all channels of the TIADC are interleaved and reach the maximum sampling rate.

[0030] In some embodiments, the processing unit is configured to perform a moving average process on the modulo function according to the modulo function formula using τ m to obtain a moving average of the modulo function Γ m ≈1 + τ m+1 -τ m , 0 ≤ m ≤ M - 2; where τ m is the normalized value of the timing deviation of the m-th channel with respect to T s and M is the total number of sub-ADC channels of the TIADC.

[0031] In some embodiments, the matrix operation unit is configured to calculate the time mismatch value τ according to the formula: τ ≈ A T (AA T ) -1 (Γ - C); where A is a constant matrix obtained by deleting the last row of matrix P, P is an MxM constant matrix, C is a constant vector with all elements equal to 1, and Γ is a column vector containing the moving average of the modulo function of all channels.

[0032] The beneficial effects of the present invention are:

[0033] 1. The TIADC time mismatch calculation method based on the feedforward structure of the present invention does not require a derivative filter to participate in the operation during the calculation process, avoiding an increase in computing resources.

[0034] 2. The time mismatch calculation method of TIADC based on the feedforward structure in the present invention can accurately calculate the time mismatch. Moreover, the feedforward method can effectively shorten the error convergence time, weaken the spectral spurs caused by time mismatch, reduce the computational complexity, and improve the dynamic performance of TIADC at the same time. Description of the Drawings

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on the provided drawings without creative efforts.

[0036] Figure 1 It is a schematic flowchart of a time mismatch calculation method of TIADC based on the feedforward structure provided by this application;

[0037] Figure 2 It is a schematic diagram of the main structure of the TIADC system provided by this application;

[0038] Figure 3 It is a timing diagram of the TIADC system provided by this application;

[0039] Figure 4 It is a schematic diagram of the spectrum comparison before and after TIADC calibration when a single-tone input signal is provided by this application;

[0040] Figure 5 It is a schematic diagram of the spectrum comparison before and after TIADC calibration when a multi-tone input signal is provided by this application;

[0041] Figure 6 It is a schematic diagram of the convergence speed of the time mismatch of the single-tone input signal and the multi-tone input signal provided by this application;

[0042] Figure 7 It is a schematic diagram of the structure of a time mismatch calculation system of TIADC based on the feedforward structure provided by this application;

[0043] Figure 8 Schematic diagram of the feedforward structure corresponding to the time mismatch calculation method of TIADC based on the feedforward structure. Detailed Embodiments Detailed Embodiment 1:

[0045] Combined with Figure 1 To illustrate this embodiment, this embodiment provides a time mismatch calculation method of TIADC based on the feedforward structure. The method includes:

[0046] S101. Calculate the first difference between the output sequences of two adjacent sub-ADC channels in the TIADC under actual conditions and the second difference between the output sequences under ideal conditions;

[0047] S102. Perform a modulo operation on the first difference and the second difference to obtain a modulo function;

[0048] S103. Process the modulo function using a moving average method based on the output sequences of the two adjacent sub-ADC channels in the TIADC under actual conditions and under ideal conditions to obtain a modulo function after moving average;

[0049] S104. Obtain a time mismatch value through a constant matrix operation based on the modulo function after moving average.

[0050] It should be noted that, as Figure 2 shown, it is a schematic diagram of the main structure of the TIADC system. As Figure 3 shown, it is a timing diagram of the TIADC system. The TIADC usually consists of several sub-ADCs, and the operating frequency of each sub-ADC is lower than the overall sampling rate required by the system. Through the method of clock interleaving, each sub-ADC samples the input signal at different times, thus forming an alternating sampling signal sequence.

[0051] A method for calculating the time mismatch of TIADC based on a feed-forward structure proposed by the present invention is used to estimate the time mismatch of the TIADC system. In the process of estimating the time mismatch of this method, a derivative filter is not required to participate in the operation, it can support the input of any signal, and the feed-forward method can effectively shorten the time for error convergence, reduce the calculation complexity while improving the dynamic performance of the TIADC.

[0052] It should be further noted that the estimation method proposed by the present invention is only applicable to the first Nyquist region, and the input signal needs to meet the condition of a wide-sense stationary (WSS) signal.

[0053] In some embodiments, the calculating the first difference between the output sequences of two adjacent sub-ADC channels in the TIADC under actual conditions and the second difference between the output sequences under ideal conditions includes:

[0054] According to the formula: y m [k]≈x m [k]+δ m x′ m [k] to calculate the output sequence y of the sub-ADC channel under actual conditions m , then the first difference can be obtained as y m+1 -y m ;

[0055] where k is an integer and can take values... -1, 0, 1, 2..., x m is the output sequence of the sub-ADC channel under ideal conditions, and δ m represents the time mismatch of the m-th sub-ADC channel, and x' m is the derivative of the output sequence of the m-th channel sub-ADC;

[0056] The second difference of the output sequence of the sub-ADC channel under ideal conditions is x m+1 -x m .

[0057] It should be noted that specifically, to simplify the calculation, it is assumed that there is no offset mismatch and gain mismatch in the input signal, the input signal is x(t), and δ i represents the time mismatch of the i-th channel. Ignoring the influence of quantization error, for the TIADC with M channels, 0 ≤ m ≤ M - 1, the output sequence of the m-th channel can be expressed as:

[0058]

[0059] where k is an integer and can take values... -1, 0, 1, 2..., represents the initial phase, and T s is the sampling time interval when all channels of the TIADC are interleaved and the maximum sampling rate is reached.

[0060] Generally speaking, the proportion of the timing deviation relative to the sampling period is very small. The output of the sub-ADC can be approximately estimated using the Taylor series. Then, the output sequence of the sub-ADC of the m-th channel can be expressed as the ideal output plus an error term:

[0061] y m [k] ≈ x m [k] + δ m x' m [k] (2)

[0062] where x' m is the derivative of the output sequence of the m-th channel sub-ADC.

[0063] In some embodiments, the modulo operation on the first difference and the second difference to obtain a modulo function includes:

[0064] According to the formula perform a modulo operation on the first difference and the second difference, and finally obtain the modulo function

[0065] where T sIt is the sampling time interval when all channels of TIADC are interleaved and reach the maximum sampling rate.

[0066] It should be noted that specifically, in order to estimate the timing deviation, the difference between adjacent channels becomes the target object for extracting errors. In actual situations, the modulo function composed of the ratio of the difference between adjacent channels to the difference between adjacent channels in the ideal situation has a linear relationship with the timing error. This modulo function Γ m can be expressed as:

[0067]

[0068] The output sequences of adjacent channels can also be approximated by the first-order Taylor series:

[0069] x m+1 ≈x m +T s x′ m (4)

[0070] For the sequences output by any sub-ADC, the expectations of their derivatives are the same. Then, formula (3) can be further simplified as:

[0071]

[0072] In some embodiments, according to the output sequences of the adjacent two sub-ADC channels in actual situations and in ideal situations, the modulo function is processed by the moving average method to obtain the modulo function after moving average, including:

[0073] According to the modulo function formula Use τ m to perform moving average processing on the modulo function to obtain the modulo function Γ after moving average m ≈1+τ m+1 -τ m ,0≤m≤M - 2;

[0074] where τ m is the normalized value of the timing deviation of the m-th channel relative to T s and M is the total number of sub-ADC channels of TIADC.

[0075] It should be noted that specifically, replacing τ m then Γ can be further simplified as: m Γ

[0076] Γ m ≈1+τ m+1 -τ m ,0≤m≤M - 2 (6)

[0077] Thus, the modulo function after moving average is obtained.

[0078] In some embodiments, performing constant matrix operation according to the modulo function after moving average to obtain a time mismatch value includes:

[0079] According to the formula: τ≈A T (AA T ) -1 (Γ - C) to calculate the time mismatch value τ;

[0080] where A is a constant matrix obtained by deleting the last row of matrix P, P is an MxM constant matrix, C is a constant vector with all elements being 1, and Γ is a column vector containing the modulo function after moving average of all channels.

[0081] It should be noted that specifically, it can be seen from formula (6) that formula (6) is a linear equation related to the timing deviation. Expanding it to the outputs of all sub - ADCs and adding a Γ M-1 function, we can get:

[0082]

[0083] The system of linear equations can be expressed in the form of the following matrix:

[0084] Γ≈C + Pτ (8)

[0085] where Γ is a column vector containing the timing error functions of all channels, C is a constant vector with all elements being 1, τ is a column vector containing the timing deviations of all sub - ADCs, and P is an M×M constant matrix. They are respectively expressed as:

[0086] τ=[τ0,τ1,…,τ M-1 T (9)

[0087]

[0088] Summing all the equations in the system of linear equations, the result is:

[0089] Γ0 + Γ1 + L + Γ M-1 =M (11)

[0090] It can be seen that the summation result is independent of the timing deviation. Ideally, the difference between adjacent channels is a constant. Combining with formula (3), the sum of the equations can also be expressed as:

[0091]

[0092] Combining formula (4) and (12), formula (11) can be further rewritten as:

[0093]

[0094] Ideally, the expectation of the difference between adjacent channels can be obtained by formula (13). The rank of matrix P is M - 1, and we can simplify formula (8) to:

[0095] Aτ≈Γ - C (14)

[0096] Where:

[0097] Γ=[Γ0,Γ1,…Γ M-2 T (15)

[0098]

[0099] Matrix A is obtained by deleting the last row of matrix P. It is a matrix with full row rank. To calculate the value of the timing deviation, the pseudo-inverse matrix of A needs to be introduced The solution of the linear equation system (14) can be expressed as:

[0100] τ≈A T (AA T ) -1 (Γ - C) (18)

[0101] The timing deviation τ, that is, the time mismatch value, can be obtained through this equation.

[0102] Working principle:

[0103] 1. The present invention provides a method for calculating the time mismatch of TIADC based on a feedforward structure. As can be seen from the above specific description of the whole method, in the whole calculation process of obtaining the time mismatch value, no derivative filter is required to participate in the operation, avoiding the technical problem of the increase in computing resources caused by the participation of the derivative filter in the operation in the prior art.

[0104] 2. The method for calculating the time mismatch of TIADC based on the feedforward structure of the present invention can accurately calculate the time mismatch. Moreover, by adopting the method of obtaining and calculating the first difference between the output sequences of adjacent two sub-ADC channels in the TIADC in the actual situation and the second difference between the output sequences in the ideal situation for feedforward, the time for error convergence can be effectively shortened, the spectral spurs caused by time mismatch can be weakened, and the dynamic performance of TIADC can be improved while reducing the computational complexity.

[0105] To verify the method for calculating the time mismatch of TIADC based on the feedforward structure proposed by the present invention, specific experimental examples are used for illustration and verification. Specifically, a 4-channel TIADC acquisition system is used as the experimental platform. As Figure 4 ​As shown, it is a schematic diagram of the spectrum comparison before and after TIADC calibration when a single-tone signal is input. As Figure 5 shown, it is a schematic diagram of the spectrum comparison before and after TIADC calibration when a multi-tone signal is input. From Figure 4 and 5 , it can be clearly seen that after calibration, the spurious amplitude caused by time mismatch is significantly reduced. The SFDR is increased by 32 dB and the SNDR is increased by 6 dB after calibration. As Figure 6 shown, it is a schematic diagram of the convergence speed of the time mismatch of a single-tone input signal and a multi-tone input signal. From Figure 6 , it can be seen that the estimated values of the time mismatch of the two input signals have reached convergence at 2000 sampling points.

[0106] Through the above experiments, it can be proved that the TIADC time mismatch calculation method based on the feedforward structure proposed by the present invention can accurately perform time mismatch estimation calculation, and combined with the compensation method, it can effectively weaken the spectrum spurs caused by time mismatch and improve the dynamic performance of the TIADC system. Specific Embodiment 2:

[0108] Based on the TIADC time mismatch calculation method based on the feedforward structure disclosed in the above embodiments of the present invention, Figure 7 a TIADC time mismatch calculation system based on the feedforward structure applying the TIADC time mismatch calculation method based on the feedforward structure is specifically disclosed.

[0109] As Figure 7 shown, an embodiment of the present invention discloses a TIADC time mismatch calculation system based on the feedforward structure. The system includes:

[0110] A calculation unit 701, configured to calculate a first difference between output sequences of two adjacent sub-ADC channels in a TIADC under actual conditions and a second difference between output sequences under ideal conditions;

[0111] A modulo operation unit 702, configured to perform a modulo operation on the first difference and the second difference to obtain a modulo function;

[0112] A processing unit 703, configured to process the modulo function by using a moving average method according to the output sequences of the two adjacent sub-ADC channels under actual conditions and under ideal conditions to obtain a modulo function after moving average;

[0113] A matrix operation unit 704, configured to perform a constant matrix operation according to the modulo function after moving average to obtain a time mismatch value.

[0114] In some embodiments, the calculation unit 701 is configured to, according to the formula: y m [k]≈xm [k] + δ m x' m [k] calculates the output sequence y of the sub-ADC channel under actual conditions m , then the first difference can be obtained as y m+1 -y m ; the second difference of the output sequence of the sub-ADC channel under ideal conditions is x m+1 -x m ; where k is an integer and can take values... -1, 0, 1, 2..., x m is the output sequence of the sub-ADC channel under ideal conditions, δ m represents the time mismatch of the m-th sub-ADC channel, x' m is the derivative of the output sequence of the m-th channel sub-ADC.

[0115] In some embodiments, the modulo operation unit 702 is configured to perform a modulo operation on the first difference and the second difference according to the formula to finally obtain a modulo function where T s is the sampling time interval when all channels of the TIADC are interleaved and reach the maximum sampling rate.

[0116] In some embodiments, the processing unit 703 is configured to perform a moving average process on the modulo function according to the modulo function formula using τ m to obtain a moving average of the modulo function Γ m ≈ 1 + τ m+1 -τ m , 0 ≤ m ≤ M - 2; where τ m is the normalized value of the timing deviation of the m-th channel relative to T s , and M is the total number of sub-ADC channels of the TIADC.

[0117] In some embodiments, the matrix operation unit 704 is configured to calculate the time mismatch value τ according to the formula: τ ≈ A T (AA T ) -1 (Γ - C); where A is a constant matrix obtained by deleting the last row of matrix P, P is an MxM constant matrix, C is a constant vector with all elements being 1, and Γ is a column vector containing the moving average of the modulo function of all channels.

[0118] For the specific working processes of the calculation unit 701, modulo operation unit 702, processing unit 703, and matrix operation unit 704 in the TIADC time mismatch calculation system based on the feedforward structure disclosed in the embodiments of the present invention above, reference may be made to the corresponding content in the TIADC time mismatch calculation method based on the feedforward structure disclosed in the above embodiments of the present invention, and details will not be elaborated here. Specific Embodiment 3:

[0120] Based on the TIADC time mismatch calculation method based on the feedforward structure proposed by the present invention, the adopted feedforward structure is as Figure 8 shown. The difference between adjacent channels will first pass through an absolute value (ABS) module to obtain its absolute value. A modified moving average (MMA) module is used to dynamically update the average value of the input sequence. An average (AVG) module is used to calculate the expectation of the difference between adjacent channels in the ideal case. After obtaining the Γ values of each sub-ADC, the time mismatch value can be obtained through simple constant operations and matrix operations.

[0121] In summary, the present application provides a TIADC time mismatch calculation method and system based on a feedforward structure, including: calculating a first difference between the output sequences of two adjacent sub-ADC channels in a TIADC in an actual case and a second difference between the output sequences in an ideal case; performing a modulo operation on the first difference and the second difference to obtain a modulo function; processing the modulo function by using a moving average method according to the output sequences of the two adjacent sub-ADC channels in the actual case and the output sequences in the ideal case to obtain a modulo function after moving average; and performing a constant matrix operation according to the modulo function after moving average to obtain a time mismatch value.

[0122] The beneficial effects of the present invention are:

[0123] 1. In the TIADC time mismatch calculation method based on the feedforward structure of the present invention, a derivative filter is not required to participate in the operation during the calculation process, avoiding an increase in computing resources.

[0124] 2. The TIADC time mismatch calculation method based on the feedforward structure of the present invention can accurately perform time mismatch calculation, and the feedforward method can effectively shorten the error convergence time, weaken the spectral spurs caused by time mismatch, reduce the computational complexity, and improve the dynamic performance of the TIADC.

[0125] The above are only the preferred embodiments of the present invention, and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with the preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art, within the scope of the technical solution of the present invention, can make some changes or modifications to the above-disclosed technical content to obtain equivalent embodiments with equivalent changes. However, as long as it does not depart from the content of the technical solution of the present invention, and based on the technical essence of the present invention, any simple modification, equivalent replacement, and improvement made to the above embodiments within the spirit and principles of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for calculating the time mismatch of TIADC based on a feedforward structure, characterized in that The method includes: Calculating a first difference between output sequences of two adjacent sub-ADC channels in a TIADC under actual conditions and a second difference between output sequences under ideal conditions; Performing a modulo operation on the first difference and the second difference to obtain a modulo function; Processing the modulo function by using a moving average method according to the output sequences of the two adjacent sub-ADC channels under actual conditions and under ideal conditions to obtain a modulo function after moving average; Performing a constant matrix operation according to the modulo function after moving average to obtain a time mismatch value.

2. The method according to claim 1, wherein The calculating a first difference between output sequences of two adjacent sub-ADC channels in a TIADC under actual conditions and a second difference between output sequences under ideal conditions includes: According to the formula: y m [k] ≈ x m [k] + δ m x′ m [k] to calculate the output sequence y of the sub-ADC channel under actual conditions m , then the first difference can be obtained as y m+1 - y m ; where k is an integer, and x m is the output sequence of the sub-ADC channel under ideal conditions, and δ m represents the time mismatch of the m-th sub-ADC channel, and x' m is the derivative of the output sequence of the m-th channel sub-ADC; The second difference of the output sequence of the sub-ADC channel under ideal conditions is x m+1 -x m .

3. The method according to claim 1, wherein The performing a modulo operation on the first difference and the second difference to obtain a modulo function includes: According to the formula perform a modulo operation on the first difference and the second difference to finally obtain a modulo function Among them, T s is the sampling time interval when all channels of TIADC are interleaved and reach the maximum sampling rate.

4. The method according to claim 1, wherein The processing the modulo function by using a moving average method according to the output sequences of the two adjacent sub-ADC channels under actual conditions and under ideal conditions to obtain a modulo function after moving average includes: According to the modulo function formula Use τ m Perform a moving average process on the modulo function to obtain the modulo function Γ after moving average m ≈1 + τ m+1 -τ m , 0 ≤ m ≤ M - 2; where τ m is the normalized value of the timing deviation of the m-th channel with respect to T s , and M is the total number of sub-ADC channels of the TIADC.

5. The method according to claim 1, characterized in that, The performing a constant matrix operation according to the modulo function after moving average to obtain a time mismatch value includes: According to the formula: τ≈A T (AA T ) -1 (Γ - C), calculate the time mismatch value τ; Wherein, A is a constant matrix obtained by deleting the last row of matrix P, P is an MxM constant matrix, C is a constant vector with all elements being 1, and Γ is a column vector containing the modulo function after moving average of all channels.

6. A TIADC time mismatch calculation system based on a feed-forward structure, characterized in that The system includes: A calculation unit for calculating a first difference between output sequences of two adjacent sub-ADC channels in a TIADC under actual conditions and a second difference between output sequences under ideal conditions; A modulo operation unit for performing a modulo operation on the first difference and the second difference to obtain a modulo function; A processing unit for processing the modulo function by using a moving average method according to the output sequences of the two adjacent sub-ADC channels under actual conditions and under ideal conditions to obtain a modulo function after moving average; A matrix operation unit for performing a constant matrix operation according to the modulo function after moving average to obtain a time mismatch value.

7. The system according to claim 6, wherein The calculation unit is used to calculate according to the formula: m [k]≈x m [k]+δ m x′ m [k] Calculate the output sequence y of the sub-ADC channel in actual situation m , then the first difference is y m+1 -y m ; The second difference of the output sequence of the sub-ADC channel in the ideal case is x m+1 -x m ; where k is an integer, x m is the ideal output sequence of the sub-ADC channel, δ m represents the time mismatch of the mth sub-ADC channel, x′ m is the derivative of the sub-ADC output sequence of the mth channel.

8. The system according to claim 6, wherein The modulo operation unit is used to perform a modulo operation on the first difference and the second difference according to the formula to finally obtain a modulo function where T s is the sampling time interval when all channels of the TIADC are interleaved and the maximum sampling rate is reached.

9. The system according to claim 6, characterized in that The processing unit is configured to perform a sliding average processing on the modulo function according to the modulo function formula using τ m to obtain a sliding-averaged modulo function Γ m ≈1 + τ m+1 - τ m , 0 ≤ m ≤ M - 2; where τ m is the normalized value of the timing deviation of the m-th channel with respect to T s and M is the total number of sub-ADC channels of the TIADC.

10. The system according to claim 6, wherein, The matrix operation unit is used to calculate the time mismatch value τ according to the formula: τ≈A T (AA T ) -1 (Γ - C); where A is a constant matrix obtained by deleting the last row of matrix P, P is an MxM constant matrix, C is a constant vector with all elements being 1, and Γ is a column vector of the modulo function after taking the moving average of all channels.

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