Relative time delay estimation method for multi-DAC parallel signal generation technology

Abstract

This invention proposes a relative time delay estimation method for multi-DAC parallel signal generation technology, belonging to the field of digital signal processing technology. It addresses the technical problem of the influence of nonlinear phase on the estimation of relative time delay. The method includes the following steps: Step 1: Input a known full-band multi-tone sinusoidal signal into a digital frequency divider filter for frequency division; Step 2: Combine the frequency-divided signals to obtain the system's broadband output signal; Step 3: Acquire the broadband output signal using an oscilloscope to obtain the system's output time-domain data, and preprocess the broadband output time-domain data; Step 4: Perform phase-frequency response analysis on the preprocessed output time-domain data to obtain the system's full-band phase-frequency response, and output the unwrapped image of the time-domain data; Step 5: Use an improved RANSAC algorithm, combined with the system's full-band phase-frequency response, to fit the preprocessed output time-domain data, obtaining the fitted image and the relative time delay.

Description

Technical Field

[0001] This invention relates to a relative time delay estimation method for multi-DAC parallel signal generation technology, belonging to the field of digital signal processing technology. Background Technology

[0002] With the continuous advancement of modern electronic technology, various industries are increasingly demanding higher signal quality. Signal quality is inextricably linked to signal bandwidth, but the output bandwidth of any signal generator is limited by the DAC sampling rate. To improve the signal bandwidth of any generator, on the one hand, chip R&D engineers are developing DAC chips with higher sampling rates, but this is technically challenging and time-consuming. On the other hand, signal processing engineers are researching parallel DAC technology, distributing the sampling task of a single DAC to multiple DACs, allowing the signal to be decomposed and combined in the frequency domain to achieve higher bandwidth requirements.

[0003] Compared to single-DAC signal generation methods, parallel multi-DAC architectures require both digital domain signal band decomposition and analog domain signal band synthesis. Since digital signal processing in each sub-channel introduces varying degrees of time delay into each sub-signal, and differences in analog device circuitry also affect analog signal propagation time, signal separation occurs simultaneously, resulting in relative time delays between sub-signals during signal synthesis. While time delays can be obtained by analyzing the linear phase of the signal, the non-ideal characteristics of analog devices introduce non-linear phases, affecting the estimation of relative time delays. To address this issue, this invention proposes a relative time delay estimation method for multi-DAC parallel signal generation technology. Summary of the Invention

[0004] This invention addresses the technical problem of how the nonlinear phase of a signal affects the estimation of its relative time delay, and proposes a relative time delay estimation method for multi-DAC parallel signal generation technology.

[0005] The technical solution adopted by this invention to solve the above problems is as follows: This invention proposes a relative time delay estimation method for multi-DAC parallel signal generation technology, including:

[0006] Step 1: Input the known full-band multi-tone sine wave signal into a digital frequency divider filter for frequency division;

[0007] Step 2: Combine the signals obtained from frequency division to obtain the system's broadband output signal;

[0008] Step 3: Use an oscilloscope to acquire the broadband output signal to obtain the system's output time-domain data, and preprocess the broadband output time-domain data;

[0009] Step 4: Perform phase frequency response analysis on the preprocessed output time-domain data to obtain the full-band phase frequency response of the system, and output the unwound image of the time-domain data;

[0010] Step 5: Using the improved RANSAC algorithm, the preprocessed output time-domain data is fitted to the full-band phase frequency response of the system to obtain the fitted image and relative time delay.

[0011] Optionally, the digital frequency divider filter in step 1 includes a low-pass filter and a high-pass filter;

[0012] The known full-band multi-tone sinusoidal signal is used as the excitation signal of the system and input into the low-pass filter and high-pass filter to obtain the low-frequency signal and the high-frequency signal, respectively.

[0013] Optionally, the steps for acquiring the system's broadband output signal in step 2 include:

[0014] Step 2.1: Downsample the low-frequency signal, input the downsampled low-frequency signal into the sub-DAC to convert it into a low-frequency analog signal, and input the low-frequency analog signal into an analog low-pass filter to filter out redundant image signals to obtain the low-frequency sub-signal;

[0015] Step 2.2: Upconvert and downsample the high-frequency signal, input the downsampled high-frequency signal into the sub-DAC to convert it into a high-frequency analog baseband signal, input the high-frequency analog baseband signal and the RF signal source into the mixer, restore the high-frequency analog baseband signal to its original frequency position, and input the restored high-frequency analog baseband signal into the bandpass filter to obtain the high-frequency sub-signal;

[0016] Step 2.3: Input the low-frequency sub-signal and the high-frequency sub-signal into the synthesizer and combine them to obtain the broadband output signal of the system.

[0017] Optionally, a fast Fourier transform is performed on the output time-domain data, and the output time-domain data after the fast Fourier transform is unwrapped.

[0018] Optionally, step 4, which involves obtaining the full-band phase frequency response of the system, includes:

[0019] Step 4.1: Obtain the estimated time delay and initial phase of sub-channel m in the system, and calculate the linear phase frequency response estimation line of sub-channel m based on the estimated time delay and initial phase of sub-channel m;

[0020] Step 4.2: Obtain the slope of the linear phase frequency response estimation line of sub-channel m, and use the slope of the linear phase frequency response estimation line of sub-channel m as the time delay estimate of sub-channel m;

[0021] Step 4.3: Repeat steps 4.1-4.2 to calculate the estimated time delay for all sub-channels;

[0022] Step 4.4: Sum the time delay estimates of all sub-channels to obtain the full-band phase frequency response of the system;

[0023] The expression for the linear phase frequency response estimation line of sub-channel m is:

[0024]

[0025] In formula (1), For the estimated time delay of sub-channel m, For the estimated initial phase of sub-channel m, The linear phase frequency response of subchannel m is estimated as a straight line;

[0026] The formula for calculating the time delay estimate of sub-channel m is:

[0027]

[0028] In formula (2), t m Let m be the estimated time delay value for sub-channel m. Estimate the slope of the linear phase frequency response line for subchannel m;

[0029] The formula for calculating the full-band phase frequency response of the system is:

[0030]

[0031]

[0032] In formula (3), Let t be the phase frequency response of subchannel m. m δ is the time delay of sub-channel m. m Let δ′ be the initial phase of sub-channel m. m Let Ω1 be the nonlinear phase of sub-channel m, and let Ω1 be the passband cutoff frequency of sub-channel one. This is the left passband cutoff frequency of sub-channel two. This is the right passband cutoff frequency of sub-channel two;

[0033] The expression for the excitation signal is:

[0034]

[0035] In formula (4), Ω test N1 is the fundamental frequency of the excitation signal, and N2 is the number of frequencies contained in the excitation signal.

[0036] Optionally, step 5, which involves obtaining the fitted image and the relative time delay, includes:

[0037] Step 5.1: Calculate the output time-domain data in Ω = [Ω test 2Ω test , ..., N2Ω test The phase frequency at point θ is... tes t(Ω);

[0038] Step 5.2: Divide the output time-domain data into interior-point data and exterior-point data;

[0039] Step 5.3: Use the Gaussian distribution model to distribute the output of the interior and exterior data;

[0040] Step 5.4: Randomly select n test samples and calculate the parameter model s, where the test samples are data groups composed of "frequency and phase" in the n output time domain data;

[0041] Step 5.5: If the interior point data is less than the set threshold T, then the parameter model s is estimated incorrectly. Iterate through all output time-domain data and remove the phase θ of the nonlinear phase frequency response. tes t(Ω), and use the threshold condition d to re-evaluate the interior and exterior point data;

[0042] Step 5.6: Based on the in-point data and out-point data obtained from the threshold condition judgment, update the probability values ​​of all test samples using the probability formula to obtain the optimal model;

[0043] Step 5.7: Repeat steps 5.4-5.6 until the maximum number of iterations is reached, and output the relative time delay and the fitted image;

[0044] The expression for the threshold condition d is:

[0045]

[0046] In formula (5), d i Let d be the distance from the i-th data point to the model, d be the distance threshold, inlier be the inlier data point, and outliner be the outliner data point;

[0047] The expression for the linear approximation of the phase frequency response function is:

[0048]

[0049] The expression for the probability formula is:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] In formulas (7)-(11), Q is the consistent set containing all interior points and the correct model. Let n be the fitness of the current parameter model on the consistent set Q. inlier Let n be the number of interior points. outlier Let N be the number of interior points and N be the total number of samples.

[0056] The beneficial effects of this invention are:

[0057] 1. This invention only requires the collected time-domain waveform data, the acquisition frequency, and the spectral range of each sub-channel to obtain the relative time delay.

[0058] 2. This invention performs unwinding operation on the original phase frequency response and utilizes information from all frequency points, resulting in high reliability.

[0059] 3. Before the iteration begins, the present invention uses a Gaussian distribution model to make an initial probability estimate of the samples, and during the iteration process, it uses the probability values ​​updated by the probability formula to select the model fitting samples, which can accelerate the convergence speed of traditional RANSAC.

[0060] 4. This invention takes into account the influence of actual analog devices and random factors in the acquisition process, and considers the nonlinear phase effects they bring, thus having a certain degree of robustness. Attached Figure Description

[0061] Figure 1 A flowchart of the relative time delay estimation method for multi-DAC parallel signal generation technology provided by the present invention;

[0062] Figure 2 A flowchart illustrating the parallel generation of a wideband output signal using two DACs provided by this invention;

[0063] Figure 3 A schematic diagram of the improved RANSAC algorithm fitting model provided by this invention;

[0064] Figure 3 In the diagram, (a) is a schematic diagram of the fitting model formed by randomly selecting two sets of data, and (b) is a schematic diagram of the optimal fitting model after the iteration ends. Detailed Implementation

[0065] Combination Figure 1-3 This embodiment will be described as follows: Figure 1 As shown, the steps of the relative time delay estimation method for multi-DAC parallel signal generation technology described in this embodiment include:

[0066] S1: Input a known full-band multi-tone sinusoidal signal to the system under test;

[0067] S101: As Figure 2 As shown, a known multi-tone sinusoidal signal with a full frequency band is divided into two signals by a digital frequency divider filter: a low-frequency signal and a high-frequency signal.

[0068] S102: The low-frequency signal is converted into an analog signal by the sub-DAC, and then filtered out by the analog low-pass filter to obtain the low-frequency sub-signal;

[0069] S103: The high-frequency signal is digitally down-converted to baseband and filtered out by a digital low-pass filter to remove redundant images. It is then converted into an analog baseband signal by a sub-DAC. The high-frequency analog baseband signal is restored to its original frequency position after analog up-conversion. Then, redundant image signals are filtered out by an analog filter to obtain the high-frequency sub-signal.

[0070] S104: Use a synthesizer to combine the low-frequency sub-signals and the high-frequency sub-signals to obtain the system's broadband output signal.

[0071] S2: Use an oscilloscope or other data acquisition instrument to acquire the output time-domain data of the system under test;

[0072] S3: Preprocess the output time-domain data;

[0073] The preprocessing specifically includes fast Fourier transform and unwinding of the output time-domain data. This invention performs unwinding operation on the original phase frequency response and utilizes information from all frequency points, resulting in high reliability.

[0074] S4: Perform phase frequency response analysis on the preprocessed output time domain data to obtain the full-band phase frequency response of the system, and output the unwound image of the time domain data;

[0075] S401: Using the known full-band multi-tone sinusoidal signal as the excitation signal of the system under test, the linearity of the phase frequency response is determined by the linear phase frequency response error. The nonlinear phase frequency response error is irregular and has a small amplitude, so it does not affect the linearity of the phase frequency response. Therefore, the linear phase frequency response estimation line of sub-channel m is denoted as:

[0076]

[0077] In formula (1), For the estimated time delay of sub-channel m, For the estimated initial phase of sub-channel m, The linear phase frequency response of subchannel m is estimated as a straight line;

[0078] S402: Obtain the slope of the linear phase frequency response estimation line of sub-channel m, and use the slope of the linear phase frequency response estimation line of sub-channel m as the time delay estimate of sub-channel m;

[0079] The formula for calculating the time delay estimate of sub-channel m is:

[0080]

[0081] In formula (2), t m Let m be the estimated time delay value for sub-channel m. Estimate the slope of the linear phase frequency response line for subchannel m;

[0082] S403: The excitation signal is composed of multiple sine waves with consistent frequency steps. The spectrum of the excitation signal is expressed as follows:

[0083]

[0084] In formula (3), Ω test N1 is the fundamental frequency of the excitation signal, and N2 is the number of frequencies contained in the excitation signal.

[0085] S404: Summing up the time delay estimates of all sub-channels yields the full-band phase frequency response of the system;

[0086] The formula for calculating the full-band phase frequency response of the system is:

[0087]

[0088]

[0089] In formula (4), Let t be the phase frequency response of subchannel m. m δ is the time delay of sub-channel m. m Let δ be the initial phase of sub-channel m. m Let Ω1 be the nonlinear phase of sub-channel m, and let Ω1 be the passband cutoff frequency of sub-channel one. This is the left passband cutoff frequency of sub-channel two. This is the right passband cutoff frequency of sub-channel two;

[0090] S5: Using the improved RANSAC algorithm, the preprocessed output time-domain data is fitted by combining the full-band phase frequency response of the system to obtain the fitted image and relative time delay.

[0091] RANSAC is an iterative algorithm that uses observed data to estimate the parameters of a mathematical model. When processing the data, it divides data points into two categories: inliers and outliers. Inliers are data points that closely match the model and can be effectively described by it, while outliers are data points that significantly deviate from expectations, cannot be described by the model, are considered outliers, and do not contribute to the model's estimation.

[0092] S501: The calculated output time-domain data is obtained in Ω={Ω test 2Ω test , ..., N2Ω test The phase frequency at point θ is... test (Ω);

[0093] S502: Divide the output time-domain data into interior-point data and exterior-point data;

[0094] S503: Use the Gaussian distribution model to perform the initial distribution of interior and exterior point data;

[0095] S504: Randomly select n test samples and calculate the parameter model s, where the test samples are data sets consisting of "frequency and phase" from n output time-domain data, such as... Figure 3 As shown, by taking any two sets of data, a fitting model can be obtained, and then the number of interior points of the model can be calculated.

[0096] S505: If the interior point data is less than the set threshold T, then the parameter model s estimation is incorrect. Iterate through all output time-domain data and remove the phase θ of the nonlinear phase frequency response. test (Ω), and use the threshold condition d to re-evaluate the interior and exterior point data;

[0097] S506: Based on the inlier data and outlier data obtained from the threshold condition judgment, the probability values ​​of all test samples are updated in combination with the probability formula to obtain the optimal model. If the number of inliers in the redesigned model is greater than that in the original model, the model data is updated, and the relationship between the number of inliers and the number threshold T is judged. If it is greater than the number threshold T, the iteration is terminated.

[0098] S507: If the number of inliers in the optimal model exceeds the threshold T or the number of iterations reaches the pre-designed maximum number of iterations, exit the RANSAC algorithm, obtain the fitted image and relative time delay, and the final iteration result is as follows: Figure 3 As shown;

[0099] The expression for the threshold condition d is:

[0100]

[0101] In formula (5), d iLet d be the distance from the i-th data point to the model, d be the distance threshold, inlier be the inlier data point, and outliner be the outliner data point;

[0102] The expression for the linear approximation of the phase frequency response function is:

[0103]

[0104] The expression for the probability formula is:

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] In formulas (7)-(11), Q is the consistent set containing all interior points and the correct model. Let n be the fitness of the current parameter model on the consistent set Q. inlier Let n be the number of interior points. outlier Let N be the number of interior points and N be the total number of samples.

[0111] In summary, this invention only requires the acquired time-domain waveform data, acquisition frequency, and spectral range of each sub-channel to obtain the relative time delay. Before the iteration begins, a Gaussian distribution model is used to initially estimate the probability of the samples. During the iteration process, the probability values ​​updated by the probability formula are used to select the model fitting samples, which can accelerate the convergence speed of traditional RANSAC. Furthermore, this invention considers the influence of actual analog devices and random factors in the acquisition process, taking into account the nonlinear phase effects they bring, thus the method has a certain degree of robustness.

[0112] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A relative time delay estimation method for multi-DAC parallel signal generation technology, characterized in that, The steps of the relative time delay estimation method for multi-DAC parallel signal generation technology include: Step 1: Input the known full-band multi-tone sine wave signal into a digital frequency divider filter for frequency division; Step 2: Combine the signals obtained from frequency division to obtain the system's broadband output signal; Step 3: Use an oscilloscope to acquire the broadband output signal to obtain the system's output time-domain data, and preprocess the broadband output time-domain data; Step 4: Perform phase frequency response analysis on the preprocessed output time-domain data to obtain the full-band phase frequency response of the system, and output the unwound image of the time-domain data; Step 5: Using the improved RANSAC algorithm, the preprocessed output time-domain data is fitted to the full-band phase frequency response of the system to obtain the fitted image and relative time delay. Step 5, which involves obtaining the fitted image and relative time delay, includes: Step 5.1: Calculate the output time-domain data. The phase frequency at that point is ; Step 5.2: Divide the output time-domain data into interior-point data and exterior-point data; Step 5.3: Use the Gaussian distribution model to perform the initial distribution of interior and exterior data; Step 5.4: Random selection n For each test sample, a parameter model s is calculated, where the test sample is a data set consisting of "frequency and phase" from n output time-domain data. Step 5.5: If the interior point data is less than the set threshold T, then the parameter model s estimation is incorrect. Iterate through all output time-domain data and remove the phase of the nonlinear phase frequency response. And using threshold conditions d Reassess the interior and exterior point data; Step 5.6: Based on the in-point data and out-point data obtained from the threshold condition judgment, update the probability values ​​of all test samples using the probability formula to obtain the optimal model; Step 5.7: Repeat steps 5.4-5.6 until the maximum number of iterations is reached, and output the relative time delay and the fitted image; Threshold condition d The expression is: （5）； In formula (5), For the first i The distance from each data point to the model. As a distance threshold, inlier For interior point data, outliner For external point data; The expression for the linear approximation of the phase frequency response function is: （6）； The expression for the probability formula is: （7）； （8）； （9）； （10）； （11）； Formula (7)-Formula (11), Q This is a consistent set containing all interior points and the correct model. For the current parameter model, the consistent set Q Adaptability, Let be the number of interior points. Let be the number of interior points. N This represents the total number of samples.

2. The relative time delay estimation method for multi-DAC parallel signal generation technology according to claim 1, characterized in that, The digital frequency divider filter mentioned in step 1 includes a low-pass filter and a high-pass filter; The known full-band multi-tone sinusoidal signal is used as the excitation signal of the system and input into the low-pass filter and high-pass filter to obtain the low-frequency signal and the high-frequency signal, respectively.

3. The relative time delay estimation method for multi-DAC parallel signal generation technology according to claim 2, characterized in that, Step 2, the steps for acquiring the system's broadband output signal, include: Step 2.1: Downsample the low-frequency signal, input the downsampled low-frequency signal into the sub-DAC to convert it into a low-frequency analog signal, and input the low-frequency analog signal into an analog low-pass filter to filter out redundant image signals to obtain a low-frequency sub-signal; Step 2.2: Upconvert and downsample the high-frequency signal, input the downsampled high-frequency signal into the sub-DAC to convert it into a high-frequency analog baseband signal, input the high-frequency analog baseband signal and the radio frequency signal source into the mixer, restore the high-frequency analog baseband signal to its original frequency position, and input the high-frequency analog baseband signal after restoring its original frequency position into the bandpass filter to obtain the high-frequency sub-signal; Step 2.3: Input the low-frequency sub-signal and the high-frequency sub-signal into the synthesizer and combine them to obtain the broadband output signal of the system.

4. The relative time delay estimation method for multi-DAC parallel signal generation technology according to claim 1, characterized in that, Step 3, the preprocessing of the output time-domain data, specifically includes: The output time-domain data is subjected to a Fast Fourier Transform (FFT), and the output time-domain data after the FFT is unwrapped.

5. The relative time delay estimation method for multi-DAC parallel signal generation technology according to claim 1, characterized in that, Step 4, which involves obtaining the full-band phase frequency response of the system, includes the following steps: Step 4.1: Obtain sub-channels in the system m The estimated time delay and initial phase, based on sub-channels m The estimated time delay and initial phase are used to calculate the sub-channel. m The linear phase frequency response is estimated as a straight line; Step 4.2: Obtain sub-channels m The slope of the linear phase frequency response estimation line is used to sub-channels. m The slope of the linear phase frequency response estimation line is used as a sub-channel. m The estimated time delay; Step 4.3: Repeat steps 4.1-4.2 to calculate the estimated time delay for all sub-channels; Step 4.4: Sum the time delay estimates of all sub-channels to obtain the full-band phase frequency response of the system; Sub-channel m The expression for the linear phase frequency response estimation line is: （1）； In formula (1), For the estimated sub-channel m Time delay, For the estimated sub-channel m The initial phase, Sub-channel m The linear phase frequency response is estimated as a straight line; Sub-channel m The formula for calculating the time delay estimate is: （2）； In formula (2), Sub-channel m The estimated time delay, Sub-channel m The slope of the linear phase frequency response estimation line; The formula for calculating the full-band phase frequency response of the system is: （3）； In formula (3), Sub-channel m phase frequency response, Sub-channel m Time delay, Sub-channel m The initial phase, Sub-channel m Nonlinear phase, This is the passband cutoff frequency of sub-channel one. This is the left passband cutoff frequency of sub-channel two. This is the right passband cutoff frequency of sub-channel two; The expression for the excitation signal is: （4）； In formula (4), The fundamental frequency of the excitation signal, This represents the number of frequencies contained in the excitation signal.

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