A method for generating a nonlinear frequency modulation signal based on a thinning algorithm

Abstract

This invention discloses a method for generating nonlinear frequency modulation (FM) signals based on a thinning algorithm, comprising the following steps: S1, designing a nonlinear frequency modulation function to obtain a discretized FM function curve; S2, constructing a piecewise linear frequency modulation function based on the Douglas-Pock thinning algorithm, such that the piecewise linear frequency modulation function approximates the ideal nonlinear FM function with a given approximation error; S3, calculating the pulse compression coefficient and frequency control word of the corresponding piecewise linear FM signal based on the approximation result of the nonlinear FM function, and compressing and storing the frequency control word data; S4, generating the piecewise linear FM signal based on DDS according to the frequency control word in the storage space. This invention employs the above-mentioned method for generating nonlinear FM signals based on a thinning algorithm to achieve a smaller approximation error in the FM curve and a better pulse compression effect.

Description

Technical Field

[0001] This invention relates to the field of electronic information technology, and in particular to a method for generating nonlinear frequency-modulated signals based on a thinning algorithm. Background Technology

[0002] The design and implementation of radar waveform signals have a significant impact on the performance indicators of radar systems. Nonlinear Frequency Modulation (NLFM) signals can achieve low sidelobes during matched filtering without windowing, thereby avoiding a decrease in the system's signal-to-noise ratio and improving target detection capabilities. There are generally two methods for generating NLFM waveforms: waveform storage and digital linear approximation. The former stores the NLFM signal waveform in non-volatile memory and then outputs the waveform signal through a digital-to-analog converter (DAC) chip according to the system timing. To ensure waveform quality, the DAC is usually performed at a high data rate, thus requiring a large amount of storage space and a high reference clock. The latter uses a piecewise linear curve to approximate the time-frequency curve of the NLFM signal, and then uses DDS technology to generate piecewise linear frequency modulation (LFM) signals to approximate the NLFM signal. The denser the segments, the higher the approximation of the time-frequency curve, but correspondingly, more storage space and a higher control word switching frequency are required.

[0003] In 2019, Fan Huanhuan et al. presented the design, hardware implementation, and verification process of nonlinear frequency modulation (FM) signals based on the window function inverse method. To simplify the design, reduce resources, and lower power consumption, a digital linear approximation method was used to generate the nonlinear FM signal. In 2021, Yang Yang et al. made two improvements to the traditional digital linear approximation method. First, to address the problem of increased approximation error when the FM function is non-monotonic, they proposed a piecewise approximation method for monotonic intervals. Second, to address the problem of low approximation accuracy in rapidly changing intervals of the FM function, they proposed a piecewise approximation method based on curvature. However, the proposed methods require calculating the first and second derivatives of the FM function, making them suitable for generating nonlinear FM signals designed using sine and tangent functions, but not directly applicable to nonlinear FM signals designed using other methods such as the window function inverse method.

[0004] Patent publication number 113504513A proposes a method for generating nonlinear frequency-modulated signals based on cosine modulation. First, a standard cosine function is sampled at 32 points, and the values ​​of the sampled sequence are fitted with a piecewise linear model. Second, the fitting result is represented as a binary sequence of step coefficients for the 32-bit sample points, and this binary sequence is used as an offset address to index the current frequency control word in a frequency control word lookup table. Finally, the corresponding nonlinear frequency-modulated signal is generated based on the frequency control word using DDS (Distributed Dynamics Module) technology. Essentially, this method still approximates the nonlinear frequency-modulated signal by uniformly sampling the modulation function.

[0005] In summary, existing digital linear approximation methods typically employ uniform segmentation when approximating frequency modulation (FM) curves. However, the linearity of an FM curve is not constant, and uniformly segmented piecewise linear curves cannot adapt to FM curves with constantly changing linearity. Using non-uniform segmentation can better approximate the time-frequency curve of a nonlinear FM signal. How to obtain a lower approximation error with less computational cost is a problem worthy of investigation in the generation of nonlinear FM signals. Summary of the Invention

[0006] The purpose of this invention is to provide a nonlinear frequency modulation signal generation method based on a thinning algorithm, which achieves nonlinear frequency modulation signal generation with smaller frequency modulation curve approximation error and better pulse compression effect.

[0007] To achieve the above objectives, this invention provides a method for generating nonlinear frequency-modulated signals based on a thinning algorithm, comprising the following steps:

[0008] S1. Design a nonlinear frequency modulation function to obtain the discretized frequency modulation function curve;

[0009] S2. Based on the Douglas-Puk thinning algorithm, construct a piecewise linear frequency modulation function so that the piecewise linear frequency modulation function approximates the ideal nonlinear frequency modulation function with a given approximation error.

[0010] S3. Based on the approximation result of the nonlinear frequency modulation function, calculate the pulse compression coefficient and frequency control word of the corresponding piecewise linear frequency modulation signal, and compress and store the frequency control word data.

[0011] S4. Based on the frequency control word in the storage space, generate a piecewise linear frequency modulation signal using DDS.

[0012] Preferably, step S1 specifically includes the following steps:

[0013] S11. Design the signal spectrum based on the frequency modulation bandwidth B and the frequency modulation time width T;

[0014] S12. Using the phase retention principle, calculate the nonlinear frequency modulation function f(t) based on the signal spectrum;

[0015] S13, Based on the sampling rate f s The discretized frequency modulation function curve f(t) is obtained. s ).

[0016] Preferably, step S2 specifically includes the following steps:

[0017] S21. Set the approximation error threshold D th Select the discretized frequency modulation curve f(t) sThe first and last two points are taken as sample points and added to the sample point set P. The two sample points are connected to construct the linear frequency modulation function f1(t).

[0018] S22. Select the discretized frequency modulation curve f(t) s Find the point on the graph that is furthest from the linear frequency modulation function f1(t), add it to the sample point set, connect the sample points, and construct a piecewise linear frequency modulation function f2(t) with two segments;

[0019] S23. Select each segment interval [t] s,i ,t s,i+1 ], i∈{1,…,N P The distance between the discretized frequency modulation curve and the piecewise linear frequency modulation function is the largest and exceeds the threshold D. th The points are added to the sample point set P, where N P Given the number of sample points in set P, connect adjacent sample points in the set to construct a piecewise linear frequency modulation function;

[0020] Repeat step S23 until the distance between each point on the frequency modulation curve and the piecewise linear frequency modulation function is less than the threshold, and output the piecewise linear frequency modulation function f′(t).

[0021] Preferably, step S3 specifically includes the following steps:

[0022] S31, According to the sampling frequency f s The piecewise linear frequency modulation function f′(t) is sampled, and the phase function of the piecewise linear frequency modulation signal is calculated by numerical integration to obtain the piecewise linear frequency modulation baseband signal. The conjugate of the piecewise linear frequency modulation baseband signal is then inverted to obtain the pulse compression coefficient corresponding to the piecewise linear frequency modulation function.

[0023] S32, Based on the digital / analog conversion rate f DAC The piecewise linear frequency modulation function f′(t) is sampled based on the carrier frequency f. c DDS module waveform lookup table address width M and kernel clock f DDS The output frequency of the piecewise linear frequency modulated signal at each moment is converted into a frequency control word with the same bit width of M.

[0024] S33. Utilizing the piecewise linearity of the approximate nonlinear frequency modulation function, the frequency control word within the piecewise linear interval, except for those passing through the endpoints, is omitted and replaced with the number of interval sampling points I. i i = 1, ..., N P -1, the space required to store frequency control word data is from Mbit × N·f DAC Compressed to M bits × 2N P -1;

[0025] S34. Store the compressed frequency control word in a non-volatile storage device.

[0026] Preferably, step S4 specifically includes the following steps:

[0027] S41. Read the compressed frequency control word from the storage device;

[0028] S42. Based on the starting frequency control word, the number of sampling points in the interval, and the cutoff frequency control word of each segmented linear interval, calculate the change step size of the frequency control word in the interval. Use the step size to accumulate the starting frequency control word to obtain the frequency control word corresponding to each sampling time in the segmented interval.

[0029] S43. Send the frequency control word into the phase accumulator, use the obtained frequency accumulation result as the address, and read the waveform amplitude value in the waveform memory.

[0030] Therefore, the present invention employs the aforementioned nonlinear frequency modulation signal generation method based on a thinning algorithm, and its technical effects are as follows:

[0031] (1) In the process of generating nonlinear frequency-modulated signals, this invention improves the performance of existing methods in terms of frequency modulation function approximation and pulse compression results by reasonably segmenting and approximating the frequency modulation curve of the nonlinear frequency-modulated signal. Since this invention directly processes the frequency modulation function curve, it has universal applicability to nonlinear frequency-modulated signals obtained by various design approaches such as sine / tangent modulation, window function inverse method, and frequency modulation function construction method.

[0032] (2) This invention utilizes existing thinning algorithms to segment the frequency modulation curve of a nonlinear frequency modulation signal, which can greatly reduce the number of segments while preserving the curve characteristics, thereby reducing the storage space required for waveform generation. In addition, thanks to the inherent characteristics of the Douglas-Peucker Algorithm (DPA algorithm), this invention can constrain the approximation error between the piecewise linear frequency modulation function and the ideal nonlinear frequency modulation function by setting a preset error threshold.

[0033] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0034] Figure 1 This is a flowchart of a nonlinear frequency modulation signal generation method based on a thinning algorithm according to the present invention.

[0035] Figure 2 This is a schematic diagram of the piecewise linear approximation of the nonlinear frequency modulation function curve based on DPA in a nonlinear frequency modulation signal generation method based on a thinning algorithm according to the present invention.

[0036] Figure 3 This is a schematic diagram of the storage space before and after compression of frequency control word data in a nonlinear frequency modulation signal generation method based on a thinning algorithm according to the present invention.

[0037] Figure 4 This is the piecewise linear approximation result of the nonlinear frequency modulation function curve based on DPA in the simulation of a nonlinear frequency modulation signal generation method based on the thinning algorithm of the present invention.

[0038] Figure 5 This is the spectrum of the nonlinear frequency modulated baseband signal in the simulation of a nonlinear frequency modulated signal generation method based on a thinning algorithm according to the present invention.

[0039] Figure 6 This is the pulse compression result of the nonlinear frequency modulation signal in the simulation of a nonlinear frequency modulation signal generation method based on the thinning algorithm of the present invention. Detailed Implementation

[0040] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0041] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0042] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0043] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can be appropriately combined to form other embodiments that can be understood by those skilled in the art. These other embodiments are also covered within the scope of protection of this invention.

[0044] It should also be understood that the specific embodiments described above are only used to explain the present invention, and the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

[0045] Techniques, methods, and apparatus known to those skilled in the art may not be discussed in detail, but where appropriate, they should be considered part of the specification.

[0046] All prior art documents cited in this specification are incorporated herein by reference in their entirety and are therefore part of the disclosure of this invention.

[0047] Example 1

[0048] A method for generating nonlinear frequency-modulated signals based on a thinning algorithm, the specific process of which is as follows: Figure 1 As shown, it includes the following steps:

[0049] (i) Design a nonlinear frequency modulation function to obtain the discretized frequency modulation function curve.

[0050] Taking the window function inverse method based on the phase dwell principle as an example, the Hamming window is chosen as the generating function W(x).

[0051] W(f) = 0.54 + 0.46cos(2πf / B)

[0052] In the formula, B is the frequency modulation bandwidth. Using the phase retention principle, the group delay of the signal can be obtained as follows:

[0053]

[0054] Wherein, constant K T = (T / B) / 0.54, substituting into the generating function yields...

[0055] T(f)=(T / B)f+(0.426T / π)sin(2πf / B)-B / 2≤f≤B / 2

[0056] In the formula, T represents the frequency modulation duration. Taking the numerical inverse of the above formula yields the frequency modulation function of the signal.

[0057] f(t) = T -1 (f)

[0058] According to the sampling frequency f s The discretized curve of the frequency modulation function is obtained.

[0059] f(t s )=f(n·T s -T / 2)n=1,…,N

[0060] Among them, T s =1 / f s The sampling period is N = T·f s This represents the number of sampling points.

[0061] (ii) Based on the Douglas-Puk thinning algorithm, a piecewise linear frequency modulation function f′(t) is constructed so that it approximates the ideal nonlinear frequency modulation function f(t) with a given approximation error.

[0062] 2.1 Setting the approximation error threshold D th Select the discretized frequency modulation function curve f(t) s The starting point P1 on ) = (t s,1 ,f(t s,1 )) and the termination point P N =(t s,N ,f(t s,N As sample points, add them to form the sample point set P = {P1, P2}. N Connect the sample points to construct the linear frequency modulation function f1(t);

[0063] 2.2 Selecting the Discretized Frequency Modulation Curve f(t) s The point P with the largest distance from the linear frequency modulation function f1(t) is... m Add it to the sample point set. Connect the sample points to construct a piecewise linear frequency modulation function f2(t) with two segments;

[0064] 2.3. Reference Figure 2 Select each segment interval [t] s,i ,t s,i+1 ], i∈{1,…,N P The distance between the discretized frequency modulation curve and the piecewise linear frequency modulation function is the largest and exceeds the threshold D. th The points are added to the sample point set P. Where N... P Let P be the number of sample points in set P. Connect adjacent sample points in the set to construct a piecewise linear frequency modulation function. Repeat this process until the distance between each point on the frequency modulation curve and the piecewise linear frequency modulation function is less than the threshold, and output the piecewise linear frequency modulation function f′(t).

[0065] (iii) Based on the approximate result f′(t) of the nonlinear frequency modulation function f(t), calculate the pulse compression coefficient and frequency control word of the corresponding piecewise linear frequency modulation signal, and compress the frequency control word data.

[0066] 3.1. Based on the sampling rate f s By sampling the piecewise linear frequency modulation function f′(t), we obtain

[0067] f′(t s )=f′(n·T s -T / 2)n=1,…,N

[0068] The discrete piecewise linear frequency modulation function f′(t) sSubstitute into the following formula and calculate the phase function using numerical integration.

[0069]

[0070] Therefore, the piecewise linear frequency modulated baseband signal is s(t) = exp(2πj·θ(t)). Taking the conjugate of this signal and inverting it yields the pulse compression coefficient s corresponding to the piecewise linear frequency modulated function. * (-t).

[0071] 3.2. Based on the digital-to-analog conversion data rate f DAC By sampling the piecewise linear frequency modulation function f′(t), we obtain

[0072] f′(t s ′)=f′(n / f DAC -T / 2)n=1,…,T·f DAC

[0073] The number of sampling points within each segment interval is denoted as I. i i = 1, ..., N p -1. Based on the carrier frequency f c The DDS module waveform lookup table address width M and the kernel system clock f DDS The frequency control word of the approximate nonlinear frequency-modulated signal to be generated is written as

[0074]

[0075] 3.3. Based on the frequency control word calculation results in step 3.2, the bit width of the storage space required to store FTW is M, and the depth is T·f. DAC Utilizing the piecewise linearity of the approximate nonlinear frequency modulation function, referencing Figure 3 The frequency control word within the piecewise linear interval, except for those passing through the endpoints, is omitted and replaced with the number of interval sampling points I. i i = 1, ..., N P -1. Therefore, the space required to store the frequency control word data is from M bit × N·f DAC Compressed to M bits × 2N P -1;

[0076] 3.4 Store the compressed frequency control word in a non-volatile storage device.

[0077] (iv) Based on the frequency control word in the storage space, generate a segmented linear frequency modulation signal using DDS.

[0078] The frequency control word read directly from the storage device is a compressed version, so it needs to be decompressed before use. First, based on the starting frequency control word, the number of sampling points in the interval, and the cutoff frequency control word for each segmented linear interval, calculate the step size of the frequency control word change within that interval using the following formula.

[0079] ΔFTW(i)=(FTW(i+1)-FTW(i)) / I i i = 1, ..., N P -1

[0080] Secondly, by accumulating the initial frequency control word using the step size, the frequency control word FTW corresponding to each sampling time n within the segmented interval can be obtained. n As shown in the following formula

[0081] FTW n =FTW(i)+(n-1)×ΔFTW(i),n=1,…,I i

[0082] Finally, the frequency control word is sent to the phase accumulator to obtain the accumulated frequency result. This result is then used as an address to read the waveform amplitude value from the waveform memory.

[0083] Test

[0084] 1. Simulation parameters:

[0085] Taking the design of a nonlinear frequency modulation signal using the Hamming window inverse method as an example, the simulation parameters are shown in Table 1.

[0086] Table 1 Simulation Parameters

[0087] parameter numerical values Time width 20us bandwidth 20MHz Sampling rate 40MHz Approximation error threshold 0.02 DDS kernel clock 240MHz Lookup table address width 32bit DAC sampling clock 240MHz

[0088] 2. Simulation content and result analysis:

[0089] Test 1

[0090] Under the simulation parameters in Table 1, the frequency modulation function of the nonlinear frequency-modulated signal is designed based on the window function inverse method. Using the technique of this invention, the designed ideal nonlinear frequency modulation function is approximated piecewise linearly, and the results are as follows. Figure 4 As shown.

[0091] Depend on Figure 4As can be seen, the hollow circles mark the endpoints of the segmented intervals based on DPA piecewise linear approximation, while the solid dots mark the endpoints of the segmented intervals based on uniform piecewise linear approximation. Both methods divide the ideal nonlinear frequency modulation function into 28 segments, but in regions with stronger nonlinearity, the piecewise linear approximation function obtained by the former is closer to the ideal frequency modulation function curve. Therefore, this invention effectively reduces the approximation error between the approximate nonlinear frequency modulation signal and the ideal nonlinear frequency modulation signal's frequency modulation function.

[0092] Test 2

[0093] Under the simulation parameters in Table 1, the piecewise linear approximation of the ideal nonlinear frequency modulation function is obtained using the technique of this invention. By calculating the phase function of the piecewise linear frequency modulation function through numerical integration, the spectrum of the approximate nonlinear frequency modulation baseband signal can be further obtained, as shown in the figure. Figure 5 As shown.

[0094] Depend on Figure 5 It can be seen that the spectrum of the nonlinear frequency modulated signal generated by the traditional method of uniform piecewise linear approximation is broadened to a certain extent; the spectrum of the nonlinear frequency modulated baseband signal obtained by the technology of this invention is closer to the ideal nonlinear frequency modulated signal.

[0095] Test 3

[0096] Under the simulation parameters in Table 1, the technology of this invention is used to simulate the output of the generated approximately nonlinear frequency-modulated signal through matched filtering. The results are as follows: Figure 6 As shown.

[0097] Solid lines represent the pulse compression result of an ideal nonlinear frequency modulated signal; dotted lines represent the pulse compression result of a nonlinear frequency modulated signal generated using the method of this patent.

[0098] The signal is divided into 28 segments. The dashed line represents the pulse compression result of the nonlinear frequency-modulated signal generated by the traditional digital approximation method using uniform segmentation, which also has 28 segments. Compared with the uniform segmentation method, this method has lower sidelobe height, a higher main-to-side lobe ratio, and a lower relative amplitude at the first zero point. Therefore, this invention can effectively improve the pulse compression result of the nonlinear frequency-modulated signal generated based on the digital linear approximation method.

[0099] Therefore, this invention employs a nonlinear frequency modulation (FM) signal generation method based on a thinning algorithm. In the process of generating the nonlinear FM signal, this invention improves the performance of existing methods in terms of FM function approximation and pulse compression results by reasonably segmenting and approximating the FM curve of the nonlinear FM signal. Since this invention directly processes the FM function curve, it is universally applicable to nonlinear FM signals obtained through various design approaches such as sine / tangent modulation, window function inverse calculation, and FM function construction. This invention utilizes existing thinning algorithms to segment the FM curve of the nonlinear FM signal, significantly reducing the number of segments while preserving curve characteristics, thereby reducing the storage space required for waveform generation. Furthermore, thanks to the inherent characteristics of the DPA algorithm, this invention can constrain the approximation error between the piecewise linear FM function and the ideal nonlinear FM function through a preset error threshold.

[0100] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for generating nonlinear frequency-modulated signals based on a thinning algorithm, characterized in that: Includes the following steps: S1. Design a nonlinear frequency modulation function to obtain the discretized frequency modulation function curve; S2. Based on the Douglas-Puk thinning algorithm, construct a piecewise linear frequency modulation function so that the piecewise linear frequency modulation function approximates the ideal nonlinear frequency modulation function with a given approximation error. S3. Based on the approximation result of the nonlinear frequency modulation function, calculate the pulse compression coefficient and frequency control word of the corresponding piecewise linear frequency modulation signal, and compress and store the frequency control word data. S4. Based on the frequency control word in the storage space, generate a piecewise linear frequency modulation signal using DDS; Step S2 specifically includes the following steps: S21. Set the approximation error threshold. Selecting Discrete Frequency Modulation Curve The first and last two points are used as sample points and added to the sample point set. In the middle, connect the two sample points to construct a linear frequency modulation function. ; S22. Select the discretized frequency modulation curve Above and linear frequency modulation function The point with the largest distance between two points is added to the sample point set. The sample points are then connected to construct a piecewise linear frequency modulation function for the two segments. ; S23. Select each segment interval The distance between the discretized frequency modulation curve and the piecewise linear frequency modulation function is the largest and exceeds the threshold. The points are added to the sample point set. In, among them, For set The number of sample points in the set is used to connect adjacent sample points in the set and construct a piecewise linear frequency modulation function. Repeat step S23 until the distance between each point on the frequency modulation curve and the piecewise linear frequency modulation function is less than the threshold, then output the piecewise linear frequency modulation function. ; Step S3 specifically includes the following steps: S31, Based on the sampling frequency Piecewise linear frequency modulation function Sampling is performed, and the phase function of the piecewise linear frequency modulated signal is calculated using numerical integration to obtain the piecewise linear frequency modulated baseband signal. The conjugate of the piecewise linear frequency modulated baseband signal is then inverted to obtain the pulse compression coefficient corresponding to the piecewise linear frequency modulated function. S32, Based on the digital / analog conversion rate Piecewise linear frequency modulation function Sampling is performed based on the carrier frequency. DDS module waveform lookup table address width and kernel clock The output frequency of the piecewise linear frequency modulated signal at each moment is converted into a bit width of the same value. Frequency control word; S33. Utilizing the piecewise linearity of the approximate nonlinear frequency modulation function, the frequency control word within the piecewise linear interval, except for those passing through the endpoints, is omitted and replaced with the number of interval sampling points. The space required to store frequency control word data is from Compress to ; S34. Store the compressed frequency control word in a non-volatile storage device.

2. The method for generating a nonlinear frequency-modulated signal based on a thinning algorithm according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11, based on the frequency modulation bandwidth Frequency modulation time width Design the signal spectrum; S12. Calculate the nonlinear frequency modulation function based on the signal spectrum using the phase retention principle. ; S13, Based on the sampling rate The discretized frequency modulation function curve is obtained. .

3. The method for generating a nonlinear frequency modulated signal based on a thinning algorithm according to claim 1, characterized in that: Step S4 Specifically, the following steps are included: S41. Read the compressed frequency control word from the storage device; S42. Based on the starting frequency control word, the number of sampling points in the interval, and the cutoff frequency control word of each segmented linear interval, calculate the change step size of the frequency control word in the interval. Use the step size to accumulate the starting frequency control word to obtain the frequency control word corresponding to each sampling time in the segmented interval. S43. Send the frequency control word into the phase accumulator, use the obtained frequency accumulation result as the address, and read the waveform amplitude value in the waveform memory.

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