Radar frequency source output waveform optimization method and device, medium and product
By sampling and stacking the periodic waveform data of the radar frequency source, frequency compensation and denoising processing are performed, the problem of low stability and accuracy of the radar frequency source is solved, and higher accuracy and stability are achieved.
Patent Information
- Application Number
- CN202411700948.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-26
- Publication Date
- 2025-03-07
AI Technical Summary
The existing radar frequency sources have low stability and accuracy due to the inherent error of clock frequency and component noise error, and there are periodic clock errors and non-periodic noise interference.
The periodic waveform data at multiple preset frequencies is obtained by high frequency sampling, the number of sample points is determined, and stacking is performed to determine the actual frequency. Then, frequency compensation and secondary stacking processing are performed, and a denoising algorithm is used to output radio waveforms with low periodic clock error and non-periodic noise interference.
It effectively reduces the periodic clock error and non-periodic noise interference of radar frequency sources, and improves the accuracy and stability of radar frequency sources.
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Figure CN119577337A_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the technical field of digital frequency synthesis, and in particular to a method, device, medium and product for optimizing the output waveform of a radar frequency source. Background Art
[0002] Digital frequency synthesis is a frequency synthesis technology based on digital signal processing. It stores the important information of the waveform in the integrated register of the chip according to a certain logic, uses the control signal to accurately read the corresponding waveform information in a logical order, and then passes through the internal integrated circuit structure, such as the digital-to-analog converter and the filter amplifier, so as to accurately synthesize the required signal. Its basic working principle: the frequency control word is input into the phase accumulator of the DDS chip. Under the action of the reference clock, the address counter will continue to accumulate and generate a phase accumulation value. Each phase accumulation value corresponds to the address in the phase amplitude converter, so the ROM table can be searched to obtain the sine wave value corresponding to the phase, and a digital sequence of the corresponding signal waveform can be generated. After being converted by the digital-to-analog converter DAC, the above digital sequence becomes an analog voltage waveform, and then a continuous true sine wave output is extracted and reconstructed through a low-pass filter. For example, the literature Xinghui W, YongjunC, Lian C, et al. Development of a high-voltage radio frequency power supply for quadrupole mass spectrometers with a wide dynamic measurement range [J]. Journal of Instrumentation, 2023, 18(12).
[0003] The frequency is controlled by the number of accumulator overflows instead of changing the accumulator step size. Therefore, the frequency generation does not cause the frequency offset caused by the truncation error in the phase due to the accumulation step size not being divisible by the accumulator length. For example, Guangyu L, Chenggen Q.Optical phase-truncation-based double-image encryption using equal modulus decomposition and random masks[J].Scientific Reports, 2024, 14(1):7155-7155.
[0004] Since the conversion characteristics of DAC are not ideal, there is a certain error between its output frequency and the driving clock frequency. In addition, during the digital-to-analog conversion process, the waveform data of each sample will be extended and the space of the two sampled waveform data will be filled, so that during the D / A conversion of the extreme sampling point, the output waveform length will be greater than the preset value. When input into the oscilloscope, the frequency is lower than the ideal frequency. For sine waves with poor linearity, the frequency error caused by this phenomenon is more obvious. For example, the literature Engineering-Circuits and Signal Processing; Recent Findings in Circuits and Signal Processing Described by Researchers from Iowa State University (An 8-bit Low-cost String Dac With Gradient Errors Suppression To Achieve 16-bit Linearity) [J]. Technology News Focus, 2020, 2168.
[0005] In addition, the noise interference caused by the disturbance of the circuit components themselves has an adverse effect on the stability of the waveform output.
[0006] To solve the above problems, starting from the hardware level is currently a commonly used method, such as improving the accuracy of the reference clock and the conversion rate and conversion accuracy of the DAC, such as the literature MingY, Shengnan Z, Fucheng Y, et al. Research on Calibrating Device of Daily Clock Time Difference Testers Based on DDS Cascade Technology[J]. Journal of Physics: Conference Series, 2021, 2029(1):;LiuS, Han C, Zhao X, et al. A 56Gb / s DAC-DSP-based transmitter with adaptive retiming clock optimization using inverse-PR-based PD achieving 8-UI convergetime in 28-nm CMOS[J]. Science China Information Sciences, 2024, 67(8): 189402-189402.
[0007] The solutions currently proposed focus on improving the performance accuracy of clocks and components, with little consideration given to software correction, compensation and optimization. Therefore, there is an urgent need to provide a software optimization method to reduce the frequency deviation and noise interference of the radar frequency source, aiming to solve the technical problem of low stability and accuracy of the radar frequency source caused by the inherent error of the clock frequency and the noise error of the components. Summary of the invention
[0008] The purpose of this application is to provide a method, device, medium and product for optimizing the output waveform of a radar frequency source, which can effectively reduce the periodic clock error and non-periodic noise interference of the radar frequency source and improve the accuracy and stability of the radar frequency source.
[0009] To achieve the above objectives, this application provides the following solutions:
[0010] In a first aspect, the present application provides a method for optimizing an output waveform of a radar frequency source, the method comprising:
[0011] Acquire periodic waveform data at multiple preset frequencies by high frequency sampling;
[0012] Determine the number of sampling points according to the periodic waveform data; the number of sampling points is the number of stacks;
[0013] Aligning the periodic waveform data at multiple preset frequencies with each preset stack in a sampling order, and performing stack processing;
[0014] Determine the actual frequency according to the phase shift relationship between the stack bottom data and the stacked data during stack processing; and compensate the actual frequency according to the preset frequency;
[0015] The frequency-compensated periodic waveform data is subjected to secondary stack processing; based on the data in each stack, a denoising algorithm is used to output a radio waveform with low periodic clock error and non-periodic noise interference.
[0016] Optionally, determining the number of sampling points according to the periodic waveform data specifically includes:
[0017] Using the formula Determine the number of sampling points;
[0018] Where N is the number of sampling points, F M is the highest frequency of the signal after anti-aliasing filtering, and Flim is the minimum frequency resolution.
[0019] Optionally, determining the actual frequency according to the phase shift relationship between the stack bottom data and the stacked data during the stack processing; and compensating the actual frequency according to the preset frequency specifically includes:
[0020] Using the formula Determine the error between the actual frequency and the preset frequency;
[0021] Where ΔF is the error between the actual frequency and the preset frequency, F is the preset frequency, T is the reaction time, and n is the number of times the inversion occurs in the stack under the given reaction time condition. It is the phase shift relationship between the data at the bottom of the stack and the data pushed into the stack, and the change in the same phase is taken as the positive direction.
[0022] Optionally, the frequency-compensated periodic waveform data is subjected to secondary stack processing; according to the data in each stack, a denoising algorithm is used to output a radio waveform with low periodic clock error and non-periodic noise interference, specifically including:
[0023] Using the formula Determine whether the data in a single stack meets the confidence condition, judge whether there is excessive noise interference, and use a denoising algorithm to denoise;
[0024] Among them, P represents the output data; M is the number of data in a single stack, a i is the data after noise reduction, b i The flag bit determines whether to process; n i The initial data in the stack.
[0025] Alternatively, using the formula Determine the data after noise reduction processing;
[0026] Using the formula Determine the flag bit to determine whether to perform processing;
[0027] Among them, z 0.9 is the confidence interval of the data, μ is the mean of the data, and σ is the variance of the data.
[0028] Optionally, the frequency-compensated periodic waveform data is subjected to secondary stack processing; according to the data in each stack, a denoising algorithm is used to output a radio waveform with low periodic clock error and non-periodic noise interference, specifically including:
[0029] Delete the frequency-compensated periodic waveform data that does not meet the confidence condition;
[0030] Perform normal distribution fitting on the periodic waveform data after data deletion to generate the corresponding digital matched filter;
[0031] According to the periodic waveform data after data deletion, a digital matched filter is used for denoising and output.
[0032] In a second aspect, the present application provides an output waveform optimization device for a radar frequency source, the output waveform optimization device for the radar frequency source comprising:
[0033] A periodic waveform data acquisition module, used for acquiring periodic waveform data at multiple preset frequencies by high-frequency sampling;
[0034] A stack number determination module is used to determine the number of sampling points according to the periodic waveform data; the number of sampling points is the number of stacks;
[0035] A stack processing module, used to align the periodic waveform data at multiple preset frequencies with each preset stack in a sampling order, and perform stack processing;
[0036] An error determination module is used to determine the actual frequency according to the phase shift relationship between the stack bottom data and the stacked data during the stack processing; and compensate the actual frequency according to the preset frequency;
[0037] The output waveform module is used to perform secondary stacking processing on the periodic waveform data after frequency compensation; according to the data in each stack, a denoising algorithm is used to output a radio waveform with low periodic clock error and non-periodic noise interference.
[0038] In a third aspect, the present application provides a computer device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the output waveform optimization method of the radar frequency source.
[0039] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the output waveform optimization method of the radar frequency source.
[0040] In a fifth aspect, the present application provides a computer program product, including a computer program, which, when executed by a processor, implements the output waveform optimization method of the radar frequency source.
[0041] According to the specific embodiments provided in this application, this application has the following technical effects:
[0042] The present application provides a method, device, medium and product for optimizing the output waveform of a radar frequency source, which determines the actual frequency according to the phase shift relationship between the stack bottom data and the stacked data during the stack processing; and compensates the actual frequency according to the preset frequency, and corrects and adjusts the frequency output accuracy of the radar frequency source according to the error, which is more flexible under the premise of ensuring high accuracy; performs secondary stack processing on the periodic waveform data after frequency compensation; and uses a denoising algorithm according to the data in each stack to output a radio waveform with low periodic clock error and non-periodic noise interference, thereby suppressing the frequency source error caused by random noise to a certain extent, and can make real-time adjustments with more noise, and has stronger robustness. The present application can solve the technical problem of low stability and accuracy of the radar frequency source caused by the inherent error of the clock frequency and the noise error of the components, and can effectively reduce the periodic clock error and non-periodic noise interference of the radar frequency source, and improve the accuracy and stability of the radar frequency source. BRIEF DESCRIPTION OF THE DRAWINGS
[0043] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.
[0044] Figure 1 This is a schematic flow chart of a method for optimizing an output waveform of a radar frequency source in one embodiment of the present application;
[0045] Figure 2 This is the spectrum diagram obtained from the actual sampling data;
[0046] Figure 3 This is the spectrum diagram obtained after period compensation;
[0047] Figure 4 This is the spectrum obtained after denoising algorithm processing. DETAILED DESCRIPTION
[0048] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.
[0049] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.
[0050] In an exemplary embodiment, Figure 1 As shown, a method for optimizing the output waveform of a radar frequency source is provided, and the method includes the following S101 to S105. Wherein:
[0051] S101, acquiring periodic waveform data at multiple preset frequencies by high frequency sampling;
[0052] S102, determining the number of sampling points according to the periodic waveform data; the number of sampling points is the number of stacks;
[0053] S102 specifically includes:
[0054] Using the formula Determine the number of sampling points;
[0055] Where N is the number of sampling points, that is, the number of stacks, F M is the highest frequency of the signal after anti-aliasing filtering, and Flim is the minimum frequency resolution.
[0056] S103, aligning the periodic waveform data at multiple preset frequencies with each preset stack in a sampling order, and performing stack processing;
[0057] S104, determining the actual frequency according to the phase shift relationship between the stack bottom data and the stacked data during the stack processing; and compensating the actual frequency according to the preset frequency;
[0058] S104 specifically includes:
[0059] Using the formula Determine the error between the actual frequency and the preset frequency;
[0060] Where ΔF is the error between the actual frequency and the preset frequency, F is the preset frequency, T is the reaction time, and n is the number of times the inversion occurs in the stack under the given reaction time condition. It is the phase shift relationship between the data at the bottom of the stack and the data pushed into the stack, and the change in the same phase is taken as the positive direction.
[0061] S105, performing secondary stacking processing on the frequency-compensated periodic waveform data; using a denoising algorithm based on the data in each stack, outputting a radio waveform with low periodic clock error and non-periodic noise interference.
[0062] S105 specifically includes:
[0063] Using the formula Determine whether the data in a single stack meets the confidence condition, judge whether there is excessive noise interference, and use a denoising algorithm to denoise;
[0064] Among them, P represents the output data; M is the number of data in a single stack, a i is the data after noise reduction, b i The flag bit determines whether to process; n i The initial data in the stack.
[0065] Using the formula Determine the data after noise reduction processing;
[0066] Using the formula Determine the flag bit to determine whether to perform processing;
[0067] Among them, z 0.9 is the confidence interval of the data, μ is the mean of the data, and σ is the variance of the data.
[0068] S105 specifically includes:
[0069] S51, deleting the frequency-compensated periodic waveform data that does not meet the confidence condition;
[0070] S52, performing normal distribution fitting on the periodic waveform data after the data is deleted to generate a corresponding digital matched filter;
[0071] S53, according to the periodic waveform data after the data is deleted, a digital matched filter is used to perform denoising and output.
[0072] Take the 100HZ sine wave produced by a pure hardware frequency source as an example, and set the minimum frequency resolution to 0.5HZ. According to the formula The sampling points required to obtain single-cycle data within the allowable frequency error range are calculated to be 512 points, and the sampling frequency is 51.2KHZ.
[0073] After the above waveform is sampled continuously for 1S at a frequency of 51.2KHZ, the spectrum of the sampled data is calculated by fast Fourier transform FFT, and the spectrum is shown as follows: Figure 2 As shown, according to the formula SNR = 20*log 10 (V s / V n ), and the signal-to-noise ratio is calculated to be about 10.6dB.
[0074] The waveform data obtained by sampling is aligned with each preset stack in the sampling order, and the corresponding data values are stacked in sequence. The number of times the waveform data in the first stack is inverted is obtained.
[0075] According to the formula The calculated deviation value ΔF between the actual frequency and the preset frequency is 1.5HZ. The frequency source is increased by 1.5HZ for frequency compensation. The spectrum obtained after period compensation is as follows: Figure 3 shown.
[0076] After completing the frequency compensation, resample, align with each preset stack in the sampling order, and push the corresponding data values into the stack in sequence. According to the formula Exclude the periodic waveform data that is too affected by noise and does not meet the confidence condition in the sampling point. After removing the excessive noise, the frequency source output is corrected in real time through a digital matched filter. The frequency compensated periodic waveform data is sampled continuously at a frequency of 51.2KHZ for 1S, and the spectrum of the sampling data is calculated by FFT. Figure 4 As shown, according to the formula SNR = 20*log 10 (V s / V n ), the signal-to-noise ratio is calculated to be about 6.4dB.
[0077] Based on the same inventive concept, the embodiment of the present application also provides a radar frequency source output waveform optimization device for implementing the above-mentioned radar frequency source output waveform optimization method. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the above-mentioned method, so the specific limitations in the embodiments of the output waveform optimization device of one or more radar frequency sources provided below can refer to the limitations of the radar frequency source output waveform optimization method above, and will not be repeated here.
[0078] In an exemplary embodiment, a device for optimizing an output waveform of a radar frequency source is provided, comprising:
[0079] A periodic waveform data acquisition module, used for acquiring periodic waveform data at multiple preset frequencies by high-frequency sampling;
[0080] A stack number determination module is used to determine the number of sampling points according to the periodic waveform data; the number of sampling points is the number of stacks;
[0081] The stack processing module is used to align the periodic waveform data under multiple preset frequencies with each preset stack in sampling order and perform stack processing; the length of the periodic sampling data is consistent, and the first sampling data of each periodic waveform data is placed in the first stack, the second sampling data is placed in the second stack, and so on.
[0082] The error determination module is used to determine the actual frequency according to the phase shift relationship between the bottom data and the stacked data during the stack processing; and compensate the actual frequency according to the preset frequency; the bottom data is the sampling data of the first cycle, and the stacked data is the sampling data of the current cycle. The phase shift relationship is determined based on the alignment of the two data, that is, the number of offset stacks.
[0083] The output waveform module is used to perform secondary stacking processing on the periodic waveform data after frequency compensation; according to the data in each stack, a denoising algorithm is used to output a radio waveform with low periodic clock error and non-periodic noise interference.
[0084] In an exemplary embodiment, a computer device is provided, which may be a server or a terminal. The computer device includes a processor, a memory, an input / output interface (I / O for short) and a communication interface. The processor, the memory and the input / output interface are connected via a system bus, and the communication interface is connected to the system bus via the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, an output waveform optimization method of a radar frequency source is implemented.
[0085] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.
[0086] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.
[0087] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.
[0088] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).
[0089] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.
[0090] In this application, all actions to obtain signals, information or data are carried out in compliance with the relevant data protection laws and policies of the country where they are located and with the authorization given by the owner of the corresponding device.
[0091] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0092] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.
Claims
1. A method for optimizing the output waveform of a radar frequency source, characterized in that: The output waveform optimization method of the radar frequency source comprises: Acquire periodic waveform data at multiple preset frequencies by high frequency sampling; Determine the number of sampling points according to the periodic waveform data; the number of sampling points is the number of stacks; Aligning the periodic waveform data at multiple preset frequencies with each preset stack in a sampling order, and performing stack processing; Determine the actual frequency according to the phase shift relationship between the stack bottom data and the stacked data during stack processing; and compensate the actual frequency according to the preset frequency; The frequency-compensated periodic waveform data is subjected to secondary stack processing; based on the data in each stack, a denoising algorithm is used to output a radio waveform with low periodic clock error and non-periodic noise interference.
2. The output waveform optimization method of the radar frequency source according to claim 1, characterized in that: Determining the number of sampling points according to the periodic waveform data specifically includes: Using the formula Determine the number of sampling points; Where N is the number of sampling points, F M is the highest frequency of the signal after anti-aliasing filtering, F lim is the minimum frequency resolution.
3. The output waveform optimization method of the radar frequency source according to claim 1, characterized in that: The method of determining the actual frequency according to the phase shift relationship between the stack bottom data and the stacked data during the stack processing; and compensating the actual frequency according to the preset frequency specifically includes: Using the formula Determine the error between the actual frequency and the preset frequency; Where ΔF is the error between the actual frequency and the preset frequency, F is the preset frequency, T is the reaction time, and n is the number of times the inversion occurs in the stack under the given reaction time condition. It is the phase shift relationship between the data at the bottom of the stack and the data pushed into the stack, and the change in the same phase is taken as the positive direction.
4. The output waveform optimization method of the radar frequency source according to claim 1, characterized in that: Perform secondary stacking processing on the frequency-compensated periodic waveform data; Based on the data in each stack, a denoising algorithm is used to output a radio waveform with low periodic clock error and non-periodic noise interference, including: Using the formula Determine whether the data in a single stack meets the confidence condition, judge whether there is excessive noise interference, and use a denoising algorithm to denoise; Among them, P represents the output data; M is the number of data in a single stack, a i is the data after noise reduction, b i The flag bit determines whether to process; n i The initial data in the stack.
5. The output waveform optimization method of the radar frequency source according to claim 4, characterized in that: Using the formula Determine the data after noise reduction processing; Using the formula Determine the flag bit to determine whether to perform processing; Among them, z 0.9 is the confidence interval of the data, μ is the mean of the data, and σ is the variance of the data.
6. The method for optimizing the output waveform of a radar frequency source according to claim 4, characterized in that: Perform secondary stacking processing on the frequency-compensated periodic waveform data; Based on the data in each stack, a denoising algorithm is used to output a radio waveform with low periodic clock error and non-periodic noise interference, including: Delete the frequency-compensated periodic waveform data that does not meet the confidence condition; Perform normal distribution fitting on the periodic waveform data after data deletion to generate the corresponding digital matched filter; According to the periodic waveform data after data deletion, a digital matched filter is used for denoising and output.
7. An output waveform optimization device for a radar frequency source, characterized in that: The output waveform optimization device of the radar frequency source comprises: A periodic waveform data acquisition module, used for acquiring periodic waveform data at multiple preset frequencies by high-frequency sampling; A stack number determination module is used to determine the number of sampling points according to the periodic waveform data; the number of sampling points is the number of stacks; A stack processing module, used to align the periodic waveform data at multiple preset frequencies with each preset stack in a sampling order, and perform stack processing; An error determination module is used to determine the actual frequency according to the phase shift relationship between the stack bottom data and the stacked data during the stack processing; and compensate the actual frequency according to the preset frequency; The output waveform module is used to perform secondary stacking processing on the periodic waveform data after frequency compensation; according to the data in each stack, a denoising algorithm is used to output a radio waveform with low periodic clock error and non-periodic noise interference.
8. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the output waveform optimization method of the radar frequency source according to any one of claims 1 to 6.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the output waveform optimization method of the radar frequency source according to any one of claims 1 to 6 is implemented.
10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the output waveform optimization method of the radar frequency source according to any one of claims 1 to 6 is implemented.