Correction method for spectrum distortion of Chirp conversion spectrum analyzer

Abstract

The invention provides a method for correcting spectrum distortion of a Chirp conversion spectrum analyzer. The method comprises the following steps: establishing a broadening line phase error model and a compression line phase error model of the Chirp conversion spectrum analyzer; estimating a broadening line phase error and a compression line phase error through a Chirp signal phase error estimation method based on the broadening line phase error model and the compression line phase error model; establishing a system simulation model of the Chirp transform spectrum analyzer according to the broadening line phase error and the compression line phase error, and predicting spectrum distortion of the detected signal generated in the Chirp transform spectrum analyzer by using the system simulation model; constructing a correction curve and a Wiener inverse filter based on the predicted spectrum distortion; and correcting the actual spectrum output by the Chirp conversion spectrum analyzer by using the correction curve and a Wiener inverse filter.

Description

Technical Field

[0001] This invention relates to the field of deep space spectral detection technology, specifically to a method for correcting spectral distortion in a Chirp transform spectrum analyzer. Background Technology

[0002] A Chirp Transform Spectrometer (CTS) is a spectrum detection system that uses the Chirp transform algorithm to analyze the spectrum of a signal under test. It mainly consists of a Chirp signal (spreading line) for spreading and a matched filter (compressor line) for matched filtering. The matched filter is typically a Chirp signal with a frequency modulation slope opposite to that of the spreading line. The signal under test is multiplied by the spreading line to broaden the signal, and then convolved with the compressor line to compress the pulse, thus obtaining the spectrum of the signal under test.

[0003] With the rapid development of deep space exploration, the types of radioactive materials to be detected are becoming increasingly diverse. Deep space spectral detection systems are also evolving towards larger bandwidths, higher frequency resolutions, and higher spectral detection accuracy. Chirp transform spectrum analyzers, due to their ability to simultaneously offer large bandwidth, high frequency resolution, high sensitivity, and low mass and power consumption, are well-suited for detecting ultrafine, weak, and wide-bandwidth spectral lines, giving them a significant advantage in deep space exploration.

[0004] The phase error introduced during the generation of a large-bandwidth chirp signal makes it difficult to maintain consistent dispersion characteristics within the band. This leads to distortions in the pulse compression results, such as pulse position shift, main lobe descent, and sidelobe rise. Consequently, the output spectrum of the chirp transform spectrum analyzer experiences frequency shift and amplitude attenuation, severely impacting the accuracy and reliability of spectrum measurements. Current technologies can only compensate for the phase error introduced by the broadening line, failing to effectively address the phase error of the compression line. Furthermore, these technologies require high-power devices such as FPGAs and DACs, making them unsuitable for applications with power constraints, such as deep space exploration. Moreover, for different input frequencies, the frequency range used by the broadening line relative to the compression line is inconsistent, making it impossible to specifically compensate the broadening line based on the compression line phase error.

[0005] Therefore, a method for correcting spectral distortion in Chirp transform spectrum analyzers is needed. Summary of the Invention

[0006] The purpose of this invention is to provide a method for correcting spectral distortion in a Chirp transform spectrum analyzer. By independently characterizing, jointly modeling, and simulating the broadening and compression lines, a distortion prediction model is constructed, and frequency / amplitude correction curves and Wiener inverse filters are generated accordingly. Finally, the measured spectrum is comprehensively corrected at the signal processing backend, thereby significantly improving the frequency accuracy, amplitude flatness, and pulse waveform quality of the CTS system.

[0007] To achieve the above objectives, the present invention provides a method for correcting spectral distortion in a Chirp transform spectrum analyzer, comprising:

[0008] Establish the broadening line phase error model and the compression line phase error model for the Chirp transform spectrum analyzer;

[0009] Based on the broadened line phase error model and the compressed line phase error model, the broadened line phase error and the compressed line phase error are estimated by the Chirp signal phase error estimation method.

[0010] Based on the phase error of the broadened line and the phase error of the compressed line, a system simulation model of the Chirp transform spectrum analyzer is established, and the system simulation model is used to predict the spectral distortion of the measured signal in the Chirp transform spectrum analyzer.

[0011] Based on the predicted spectral distortion, a correction curve and a Wiener inverse filter are constructed.

[0012] The actual spectrum output by the Chirp transform spectrum analyzer is corrected using the aforementioned correction curve and Wiener inverse filter.

[0013] Preferably, the phase error model of the broadening line is:

[0014]

[0015] Where k1 is the frequency modulation slope of the broadened line, and f1 is the initial frequency of the broadened line. The phase error of the broadened line is denoted by t, which represents the time domain, and T1 is the duration of the broadened line.

[0016] The compression line phase error model is as follows:

[0017]

[0018] Where k2 is the frequency modulation slope of the compression line, and f2 is the initial frequency of the compression line. T1 represents the phase error of the compressed line, t represents the time domain, and T2 represents the duration of the compressed line response.

[0019] Specifically, the phase error of the broadening line and the phase error of the compression line are estimated using the Chirp signal phase error estimation method, including:

[0020] The phase information and frequency range of the broadened and compressed lines are extracted, and the phase information is unwrapped to obtain continuous frequency-phase characteristics. The continuous frequency-phase characteristics are fitted with a quadratic polynomial using the least squares method to obtain a fitted quadratic phase curve. Based on the fitted quadratic phase curve, the actual frequency modulation slope of the broadened and compressed lines is determined. The continuous frequency-phase characteristics are subtracted from the fitted quadratic phase curve to obtain the phase error curves within the frequency range of the broadened and compressed lines.

[0021] Specifically, based on the phase error of the broadening line and the phase error of the compression line, a system simulation model of the Chirp transform spectrum analyzer is established, and the system simulation model is used to predict the spectral distortion of the measured signal generated in the Chirp transform spectrum analyzer, including:

[0022] Construct an ideal expansion line model and an ideal compression line model. Add the phase error of the expansion line to the ideal expansion line model to obtain an expansion line simulation model. Add the phase error of the compression line to the ideal compression line model to obtain a compression line simulation model.

[0023] A Chirp variable spectrum analyzer is selected to measure N test signals of different frequencies within the bandwidth. The predicted frequency f of each test signal is then predicted using the system simulation model. p (k) Predicted amplitude A p (k) and the predicted distortion pulse compression output spectrum Calculate the frequency offset for each test signal:

[0024] Δf(k)=f p (k)-f i (k), k = 1, 2, 3, ..., N

[0025] Where Δf(k) represents the frequency offset, k is the index of the frequency point, and f p (k) represents the predicted frequency, f i (k) represents the true frequency of the signal; calculate the amplitude attenuation coefficient for each test signal:

[0026] α(k)=A p (k) / A1(k), k=1,2,3,……,N

[0027] Where α(k) represents the amplitude attenuation coefficient, k is the index of the frequency point, and A p (k) represents the predicted spectral amplitude, A i (k) represents the spectral amplitude under ideal conditions; calculate the distortion channel response for each test signal:

[0028]

[0029] Where H(f) represents the distortion channel response, and f is the frequency. P(f) represents the predicted distorted pulse compression output spectrum, and P(f) represents the ideal pulse compression output spectrum.

[0030] Preferably, the N test signals of different frequencies are distributed at equal frequency intervals within the measurement bandwidth.

[0031] Specifically, based on the predicted spectral distortion, a correction curve and a Wiener inverse filter are constructed, including:

[0032] The frequency offset and amplitude attenuation coefficient of N test signals are resampled to make their sampling rate consistent with the sampling rate of the Chirp transform spectrum analyzer, so as to obtain the resampled frequency offset curve Δf(ω) and amplitude attenuation coefficient curve α(ω), where ω is the angular frequency of the test signal;

[0033] The calculated frequency correction curve is as follows:

[0034] C f (ω)=-Δf(ω)

[0035] Among them, C f (ω) is the frequency correction curve, where ω is the angular frequency of the input signal, and Δf(ω) is the frequency offset curve after resampling.

[0036] The amplitude correction curve is calculated as follows:

[0037] G A (ω)=1 / α(ω)

[0038] Among them, G A (ω) is the amplitude correction curve, where ω is the angular frequency of the input signal, and α(ω) is the amplitude attenuation coefficient curve after resampling;

[0039] The Wiener inverse filter is constructed as follows:

[0040]

[0041] Among them, P ss (f) represents the ideal signal to be recovered, P nn H(f) is the power spectral density of the system noise, and H(f) is the distortion channel response. * (f) is the complex conjugate of H(f), and G(f) is the Wiener inverse filter formula.

[0042] Preferably, the actual spectrum output by the Chirp transform spectrum analyzer is corrected using the correction curve and the Wiener inverse filter, including:

[0043] The spectrum of the actual signal is obtained by measuring it with a Chirp transform spectrum analyzer. The frequencies in the spectrum are added with the corresponding correction values ​​from the frequency correction curve, and the amplitudes in the spectrum are multiplied by the corresponding correction values ​​from the amplitude correction curve. The waveform distortion of the pulse compression result is then corrected by a Wiener inverse filter. Attached Figure Description

[0044] Figure 1 A schematic diagram of the Chirp transform provided in an embodiment of the present invention;

[0045] Figure 2 A flowchart of a method for correcting spectral distortion in a Chirp transform spectrum analyzer, provided in an embodiment of the present invention;

[0046] Figure 3 A block diagram of a Chirp transform spectrum analyzer system provided in an embodiment of the present invention;

[0047] Figure 4 This is a schematic diagram of the frequency modulation slope of a compression line provided in an embodiment of the present invention;

[0048] Figure 5 A phase error curve of a compressed line in the frequency range of 1.1 GHz to 2.1 GHz, provided for an embodiment of the present invention;

[0049] Figure 6 A phase error curve diagram in the frequency range of 0.4GHz to 2.4GHz after offline frequency conversion is provided for an embodiment of the present invention;

[0050] Figure 7 This is a schematic diagram of the frequency offset predicted by a simulation model provided in an embodiment of the present invention;

[0051] Figure 8 This is a schematic diagram of the amplitude response predicted by a simulation model, provided in an embodiment of the present invention.

[0052] Figure 9 This is a schematic diagram of the frequency offset of a Chirp transform spectrum analyzer before distortion correction, provided in an embodiment of the present invention.

[0053] Figure 10 This is a schematic diagram of the amplitude response of a Chirp transform spectrum analyzer before distortion correction, provided in an embodiment of the present invention.

[0054] Figure 11 This is a schematic diagram of the frequency offset after distortion correction of a Chirp transform spectrum analyzer, provided in an embodiment of the present invention.

[0055] Figure 12This is a schematic diagram of the amplitude response of a Chirp transform spectrum analyzer after distortion correction, provided in an embodiment of the present invention.

[0056] Figure 13 The image shows pulse compression waveforms before and after distortion correction in a Chirp transform spectrum analyzer, as provided in an embodiment of the present invention. Detailed Implementation

[0057] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0058] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be described below with reference to the accompanying drawings. It should be noted that similar reference numerals and letters in the following drawings indicate similar items; therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0059] In the description of the embodiments of the present invention, the words "exemplary," "for example," or "for instance" are used to indicate that they are examples, illustrations, or descriptions. Any embodiment or design that is described as "exemplary," "for example," or "for instance" in the embodiments of the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Rather, the use of the words "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a specific manner.

[0060] A chirp transform spectrum analyzer mainly consists of two parts: a stretching line and a compression line. The stretching line generates a wide-bandwidth chirp signal, which is multiplied by the signal under test to achieve signal stretching. The compression line performs convolution operations on the stretched signal to achieve pulse compression, ultimately obtaining the spectrum of the signal under test. The specific principle is as follows: Figure 1 The diagram illustrates a Chirp transform principle. The frequency modulation slope of the broadened line should be opposite to that of the compressed line, and the measurement bandwidth of the Chirp transform spectrum analyzer is the difference between the bandwidth of the broadened line and the bandwidth of the compressed line.

[0061] During the generation of wide-bandwidth chirp signals, the introduced phase error makes it difficult to maintain consistent dispersion characteristics across the entire bandwidth. This problem directly leads to a series of distortions in the pulse compression results, including pulse position shift, main lobe amplitude reduction, and side lobe rise. These distortions ultimately cause frequency shifts and amplitude attenuation in the output spectrum of the Chirp Transform Spectrometer (CTS), severely affecting the accuracy and reliability of the spectrum measurement results. Current phase error compensation techniques have significant limitations, only correcting phase errors introduced by the broadening line and failing to effectively address phase errors in the compression line. More importantly, when CTS processes input signals of different frequencies, the frequency bands involved in the broadening and compression lines inherently differ. This characteristic directly prevents targeted and precise compensation of the broadening line using the phase error data from the compression line.

[0062] To overcome the shortcomings of existing technologies, a method for correcting spectral distortion in Chirp transform spectrum analyzers is proposed. The broadening and compression lines are independently characterized, jointly modeled and simulated to construct a distortion prediction model. Based on this model, frequency / amplitude correction curves and Wiener inverse filters are generated. Finally, the measured spectrum is comprehensively corrected at the signal processing backend, thereby significantly improving the frequency accuracy, amplitude flatness and pulse waveform quality of the CTS system.

[0063] Figure 1 A flowchart of a method for correcting spectral distortion in a Chirp transform spectrum analyzer, provided as an embodiment of the present invention, is shown in the figure. The method includes:

[0064] S101: Establish the broadening line phase error model and the compression line phase error model for the Chirp transform spectrum analyzer.

[0065] In one embodiment, the phase error model for the broadening line is established as follows:

[0066]

[0067] Where k1 is the frequency modulation slope of the broadened line, and f1 is the initial frequency of the broadened line. The phase error of the broadened line is denoted by t, which represents the time domain, and T1 is the duration of the broadened line.

[0068] The compression line phase error model is as follows:

[0069]

[0070] Where k2 is the frequency modulation slope of the compression line, and f2 is the initial frequency of the compression line. T1 represents the phase error of the compressed line, t represents the time domain, and T2 represents the duration of the compressed line response.

[0071] In this context, the frequency modulation slope k1 of the broadened line and the frequency modulation slope k2 of the compressed line are opposites, i.e., k1 = -k2. The bandwidth of the broadened and compressed lines is the absolute value of the product of their frequency modulation slopes and durations. The difference between the bandwidths of the broadened and compressed lines is the measurement bandwidth of the Chirp transform spectrum analyzer, i.e., B = ||k1T1| - |k2T2||.

[0072] For example, a Chirp transform spectrum analyzer for measuring the spectrum of signals in the 2.5 GHz to 3.5 GHz frequency range uses a Direct Digital Synthesizer (DDS) to generate a 500 MHz bandwidth Chirp signal. After filtering, amplification, and frequency multiplication, a Chirp signal with a bandwidth of 2 GHz, a frequency range of 3.6 GHz to 5.6 GHz, and a modulation slope of 100 MHz / μs is finally obtained. The compression line uses a surface acoustic wave (SAW) dispersion delay line with a bandwidth of 1 GHz, a center frequency of 1.6 GHz, and a dispersion time of 10 μs. Figure 3 The diagram shows a Chirp transform spectrum analyzer system block diagram. The signal under test is mixed with a spreader by a mixer and then pulse compressed by a surface acoustic wave delay line.

[0073] For example, the phase error model of the Chirp signal generated by the Chirp transform spectrum analyzer's stretching line is:

[0074]

[0075] Where k1 = 100MHz / μs is the frequency modulation slope of the broadened line, and f1 = 3.6GHz is the initial frequency of the broadened line.

[0076] Let t represent the phase error of the broadened line, t represent the time domain, and T1 = 20 μs represent the duration of the broadened line.

[0077] The compression line of the Chirp transform spectrum analyzer is a surface acoustic wave linear frequency-modulated dispersion delay line, and the compression line phase error model is as follows:

[0078]

[0079] Where k2 = -100MHz / μs is the frequency modulation slope of the compression line, and f2 = 2.1GHz is the initial frequency of the compression line. Let T2 be the phase error of the compressed line, t represent the time domain, and T2 = 10 μs be the duration of the compressed line response.

[0080] S102: Based on the phase error model of the broadened line and the phase error model of the compressed line, the phase error of the broadened line and the phase error of the compressed line are obtained.

[0081] For example, the phase information and frequency range of the broadened line and the compressed line are extracted, and the phase information is unwrapped to obtain continuous frequency-phase characteristics; the continuous frequency-phase characteristics are fitted with a quadratic polynomial using the least squares method to obtain a fitted quadratic phase curve; the actual frequency modulation slope of the broadened line and the compressed line is determined based on the fitted quadratic phase curve; the continuous frequency-phase characteristics are subtracted from the fitted quadratic phase curve to obtain the phase error curve within the frequency range of the broadened line and the compressed line.

[0082] For an ideal Chirp signal, its phase spectrum It exhibits as a quadratic function related to frequency:

[0083]

[0084] Therefore, by extracting the phase information of the broadening line and the compression line, and obtaining the continuous phase after unwinding, the frequency modulation slope and phase error of the broadening line and the compression line can be estimated by performing a quadratic polynomial fitting on the unwound phase using the least squares method.

[0085] For example, a vector network analyzer is used to acquire the forward transmission coefficient of a surface acoustic wave linear dispersion delay line. Then, MATLAB tools are used to unwrap the compressed line phase data, obtaining the frequency-phase characteristic curve of the compressed line signal. Finally, the least squares method is used to perform a quadratic polynomial fitting on the unwrapped phase to obtain the actual frequency modulation slope and the phase error curve within the frequency band of the compressed line. Figure 4 The diagram shows the frequency modulation slope of a compression line. Figure 5 The figure shows the phase error curve of a compressed line in the frequency range of 1.1 GHz to 2.1 GHz.

[0086] Because the frequency of the stretched line is relatively high, existing analog-to-digital converters (ADCs) cannot directly acquire it. Therefore, the stretched line signal is down-converted to the 0.6–2.6 GHz band, and the down-converted stretched line signal is acquired using an ADC with a sampling rate of 6.4 GHz. Subsequently, MATLAB tools are used to unwrap the phase of the stretched line signal to obtain continuous frequency-phase characteristics. Based on the frequency modulation slope of the compressed line, a quadratic polynomial fitting is performed on the unwrapped phase using the least squares method to obtain the phase error curve within the stretched line frequency band, as shown below. Figure 6 The figure shows a phase error curve in the frequency range of 0.4GHz to 2.4GHz after widening the offline frequency conversion.

[0087] S103: Based on the phase error of the broadened line and the phase error of the compressed line, establish a system simulation model of the Chirp transform spectrum analyzer, and use the system simulation model to predict the spectral distortion of the measured signal generated in the Chirp transform spectrum analyzer.

[0088] For example, an ideal expansion line model and an ideal compression line model are constructed; the phase error of the expansion line is added to the ideal expansion line model to obtain an expansion line simulation model; the phase error of the compression line is added to the ideal compression line model to obtain a compression line simulation model.

[0089] A Chirp variable spectrum analyzer is selected to measure N test signals of different frequencies within the bandwidth. The predicted frequency f of each test signal is then predicted using the system simulation model. p (k) Predicted amplitude A p (k) and the predicted distortion pulse compression output spectrum Calculate the frequency offset for each test signal:

[0090] Δf(k)=f p (k)-f i (k), k = 1, 2, 3, ..., N

[0091] Where Δf(k) represents the frequency offset, k is the index of the frequency point, and f p (k) represents the predicted frequency, f i (k) represents the true frequency of the signal; calculate the amplitude attenuation coefficient for each test signal:

[0092] α(k)=A p (k) / A1(k), k=1,2,3,……,N

[0093] Where α(k) represents the amplitude attenuation coefficient, k is the index of the frequency point, and A p (k) represents the predicted spectral amplitude, A i (k) represents the spectral amplitude under ideal conditions; calculate the distortion channel response for each test signal:

[0094]

[0095] Where H(f) represents the distortion channel response, and f is the frequency. P(f) represents the predicted distorted pulse compression output spectrum, and P(f) represents the ideal pulse compression output spectrum.

[0096] In one embodiment, the N test signals of different frequencies are distributed at equal frequency intervals within the measurement bandwidth.

[0097] For example, an ideal broadened line with a frequency range of 3.6GHz to 5.6GHz is modeled using a sampling rate of 32GHz. The extracted phase error curve of the broadened line is resampled to match the data sampling rate of the ideal broadened line. The phase error of the broadened line is then added to the ideal broadened line, completing the establishment of the simulation model for the broadened line. Similarly, an ideal compressed line with a frequency range of 1.1GHz to 2.1GHz is modeled using a sampling rate of 32GHz. The extracted phase error curve of the compressed line is resampled to match the data sampling rate of the ideal compressed line. The phase error of the compressed line is then added to the ideal compressed line, completing the establishment of the simulation model for the compressed line. 100 equally spaced signals within the operating range of the Chirp Transform spectrum analyzer (2.5GHz to 3.5GHz) are selected, and their frequency offset and amplitude response are predicted using a CTS system simulation model. Figure 7 A schematic diagram of frequency offset predicted by a simulation model provided in an embodiment of the present invention and Figure 8 The diagram shows the amplitude response predicted by a simulation model. Frequency correction curves and amplitude correction curves are calculated based on the predicted frequency offset and amplitude response.

[0098] S104: Based on the predicted spectral distortion, construct the correction curve and the Wiener inverse filter.

[0099] For example, the frequency offset and amplitude attenuation coefficient of N test signals are resampled so that their sampling rate is consistent with the sampling rate of the Chirp transform spectrum analyzer, and the resampled frequency offset curve Δf(ω) and amplitude attenuation coefficient curve α(ω) are obtained, where ω is the angular frequency of the test signal.

[0100] The calculated frequency correction curve is as follows:

[0101] C f (ω)=-Δf(ω)

[0102] Among them, C f (ω) is the frequency correction curve, where ω is the angular frequency of the input signal, and Δf(ω) is the frequency offset curve after resampling.

[0103] The amplitude correction curve is calculated as follows:

[0104] G A (ω)=1 / α(ω)

[0105] Among them, G A (ω) is the amplitude correction curve, where ω is the angular frequency of the input signal, and α(ω) is the amplitude attenuation coefficient curve after resampling;

[0106] The Wiener inverse filter is constructed as follows:

[0107]

[0108] Among them, P ss (f) represents the ideal signal to be recovered, P nn H(f) is the power spectral density of the system noise, and H(f) is the distortion channel response. * (f) is the complex conjugate of H(f), and G(f) is the Wiener inverse filter formula. Since P ss (f) and P nn (f) This is difficult to obtain in practical systems. Therefore, we introduce constant regularization to simplify the Wiener inverse filter. The regularized Wiener inverse filter is:

[0109]

[0110] Where α is a constant.

[0111] For example, frequency correction curves and amplitude correction curves are calculated based on the predicted frequency offset and amplitude response. A signal source inputs 100 test signals with equal frequency intervals in the frequency range of 2.5 GHz to 3.5 GHz to a Chirp transform spectrum analyzer. The frequency offset between the frequency obtained after these 100 test signals passes through the Chirp transform spectrum analyzer and their actual frequency is as follows: Figure 9 The diagram shows the frequency offset before distortion correction using a Chirp transform spectrum analyzer. At this point, the average frequency offset within the Chirp transform spectrum analyzer band is 19.2621 kHz. The amplitude response of these 100 test signals after passing through the Chirp transform spectrum analyzer is as follows: Figure 10 The diagram shows the amplitude response of a Chirp transform spectrum analyzer before distortion correction, at which point the amplitude flatness of the Chirp transform spectrum analyzer is 2.701 dB.

[0112] S105: Using the frequency correction curve and amplitude correction curve, the actual measured spectrum output by the Chirp transform spectrum analyzer is corrected.

[0113] For example, the spectrum of the actual signal is obtained by measuring it with a Chirp transform spectrum analyzer, the frequency in the spectrum is added to the corresponding correction value in the frequency correction curve, and the amplitude in the spectrum is multiplied by the corresponding correction value in the amplitude correction curve. The waveform distortion of the pulse compression result is corrected by a Wiener inverse filter.

[0114] For example, the frequency correction curve and amplitude correction curve are used to correct the spectrum of the above test signal to obtain the corrected frequency offset, such as... Figure 11The diagram shows the frequency offset after distortion correction in a Chirp transform spectrum analyzer. The average frequency offset within the band of the Chirp transform spectrum analyzer after correction is 4.0182 kHz. The corrected amplitude response is as follows: Figure 12 The diagram shows the amplitude response of a Chirp transform spectrum analyzer after distortion correction. The amplitude flatness of the Chirp transform spectrum analyzer after correction is 0.642 dB. A Wiener inverse filter is constructed for the aforementioned arbitrary test signal, and the signal is corrected using the Wiener inverse filter. The peak-to-side-lobe ratio of the pulse is optimized from -10 dB to -13.8 dB after correction. The pulse waveforms before and after correction are shown below. Figure 13 The diagram shows pulse compression waveforms before and after distortion correction in a Chirp transform spectrum analyzer. It is evident that the Chirp transform spectrum analyzer distortion correction method proposed in this invention can effectively correct frequency shift, amplitude attenuation, and sidelobe rise caused by phase errors, significantly improving the system's spectrum measurement accuracy.

[0115] It is understood that the method steps in the embodiments of the present invention can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0116] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0117] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for correcting spectral distortion in a Chirp transform spectrum analyzer, comprising: Establish the broadening line phase error model and the compression line phase error model for the Chirp transform spectrum analyzer; Based on the broadened line phase error model and the compressed line phase error model, the broadened line phase error and the compressed line phase error are estimated by the Chirp signal phase error estimation method. Based on the phase error of the broadened line and the phase error of the compressed line, a system simulation model of the Chirp transform spectrum analyzer is established, and the system simulation model is used to predict the spectral distortion of the measured signal in the Chirp transform spectrum analyzer. Based on the predicted spectral distortion, a correction curve and a Wiener inverse filter are constructed. The actual spectrum output by the Chirp transform spectrum analyzer is corrected using the aforementioned correction curve and Wiener inverse filter.

2. The correction method according to claim 1, wherein, The phase error model for the broadened line is as follows: Where k1 is the frequency modulation slope of the broadened line, and f1 is the initial frequency of the broadened line. The phase error of the broadened line is denoted by t, which represents the time domain, and T1 is the duration of the broadened line. The compression line phase error model is as follows: Where k2 is the frequency modulation slope of the compression line, and f2 is the initial frequency of the compression line. T1 represents the phase error of the compressed line, t represents the time domain, and T2 represents the duration of the compressed line response.

3. The correction method according to claim 2, wherein, The phase error of the broadened line and the phase error of the compressed line are estimated using the Chirp signal phase error estimation method, including: The phase information and frequency range of the broadened and compressed lines are extracted, and the phase information is unwrapped to obtain continuous frequency-phase characteristics. The continuous frequency-phase characteristics are fitted with a quadratic polynomial using the least squares method to obtain a fitted quadratic phase curve. Based on the fitted quadratic phase curve, the actual frequency modulation slope of the broadened and compressed lines is determined. The continuous frequency-phase characteristics are subtracted from the fitted quadratic phase curve to obtain the phase error curves within the frequency range of the broadened and compressed lines.

4. The correction method according to claim 3, wherein, Based on the phase error of the broadened line and the phase error of the compressed line, a system simulation model of the Chirp transform spectrum analyzer is established, and the system simulation model is used to predict the spectral distortion of the measured signal in the Chirp transform spectrum analyzer, including: Construct an ideal expansion line model and an ideal compression line model. Add the phase error of the expansion line to the ideal expansion line model to obtain an expansion line simulation model. Add the phase error of the compression line to the ideal compression line model to obtain a compression line simulation model. A Chirp variable spectrum analyzer is selected to measure N test signals of different frequencies within the bandwidth. The predicted frequency f of each test signal is then predicted using the system simulation model. p (k) Predicted amplitude A p (k) and the predicted distortion pulse compression output spectrum Calculate the frequency offset for each test signal: Δf(k)=f p (k)-f i (k),k=1,2,3,……,N Where Δf(k) represents the frequency offset, k is the index of the frequency point, and f p (k) represents the predicted frequency, f i (k) represents the true frequency of the signal; calculate the amplitude attenuation coefficient for each test signal: α(k)=A p (k) / A i (k),k=1,2,3,……,N Where α(k) represents the amplitude attenuation coefficient, k is the index of the frequency point, and A p (k) represents the predicted spectral amplitude, A i (k) represents the spectral amplitude under ideal conditions; calculate the distortion channel response for each test signal: Where H(f) represents the distortion channel response, and f is the frequency. P(f) represents the predicted distorted pulse compression output spectrum, and P(f) represents the ideal pulse compression output spectrum.

5. The correction method according to claim 4, wherein, The N test signals of different frequencies are distributed at equal frequency intervals within the measurement bandwidth.

6. The correction method according to claim 4, wherein, Based on the predicted spectral distortion, a correction curve and a Wiener inverse filter are constructed, including: The frequency offset and amplitude attenuation coefficient of N test signals are resampled to make their sampling rate consistent with the sampling rate of the Chirp transform spectrum analyzer, so as to obtain the resampled frequency offset curve Δf(ω) and amplitude attenuation coefficient curve α(ω), where ω is the angular frequency of the test signal; The calculated frequency correction curve is as follows: C f (ω)=-Δf(ω) Among them, C f (ω) is the frequency correction curve, where ω is the angular frequency of the input signal, and Δf(ω) is the frequency offset curve after resampling. The amplitude correction curve is calculated as follows: G A (ω)=1 / α(ω) Among them, G A (ω) is the amplitude correction curve, where ω is the angular frequency of the input signal, and α(ω) is the amplitude attenuation coefficient curve after resampling; The Wiener inverse filter is constructed as follows: Among them, P ss (f) represents the ideal signal to be recovered, P nn H(f) is the power spectral density of the system noise, and H(f) is the distortion channel response. * (f) is the complex conjugate of H(f), and G(f) is the Wiener inverse filter formula.

7. The correction method according to claim 6, wherein, The actual spectrum output by the Chirp transform spectrum analyzer is corrected using the aforementioned correction curve and the Wiener inverse filter, including: The spectrum of the actual signal is obtained by measuring it with a Chirp transform spectrum analyzer. The frequencies in the spectrum are added with the corresponding correction values ​​from the frequency correction curve, and the amplitudes in the spectrum are multiplied by the corresponding correction values ​​from the amplitude correction curve. The waveform distortion of the pulse compression result is then corrected by a Wiener inverse filter.

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