A method and system for computing the hyperfine spectrum of a sampled signal

Abstract

This invention discloses a method and system for calculating the ultra-fine spectrum of a sampled signal, belonging to the field of weak signal detection technology. Calculating the spectrum of signals with extremely long sampling times presents problems such as large data volume and high computer memory requirements. This method divides the sampled data sequence of an ultra-low bandwidth modulated signal into segments of equal duration. Each segment is then subjected to quadrature demodulation, filtering, and decimation concatenation. The processed segments are then sequentially concatenated, and finally, a time-frequency transformation is performed to obtain the signal spectrum with ultra-fine frequency resolution. This calculation method significantly reduces the amount of data required for time-frequency transformation, allowing the processing of massive amounts of sampled data to be completed on a conventionally configured computer, yielding signal spectra with frequency resolution at the millihertz or even microhertz level. This allows for the observation and understanding of the extremely low-frequency spectral structure or near-end phase noise of the signal. This calculation method has strong versatility.

Description

Technical Field

[0001] This invention belongs to the field of weak signal detection technology, and more specifically, relates to a method and system for calculating the ultra-fine spectrum of a sampled signal. Background Technology

[0002] Signal detection and recognition technology is widely used in aerospace, communication equipment, satellite communication, space gravitational wave detection and other fields, and is one of the important research contents in communication, aerospace equipment design and other fields.

[0003] The detection and analysis of weak signals require a significant increase in the signal-to-noise ratio (SNR) and effective suppression of noise interference. Analyzing and detecting weak signals extremely close to the carrier frequency is very difficult, requiring not only a high SNR but also the acquisition of a signal spectrum with extremely high frequency resolution. Currently, classic signal spectrum estimation methods include: periodogram method, autocorrelation method, Bartlett method, and Welch method. The periodogram method, also known as the direct spectrum calculation method, treats N-point observations of a random signal as a finite-energy signal and directly performs a Fourier transform on the discrete sequence to obtain the signal spectrum. The autocorrelation method, also known as the indirect method or BT method, is based on the Wiener-Schenchin theorem and requires that the signal length beyond N be zero, thus having certain limitations. The Bartlett method uses a random sampled sequence x... N (n) Divide the data into L segments, each with a length of N / L. Window each segment and calculate the power spectrum, then calculate the average of the total power spectrum. The Welch method is an improvement on the Bartlett method, allowing partial overlap between data segments and allowing the use of non-rectangular windows (e.g., Hanning or Hamming windows) for each segment, effectively mitigating the spectral distortion caused by large sidelobes in rectangular windows. However, due to limitations in sampling sequence length, these methods result in insufficient frequency resolution and low computational efficiency.

[0004] In summary, the limitations of commonly used signal spectrum calculation methods lie in their inability to calculate ultra-fine spectra of sampling sequences with extremely long sampling times and massive amounts of data. Under conventional computer configurations, classical spectrum analysis and estimation methods are no longer sufficient to meet application requirements when calculating spectra with frequency resolutions at the millihertz or even microhertz levels, observing the ultra-low frequency spectral structure of signals, and analyzing the very near-end phase noise of signals. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a method and system for calculating the ultra-fine spectrum of a sampled signal. This method addresses the problems of existing signal spectrum calculation methods, such as the inability to calculate the spectrum of signals with ultra-long sampling times, the difficulty in calculating signal sequences and their spectra with high sampling frequencies and large data volumes, the low frequency resolution of the obtained signal spectrum, and the stringent hardware configuration requirements for calculation.

[0006] To achieve the above objectives, the present invention provides a method for calculating the hyperfine spectrum of a sampled signal, comprising the following steps:

[0007] Step 1: For a modulated signal sampling sequence with an extremely long sampling time and a very small signal bandwidth, based on the total sampling duration T and the sampling frequency f... s Calculate the total number of sampling points in the sampling sequence;

[0008] Step 2: According to the preset data segmentation duration dT, the aforementioned sampling sequence is segmented into equal duration segments. Within each segment, the signal sequence is subjected to digital quadrature downconversion and cascaded filtering decimation to obtain the complex baseband IQ data sequence of the segmented data. The data rate of the complex baseband IQ data sequence must meet the minimum requirements of the Nyquist low-pass sampling theorem.

[0009] Step 3: Concatenate the complex baseband IQ data sequences of each segment according to their sequence numbers to obtain a complete duration complex baseband IQ sequence that corresponds to the duration of the original sampling sequence but has an extremely low data rate;

[0010] Step 4: Perform time-frequency transformation on the above complete duration complex baseband IQ sequence to obtain the signal spectrum corresponding to the original sampling sequence. This spectrum has ultra-fine frequency resolution.

[0011] Furthermore, in step 1, when sampling the modulated signal with an effective bandwidth of extremely small duration for a total duration of T, the sampling frequency f s The Nyquist low-pass sampling theorem must be satisfied, i.e., f s ≥2f0+BW, where f0 and BW are the center frequency and effective bandwidth of the modulated signal, respectively. Bandpass sampling is not used to avoid effective amplitude attenuation when using a high Nyquist band due to f0 >> BW, and to avoid spectral aliasing that may occur due to unstable spurious signals or interference outside the effective bandwidth. This results in an extremely large number of sampling points, making it impossible to complete the time-frequency analysis of the sampled sequence in one go due to computer memory limitations.

[0012] Furthermore, in step 2, when segmenting the sampling sequence, data continuity must be ensured, that is, there should be no duplicate sampling points or missing sampling points in two adjacent segments.

[0013] Furthermore, in step 2, when performing digital orthogonal downconversion and filtering decimation on the segmented data sequence, the local oscillator frequency is set to the center frequency f0 of the modulation signal. The input / output signal bandwidth ratio and decimation factor of the low-pass filter are both much greater than 1. Therefore, it is necessary to design multi-stage cascaded filtering-decimation units to achieve the same effect as single-stage high-order filtering-decimation processing and significantly reduce the amount of computation.

[0014] Furthermore, in step 2, the designed multi-stage cascaded filter-decimation unit needs to set the initial values ​​of the filter to ensure the correctness of the filtered output data. For the IQ complex baseband data sequence s after down-conversion to zero intermediate frequency within the m-th segment (m=1,2,…,T / dT),... m When performing cascaded filtering-decimation processing, if the orders of the designed L-stage cascaded filters are P1, P2, ..., P... j-1 ,P j ,…,P L (L≥2 is a positive integer), after each filtering stage, k1, k2, ..., k are extracted respectively. j-1 ,k j ,…,k L-1 ,k L If the filter initial value is multiplied by a factor of 1, the decimation rules are as follows:

[0015] Step 2-1: Considering the initial conditions required by each stage of the filter to filter the input data, the filter-decimation output sequence of the L-stage cascaded filter in the first segment is used as the initial value of the L-stage cascaded filter in the second segment. The input sequence s1 of the first stage filter in the first segment of data has N... m Given _ data points, output sequence y 1,1 After extracting k1 times, the sequence z is obtained. 1,1 Ignoring the initial values ​​of the filter, z 1,1 As the input sequence of the second-stage filter x 1,2 At this time, sequence x 1,2 Contains N m / k1 data points. And so on, the input sequence x of the last cascaded filter. 1,L Filter the previous stage filter and decimate k L-1 The output sequence z is multiplied by 1 1,(L-1) The sequence contains N m / (k1×k2…×k L-1 ) data points. Within the first data segment, sequences s1 and z 1,1 z 1,2 ... z 1,(L-2) z 1,(L-1) The last (P1-1), (P2-1), ..., (P L-1 -1), (P L-1) points are used as the initial values ​​for the L-stage cascaded filter in the second time segment. To ensure that each stage of the filter in the first segment has a sufficient number of correct output data points after filtering and decimation, these points are used as the initial values ​​for each stage of the filter in the second segment. The total number of data points N in the input sequence s1 is... m Conditions to be met:

[0016] N m ≥[(P1-1)+k1·(P2-1)+k1k2·(P3-1)+…+(k1k2…k L-2 k L-2 )·(P L-1 -1)+(k1k2…k L- 2k L-1 )·(P L -1)]

[0017] Step 2-2: Extract k = k1k2…k from the sampling data of total duration T. j …k L-1 k L To ensure continuity in the time-segmented sampling, the number of points sequentially spliced ​​after time-segmented sampling should be directly extracted from the sampling data of total duration T, k = k1k2…k. j …k L-1 k L The number of sampling points is the same as the number of points in each segment. Therefore, the number of sampling data points N in each segment is... m Conditions to be met:

[0018] N m =n·k, (n is a positive integer, i.e. )

[0019] Steps 2-3: For the zero-IF IQ complex baseband data sequence s in the m-th (m≥2) segment... m During filtering and decimation, the initial values ​​of the first-stage filter are set to the sequence s. m-1 The last (P1-1) data. That is: in data block s m Add sequence s before the sequence m-1 The last (P1-1) data points are used to obtain a new data block x. m,1 This is the input sequence for the first-stage filter within the m-th (m≥2) segment. The output sequence after filtering by the first-stage filter is y. m,1 Then remove sequence y m,1 The first (P1-1) data points are then decimated by a factor of k1 to obtain the output sequence z of the m-th segment after filtering and decimation by the first-stage filter. m,1 .

[0020] In steps 2-4, the initial value of the j-th (2≤j≤L)-th level filter within the m-th (m≥2)-th segment must be set to the output sequence z of the (j-1)-th level filter after filtering and decimation within the (m-1)-th segment. (m-1),(j-1) The last (P) j -1) data points. That is: in sequence z m,j Pre-increment sequence z (m-1),(j-1) The last (P) j -1) data points are used to obtain a new data sequence x. m,j The input data sequence is used as the input data sequence for the j-th (2≤j≤L) level filter in the current time period, and then the filtered output sequence y is removed from this sequence. m,j The front (P) j After obtaining -1) data points, extract k more data points. j This yields the filtered-decimated output sequence z of the j-th (2≤j≤L)-th level filter within the m-th (m≥2) segment. m,j .

[0021] Furthermore, in step 3, when concatenating the complex baseband IQ data sequences of each segment according to their sequence numbers, it is necessary to discard the sequence z extracted by cascaded filtering within the first segment. 1,L Starting from the second segment, sort z in sequence. 2,L z 3,L ... z m-1,L z m,L The complete duration complex baseband IQ output sequence z is obtained by splicing together the data with an extremely low data rate.

[0022] Furthermore, in step 4, when performing time-frequency transformation on the complete complex baseband IQ sequence z to obtain the signal spectrum and display it, it is necessary to convert both the horizontal and vertical axes of the spectrum graph to logarithmic scales in order to observe the ultra-fine spectrum of this ultra-low bandwidth signal.

[0023] Another aspect of the present invention provides a calculation system for ultrafine spectrum of a sampled signal, comprising: a computer-readable storage medium and a processor;

[0024] The computer-readable storage medium is used to store executable instructions;

[0025] The processor is used to read executable instructions stored in the computer-readable storage medium and execute the above-described method for calculating the ultrafine spectrum of the sampled signal.

[0026] Compared with the prior art, the above-described technical solution of this invention can calculate the ultra-fine spectrum of sampling sequences with extremely long sampling times and extremely large data volumes under conventional computer configuration conditions, thus achieving the following beneficial effects:

[0027] (1) This invention effectively solves the problem of spectrum calculation for extremely narrow bandwidth signal sequences with extremely long durations and large data volumes by continuously segmenting and breaking down the ultra-long duration sampling signal sequence into smaller parts. The segmentation method of this invention for ultra-long duration sampling sequences can be applied to the frequency domain detection of extremely low frequency signals, such as in space gravitational wave detection.

[0028] (2) Cascading and decimating multi-stage filters in different time periods is a method to effectively reduce the amount of data while ensuring the frequency domain characteristics of the sequence. The initial conditions of the cascaded filters and the equal-interval decimation of the output sequence of each filter stage during segmented filtering are key technologies in the method for calculating the ultra-fine spectrum of the sampled signal in this invention. These technologies have great engineering application value in analyzing the ultra-low frequency spectrum structure of the signal or calculating its near-end phase noise.

[0029] (3) When the effective bandwidth of the sampled signal sequence is extremely small, the passband bandwidth of the designed filter is also very small. At this time, an extremely high data extraction rate can be designed, thereby effectively reducing the amount of data in the time-frequency transformation of the ultra-long sampling time signal sequence. The ultra-long sampling time signal sequence is processed in time segments in the program, making it feasible to perform time-frequency transformation with a large amount of data on a computer with a conventional configuration.

[0030] (4) This invention proposes a method for calculating the ultrafine spectrum of a sampled signal, which can be applied to signal processing and analysis scenarios in multiple fields, improving the ability to detect and analyze ultra-low frequency weak signals in practical engineering applications. It can accurately and efficiently calculate the ultrafine spectrum of a sampled signal under conventional computer configuration conditions. This invention has high engineering application value, low computational complexity, and good versatility in its design program. Attached Figure Description

[0031] Figure 1 This is the overall flowchart of the method for calculating the ultrafine spectrum of the sampled signal according to the present invention.

[0032] Figure 2 This is a flowchart illustrating the design process of cascaded filtering and extraction of segmented data in this invention. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0034] This invention provides a method for calculating the hyperfine spectrum of a sampled signal, comprising the following steps:

[0035] Step 1: For a modulated signal sampling sequence with an extremely long sampling time and a very small signal bandwidth, based on the total sampling duration T and the sampling frequency f... s Calculate the total number of sampling points in the sampling sequence;

[0036] Step 2: According to the preset data segmentation duration dT, the aforementioned sampling sequence is segmented into equal duration segments. Within each segment, the signal sequence is subjected to digital quadrature downconversion and cascaded filtering decimation to obtain the complex baseband IQ data sequence of the segmented data. The data rate of the complex baseband IQ data sequence must meet the minimum requirements of the Nyquist low-pass sampling theorem.

[0037] Step 3: Concatenate the complex baseband IQ data sequences of each segment according to their sequence numbers to obtain a complete duration complex baseband IQ sequence that corresponds to the duration of the original sampling sequence but has an extremely low data rate;

[0038] Step 4: Perform time-frequency transformation on the above complete duration complex baseband IQ sequence to obtain the signal spectrum corresponding to the original sampling sequence. This spectrum has ultra-fine frequency resolution.

[0039] Example

[0040] Figure 1 This is the overall flowchart of the method for calculating the ultrafine spectrum of the sampled signal in this invention. The total calculation time is T = 1024 seconds, and the sampling frequency is 2... 19 Taking the hyperfine spectrum of a narrowband modulated signal with a center frequency of f0 = 100kHz as an example, the specific calculation steps are as follows:

[0041] Step 1: Calculate the total number of sampling points N = 536,870,912 for the time-domain signal sequence. Take the duration of the segmented calculation as dT = 4 seconds. The total number of sampled data points within each segment is N. m =2097152. Based on the calculation results, initial values ​​are assigned to each variable in the designed program. Define a variable z to store the final result of the segmented calculation output signal sequence, and allocate memory space for it.

[0042] Step 2, calculate the total number of segments M = 1024 / 4 = 256, and the sampling interval of the signal sampling sequence is dt = 1 / f s =2 -19 Seconds. Iterate through each sequence variable, with the loop structure condition being that the number of segments m ≤ 256.

[0043] Step 3: Based on the conditions satisfied by the sampling sequence to be determined and the center frequency f0 = 100kHz of the modulation signal, calculate the IQ complex baseband sequence s down-converted to zero intermediate frequency in each segment. m (n), this sequence is the data sequence waiting for cascaded filtering-decomposition within the m-th segment. After calculating the sequence s within each segment...m After (n), the initial conditions for calculating the next segment need to be updated in a timely manner.

[0044] Step 4, due to s m The total number of data in (n) is N. m =2097152, the final sequence data volume after segmented calculation is relatively large; consider designing a cascaded filtering structure of three-stage filtering-decimation units, performing downsampling with a total factor of k = 1024, the data volume in each segment after decimation is N. m When / k = 2048, the amount of data in the sequence decreases significantly. The detailed design of the three-stage cascaded filter-decimation unit is as follows:

[0045] 1) Designing three cascaded low-pass FIR filters presents high computational complexity when the filter order is large. Choosing an equiripple design can effectively reduce the filter order. The sampling frequency of the first-stage FIR filter is the low-pass sampling frequency f1 = f... s =524288Hz, and decimated by k1 = 16; the sampling frequency of the second-stage FIR filter is f2 = f1 / k1 = 32768Hz, and the decimation factor is k2 = 16; the sampling frequency of the third-stage FIR filter is designed to be f3 = f2 / k2 = 2048Hz, and the decimation factor is k3 = k / (k1·k2) = 4. The calculated orders of the designed three-stage FIR filters are: P1 = 120, P2 = 94, P3 = 72.

[0046] 2) Because it is necessary to consider the initial value settings of each cascaded filter in each segment, as well as the number of data points N in a single segment. m =2097152 needs to meet the value conditions to ensure equal-interval decimation of data. To ensure that the three-stage cascaded filter outputs sufficient correct initial filter values ​​and equal-interval decimation within the first segment, then:

[0047]

[0048] Calculations show that N m =2097152, n=2048 satisfy the above conditions.

[0049] 3) After the sequence s1(n) in the first segment is filtered and decimated by three cascaded filters, the last 119, 93 and 72 points in the output sequences s1(n), z1(n) and z2(n) are used as the initial values ​​of the three cascaded filters in the second segment.

[0050] 4) When the number of segments m ≥ 2, the input sequence of the first-stage FIR filter in the m-th segment is [s m-1 ((end-118):end),s m (n)]. After filtering, the sequence y needs to be removed.m,1 The first 119 data points are extracted, and then the output sequence z is obtained by extracting 16 times the amount of each data point. m,1 At this time, z m,1 It contains 131,072 data points. The input sequence of the second-stage FIR filter in the m-th segment is [z m-1,1 ((end-92):end),z m,1 (n)], the output sequence y after filtering by the second-stage filter m,2 The first 93 data points of the sequence need to be removed, and then the output sequence z is obtained by extracting 16 times the data. m,2 At this time, z m,2 It contains 8192 data points. The input sequence of the third-stage FIR filter in the m-th segment is [z m-1,2 ((end-70):end),z m,2 (n)], the output sequence y after filtering by the third-stage filter m,3 The first 71 data points of the sequence need to be removed, and then the output sequence z is obtained by extracting 4 times the amount of data. m,3 At this time, z m,3 It contains only 2048 data points.

[0051] 5) Discard the final output sequence z obtained from the three-stage cascaded filtering and decimation in the first segment. 1,3 Following the segmentation order, the sequence z from segment 2 to 256 is calculated and cascaded for filtering and extraction. 2,3 z 3,3 ... z 255,3 z 256,3 The data is then concatenated to obtain the final downsampled, complete duration complex baseband IQ data sequence z. At this point, sequence z contains only 524,288 data points.

[0052] 6) Perform time-frequency transformation on the complex baseband IQ data sequence z after downsampling and convert the horizontal and vertical axes of the calculated spectrum to a logarithmic scale to obtain an ultra-fine signal spectrum with a total duration of 1020 seconds and a frequency resolution of RBW = 0.9803922 mHz.

[0053] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements 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 calculating the hyperfine spectrum of a sampled signal, characterized in that, Includes the following steps: Step 1: Sample the modulation signal sequence according to the total sampling duration. T and sampling frequency Calculate the total number of sampling points in the sampling sequence; Step 2: Divide the data into segments based on the preset duration. The sampling sequence is divided into segments of equal duration. Within each segment, the sampling sequence is subjected to digital quadrature downconversion and cascaded filtering decimation to obtain the complex baseband IQ data sequence of the segmented data. For the first m IQ complex baseband data sequence down-converted to zero intermediate frequency within each segment When performing cascaded filtering-decimation processing, if the design The orders of the cascaded low-pass filters are respectively After each stage of filtering, samples are extracted. times, of which, , , ; When segment number At that time, for the first The quadrature downconversion IQ complex baseband data sequence within each segment When performing cascaded filtering-decimation processing, the initial values ​​of the first-stage filter are set to the sequence. The end One data point; that is: in the data block Add sequence before sequence The end From the given data, a new data block sequence is obtained. As the first The input sequence of the first-stage filter within each segment, where ; The output sequence after filtering by the first-stage filter is: Remove the first part of the sequence. Then extract the data. times, to get the first The output sequence after the first-stage filtering and extraction of the segmented data ; No. The first segment of data j The initial value of the first-stage filter is set to the value of the second-stage filter. The first segment of data Level 1 filtering - decimation output sequence The end Data; that is: in the sequence Pre-addition sequence The last From the given data, a new data sequence is obtained. As the current time period j The input data sequence of the stage filter, and the filtered output sequence after deleting this sequence. The former Then extract data points. times, to get the first The first segment of data j Level 1 filtering - decimation output sequence ; Step 3: Concatenate the complex baseband IQ data sequences of each segment according to their sequence numbers to obtain a complete duration complex baseband IQ sequence corresponding to the duration of the original sampling sequence; Step 4: Perform time-frequency transformation on the above complete duration complex baseband IQ sequence to obtain the signal spectrum corresponding to the original sampling sequence. This spectrum has ultra-fine frequency resolution.

2. The method according to claim 1, characterized in that, Sampling frequency in step 1 The requirements of the Nyquist low-pass sampling theorem must be met, i.e. ,in, , These are the center frequency and effective bandwidth of the modulated signal, respectively.

3. The method according to claim 1, characterized in that, In step 2, when segmenting the sampling sequence, it is necessary to ensure data continuity, that is, there should be no duplicate sampling points or missing sampling points in two adjacent segments.

4. The method according to claim 1, characterized in that, In step 2, when performing digital quadrature downconversion on the sampled sequence within each segment, the local oscillator frequency is set to the center frequency of the modulation signal. .

5. The method according to claim 1, characterized in that, In step 2, Considering the initial conditions required by each stage of the filter to filter the input data, the first segment... The filtered-decimated output sequence of the cascaded filter is used as the second segment. Initial values ​​for the cascaded filter; input sequence of the first-stage filter in the first segment. have Given 10 data points, output sequence Extract The sequence is obtained after multiplication. ; Ignoring the initial values ​​of the filter, As the input sequence of the second-stage filter At this time, the sequence Contains One data point; And so on, the input sequence of the last stage filter The output of the previous stage filter is decimated. The output sequence of times The sequence has One data point; within the first segment, the sequence... The last one These points are used as the second segment. Initial values ​​for the cascaded filter; To ensure that the output data sequence of each stage of the filtering-decimation process for the first data segment has enough data points to serve as the initial values ​​for each stage of the filters for the second data segment, the input sequence must... Total points Must meet: For a total duration of Extraction of sampling data The extraction time must be multiplied by a factor of 100 to ensure continuity in the segmented extraction process; that is, the points extracted in time segments and then sequentially spliced ​​together must equal the total duration. The sampling data was directly extracted. If the number of output points is the same as the number of times the output points are multiplied, then the amount of sampled data in each segment is... Conditions must be met: 。 6. The method according to claim 5, characterized in that, In step 3, when concatenating the complex baseband IQ data sequences of each segment according to their sequence numbers, it is necessary to discard the cascaded filtering-decimation output sequence of the first segment. Starting from the second data segment, sequentially... , … , The splicing yielded a complete duration complex baseband IQ sequence with an extremely low data rate. .

7. The method according to claim 6, characterized in that, Step 4: Perform a full-length complex baseband IQ sequence When performing time-frequency transformation to obtain the signal spectrum corresponding to the original sampling series, it is necessary to convert both the horizontal and vertical axes of the spectrum graph to logarithmic scales for display.

8. The method according to claim 1, characterized in that, The data rate of the complex baseband sequence in step 2 must meet the minimum requirements of the Nyquist low-pass sampling theorem.

9. A system for calculating the hyperfine spectrum of a sampled signal, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the method for calculating the ultrafine spectrum of the sampled signal according to any one of claims 1 to 8.

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