Frequency spectrum leakage suppression method based on multi-stage frequency correction

Abstract

The invention discloses a spectrum leakage suppression method based on multi-stage frequency correction, which comprises the following steps of: firstly, carrying out coarse-grained spectrum sensing and component range definition on an original time domain signal to obtain a plurality of initial search intervals; performing frequency fine correction based on a swarm intelligence optimization algorithm on each initial search interval to obtain a corrected frequency value of a sub-resolution level; and then, performing single-frequency-point time domain signal reconstruction on any corrected frequency, performing frequency spectrum value calculation on the reconstructed signal, and finally performing frequency spectrum synthesis on the frequency spectrum value under any corrected frequency to form a high-fidelity complete frequency spectrum.

Description

Technical Field

[0001] This invention belongs to the field of signal processing and spectrum analysis technology, and more specifically, relates to a spectrum leakage suppression method based on multi-stage frequency correction. Background Technology

[0002] Spectrum analysis, a core technology in signal processing, aims to extract key parameters such as frequency, amplitude, and phase of a signal through frequency domain transformation. The Fast Fourier Transform (FFT) has become the mainstream method for spectrum analysis due to its computational efficiency, but its inherent limitations in practical applications are significant. For example, when the signal frequency does not strictly satisfy the synchronization conditions of the sampling theorem (such as non-integer period truncation or frequency misalignment with the frequency resolution interval), energy diffusion (i.e., spectral leakage) occurs in the FFT spectrum, causing the main lobe energy to disperse to the side lobes. This not only reduces the accuracy of amplitude estimation but may also lead to misjudgments of false frequency components. Furthermore, the discretization characteristic of the FFT means that the spectrum is sampled only at a limited number of frequency points, making it difficult to capture the sub-resolution shift of the true frequency components. This phenomenon, known as the picket fence effect, further exacerbates frequency estimation errors. For complex signal scenarios (such as dense multi-component signals), the side lobe overlap caused by spectral leakage can mask weak signal components. Especially in scenarios with a large dynamic range, the leakage of strong signals may completely overwhelm neighboring weak signals, leading to severe distortion in the spectral representation.

[0003] To address these issues, traditional improvement methods focus on suppressing spectral leakage or improving parameter estimation accuracy. For example, windowing methods suppress sidelobe leakage by applying time-domain windowing (such as the Hanning window and Blackman window), but the choice of window function requires a trade-off between the main lobe width and sidelobe attenuation, and cannot eliminate the frequency resolution loss caused by main lobe widening. Interpolation correction methods improve frequency estimation accuracy based on amplitude or phase interpolation near the peak frequency of the FFT (such as the Rife-Vincent algorithm and the phase difference method), however, these methods rely on ideal assumptions about the signal model (such as single-frequency components and low-noise environments), making them less adaptable to multi-component or high-noise scenarios. Parametric model methods (such as the ESPRIT and MUSIC algorithms) employ time-domain parameter estimation methods based on the signal model, which theoretically can avoid the spectral leakage problem; however, they have high computational complexity and are sensitive to model mismatch (such as noise models and incorrect estimation of the number of signal sources), making them difficult to meet real-time processing requirements. In addition, optimization methods based on global search strategies such as genetic algorithms and particle swarm optimization (PSO) can improve the accuracy of frequency estimation, but traditional implementations require searching in the entire frequency domain, which is computationally inefficient and prone to getting trapped in local optima in multi-component scenarios.

[0004] Overall, existing technologies still face numerous bottlenecks: high-precision parameter estimation often relies on complex iterative optimization or modeling processes, making it difficult to meet real-time processing requirements; insufficient suppression of strong signal leakage leads to the failure of weak signal detection, limiting dynamic range performance; parameter estimation errors accumulate during time-frequency domain conversion, further exacerbating signal reconstruction distortion. Therefore, how to achieve high-precision, low-distortion spectral leakage suppression under limited computing resources, while simultaneously considering multi-component signal separation and dynamic range adaptability, has become a pressing technical challenge in the field of spectrum analysis. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a spectrum leakage suppression method based on multi-stage frequency correction. This method achieves sub-resolution frequency correction by using coarse-grained spectrum sensing to constrain the search space, dynamic optimization by swarm intelligence algorithms, parameter decoupling of similarity algorithms, and spectrum shifting to eliminate interference. While ensuring computational efficiency, this method significantly improves the accuracy and robustness of spectrum analysis, providing an innovative solution for high-fidelity spectrum reconstruction in complex scenarios.

[0006] To achieve the above-mentioned objective, the present invention provides a spectral leakage suppression method based on multi-stage frequency correction, characterized by comprising the following steps:

[0007] (1) Acquire the original time-domain signal;

[0008] (2) Coarse-grained spectrum sensing and component range definition to obtain the initial search interval;

[0009] (3) Perform frequency fine correction on each initial search interval based on swarm intelligence optimization algorithm;

[0010] (4) Signal parameter calculation and component reconstruction;

[0011] (5) Obtaining the spectrum value;

[0012] (6) Spectrum synthesis to form a high-fidelity complete spectrum.

[0013] The objective of this invention is achieved as follows:

[0014] This invention relates to a spectral leakage suppression method based on multi-stage frequency correction. First, coarse-grained spectral sensing and component range definition are performed on the original time-domain signal to obtain multiple initial search intervals. Then, frequency fine correction based on a swarm intelligence optimization algorithm is performed on each initial search interval to obtain sub-resolution corrected frequency values. Next, time-domain signal reconstruction is performed on any corrected frequency, and the spectral value is obtained from the reconstructed signal. Finally, the spectral values ​​at any corrected frequency are synthesized to form a high-fidelity complete spectrum.

[0015] Meanwhile, the spectral leakage suppression method based on multi-stage frequency correction of this invention also has the following beneficial effects:

[0016] (1) This invention determines the frequency domain distribution range of signal components through FFT coarse-grained spectrum sensing, and uses swarm intelligence optimization algorithm to dynamically optimize the frequency components, thereby achieving sub-resolution level frequency fine correction.

[0017] (2) The present invention uses a similarity algorithm to calculate the amplitude and phase parameters of the corrected frequency components to ensure the integrity of the time-domain signal reconstruction;

[0018] (3) The present invention eliminates the spectral overlap interference between components by independently extracting the time-domain signal components and performing spectrum shifting operations. Attached Figure Description

[0019] Figure 1 This is a flowchart of the spectrum leakage suppression method based on multi-stage frequency correction of the present invention;

[0020] Figure 2 This is a waveform diagram of a time-domain signal;

[0021] Figure 3 It is a spectral energy distribution characteristic map of a time-domain signal;

[0022] Figure 4 This is a schematic diagram of the auxiliary sequence;

[0023] Figure 5 It is the fitness function value curve of the frequency candidate set;

[0024] Figure 6 It is the initial velocity trajectory of the particle;

[0025] Figure 7 It is the particle motion velocity trajectory after the first round of updates;

[0026] Figure 8 This is the frequency candidate set after the first round of updates;

[0027] Figure 9 This is the fitness function value curve after the first round of updates;

[0028] Figure 10 This is a schematic diagram of the noise floor signal;

[0029] Figure 11 This is the spectrum of the noise floor signal after the first iteration;

[0030] Figure 12 This is the time-domain noise spectrum after the second iteration;

[0031] Figure 13 This is the time-domain noise spectrum after the third iteration;

[0032] Figure 14 This is the time-domain noise spectrum after the last iteration;

[0033] Figure 15 This is a complete spectrum diagram;

[0034] Figure 16 This is a comparison chart of the complete spectrum after processing by the present invention and the traditional method. Detailed Implementation

[0035] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be particularly noted that in the following description, detailed descriptions of known functions and designs that might obscure the main content of the invention will be omitted here.

[0036] Example

[0037] In this embodiment, as Figure 1 As shown, the present invention provides a spectral leakage suppression method based on multi-stage frequency correction, comprising the following steps:

[0038] (1) Let the time-domain signal being analyzed be S = [s1, s2, ..., s2]. m ,…,s M ], where s m This represents the m-th sample value, where M is the total number of sample points;

[0039] In this embodiment, it is assumed that the waveform of the time-domain signal being analyzed is as follows: Figure 2 As shown, its frequency components include: 100MHz, 102MHz, 1GHz, 3.8GHz, 5GHz, and 6GHz, with corresponding amplitudes of 1.0, 2.0, 3.0, 2.0, 1.0, and 4.0, and phases (in radians) of 0, 0.2, 0.8, 1.0, 1.5, and 0, respectively. The number of sampling points is 16kpts, and the sampling rate is 20GSPS.

[0040] (2) Coarse-grained spectrum sensing and component range definition;

[0041] (2.1) Perform a Fast Fourier Transform on the time-domain signal S to obtain the spectral energy distribution characteristic map, as shown below. Figure 3 As shown;

[0042] (2.2) Set the noise energy threshold τ in the frequency domain, which is set to 120dB in this example;

[0043] (2.3) Traverse the spectral energy distribution feature map, count all frequency components whose spectral energy is greater than or equal to the noise energy threshold τ, and then take a continuous frequency component as an initial search interval, resulting in a total of N initial search intervals, denoted as:

[0044]

[0045] Among them, f n Let fmin represent any frequency point in the nth initial search interval. n fmax n ] represents the upper and lower limits of the nth initial search interval;

[0046] In this embodiment, as Figure 3 As shown, there are a total of 6 intervals: [0, 1220703.12], [84228515.62, 112304687.50], [986328125.00, 1009521484.38], [3798828125.00, 3801269531.25], [5000000000.00, 5001220703.12], [5981445312.50, 6011962890.62];

[0047] (3) Perform frequency fine correction on each initial search interval based on swarm intelligence optimization algorithm;

[0048] (3.1) For any initial search interval [fmin] n fmax n Initialize P candidate frequencies, each candidate frequency satisfying: in, Indicates the frequency of the p-th candidate;

[0049] In this embodiment, taking the first interval [0, 1220703.12] as an example, 200 candidate frequencies are first generated in a uniform distribution manner; other intervals are similar and will not be listed again.

[0050] (3.2) Calculate each candidate frequency fitness function value

[0051] (3.2.1) Generate two auxiliary sequences of length M;

[0052]

[0053] Among them, the m-th element satisfy: F s Let S be the sampling rate of the time-domain signal S;

[0054] In this embodiment, two auxiliary sequences are generated for each candidate frequency, each with a length of 16 Kpts. Taking frequency point 1220703.12Hz as an example, the generated sequences are... Figure 4 The two auxiliary sequences shown are:

[0055]

[0056] Where m = 1, 2, ..., 16384

[0057] (3.2.2) Constructing complex sequences based on two auxiliary sequences Among them, the m-th element satisfy:

[0058] Continuing with the frequency 1220703.12Hz as an example, multiply the two sequences from the previous step by the original signal frequency, and then use these as the real and imaginary parts to form a new complex number sequence:

[0059]

[0060] (3.2.3) For each complex element Calculate the modulus, then sum all the moduli to obtain the candidate frequencies. fitness function value Finally, the fitness function values ​​of the frequency candidate set uniformly distributed between [0, 1220703.12] are obtained, as follows: Figure 5 As shown;

[0061] (3.3) Based on P fitness function values and the corresponding candidate frequencies A swarm intelligence algorithm is used for iterative optimization to obtain sub-resolution level corrected frequency values.

[0062] The following describes the iterative optimization process of the swarm intelligence algorithm:

[0063] In this embodiment, the swarm intelligence algorithm includes, but is not limited to, particle swarm optimization, simulated annealing, and tuna swarm optimization; first, the number of iterations T is determined, and in this example, it is set to 100;

[0064] In the first iteration, based on P fitness function values and the corresponding candidate frequencies The new P frequency points are calculated using an iterative algorithm. Then, this is used as a new candidate frequency set and substituted back into step (3.2) to calculate the corresponding P fitness function values.

[0065] Similarly, in the t-th iteration, based on the previous iteration... and corresponding Calculate the new P frequency points and the corresponding fitness function value This process repeats until the Tth round of calculation is completed, yielding the result. With the corresponding Then in all Find the largest one, and its corresponding This refers to the final output of sub-resolution level precise frequency estimates.

[0066] Taking the particle swarm optimization algorithm as an example, in the first iteration, additional auxiliary parameters are needed: inertia weight w, learning factors c1 and c2, and random initial velocity at each frequency point. In this example, the inertia weight w = 1, the learning factors c1 = 2.0, c2 = 2.0, and the random initial velocity at each frequency point are set. like Figure 6 As shown;

[0067] Then combine Figure 5 Find the maximum value among P fitness functions and assign its corresponding value to the maximum value. As the group's best pbest1 and historical best gbest; in this example, the maximum value is 0.0576, corresponding to a frequency of 0Hz, and all group best pbest1 and historical best gbest are 0Hz;

[0068] Next, the velocity at each frequency point is calculated using the formula:

[0069]

[0070] Where r1 and r2 are uncorrelated random values ​​between 0 and 1, generated randomly for each calculation.

[0071] In this embodiment, the updated particle velocity is as follows: Figure 7 As shown, a new set of frequency points is then iterated using the formula:

[0072]

[0073] In this embodiment, the frequency candidate set after the first round of updates is as follows: Figure 8 As shown, step (3.2) is then used to calculate P items. corresponding like Figure 9 As shown;

[0074] Similarly, in the t-th iteration, the frequency point with the maximum fitness function value in the previous iteration is first denoted as pbest. t All previous pbest t The frequency point corresponding to the maximum fitness function value is updated to gbest, and then the motion velocity of each frequency point is updated using the following formula:

[0075]

[0076] Then, the frequency value of the t-th round is obtained through iteration:

[0077]

[0078] After T iterations, gbest is the final sub-resolution frequency estimate.

[0079] In this example, after 100 iterations, gbest = 0, meaning the sub-resolution frequency estimate for the interval [0, 1220703.12] is...

[0080] Similarly, the above process is applied to each interval, and the frequency estimate for each interval is obtained:

[0081] The frequency corresponding to [0,1220703.12] is 0Hz;

[0082] The frequency corresponding to [[84228515.62,112304687.50] is 102005388.27Hz;

[0083] The frequency corresponding to [986328125.00,1009521484.38] is 999964421.72Hz;

[0084] The frequency corresponding to [3798828125.00,3801269531.25] is 3799993620.45Hz;

[0085] The frequency corresponding to [5000000000.00,5001220703.12] is 5000000000.00Hz;

[0086] The frequency corresponding to [5981445312.50,6011962890.62] is 6000001226.84Hz;

[0087] (4) Signal parameter calculation and component reconstruction;

[0088] (4.1) Parameter estimation based on similarity algorithm:

[0089] (4.1.1) For any corrected frequency Constructing a signal model: Among them, C n D n B n The coefficients to be estimated;

[0090] by For example, after substituting into the formula, the signal model is:

[0091] X(t)=C1×sin(2×π×0×t)+D1×cos(2×π×0×t)+B1

[0092] Other frequency values ​​are similar and will not be listed further;

[0093] (4.1.2) Estimation coefficient C n D n B n ;

[0094] Constructing the auxiliary matrix Y n :

[0095]

[0096] Among them, elements element

[0097] by For example, after substituting into the formula, we get: the first column is always 0, and the second column is always 1;

[0098] Other frequency values ​​are similar and will not be listed further;

[0099] (4.1.3) Set vector λ = [C n D n B n Solving the least squares problem using the Moore-Penrose pseudo-inverse: solving λ×Y n =Sλ×Y n The vector λ in -S yields the coefficients C to be estimated. n D n B n ;

[0100] Substituting each frequency point into the calculation formula in turn, the results are shown in Table 1:

[0101] Frequency (Hz) C D B 0 0 0.0581 0 102005388.27 1.8892 0.2165 -0.0069 999964421.72 1.8821 2.3306 -0.0074 3799993620.45 1.0531 1.7008 -0.0074 5000000000.00 0.0708 0.9976 -0.0074 6000001226.84 4.0002 -0.0126 -0.0073

[0102] Table 1

[0103] (4.2) Time-domain signal reconstruction;

[0104] (4.2.1) Time-domain signal reconstruction at a single frequency point;

[0105] For any corrected frequency According to coefficient C n D n B n Calculate the corresponding amplitude A n With phase

[0106]

[0107] Substitute each frequency obtained from step 3.3 into the above steps to obtain the amplitude and phase of each frequency, as shown in Table 2.

[0108] Frequency (Hz) Amplitude (V) phase 0 0.06 1.57° 102005388.27 1.90 0.11° 999964421.72 3.00 0.89° 3799993620.45 2.00 1.02° 5000000000.00 1.00 1.50° 6000001226.84 4.00 -0.00°

[0109] Table 2

[0110] According to amplitude A n With phase Generate each frequency point Ideal time-domain waveform in,

[0111] (4.2.2) Temporal decomposition of noise floor;

[0112] Let the ideal time-domain waveform sequence at N frequency points be: [X1, X2, ..., X n ,…,X N ];

[0113]

[0114] By successively subtracting the ideal time-domain waveforms of each component from the original time-domain signal S, we obtain... Figure 10 The noise floor signal X shown R :

[0115]

[0116] in,

[0117] (4.3) Verification of background noise effectiveness;

[0118] (4.3.1) Using the noise floor signal X R Based on this, the noise floor signal X is processed according to step (2). R Perform energy detection; if the noise floor signal X R If the spectral energy distribution of X is all less than the noise energy threshold τ, then it indicates that the noise floor signal X is... R If valid, the iterative decomposition ends, proceed to step (5); otherwise, the noise floor signal X is...R Substituting the time-domain signal into step (2) yields N1 new initial search spaces. Then, following step (3), N1 sub-resolution level corrected frequency values ​​are obtained from these N1 search spaces. Next, generate N1 ideal time-domain waveforms according to steps (4.1) and (4.2). This leads to the decomposition of new noise signals.

[0119] The signal spectrum after the first iteration is as follows: Figure 11 As shown, three search intervals were obtained: [97656250.00, 101318359.38], [102539062.50, 103759765.62], and [1000976562.50, 1002197265.62].

[0120] The solution yields three frequency values: 99974972.52Hz, 102539062.50Hz, and 1000976562.50Hz.

[0121] The amplitude and phase of the signal are then obtained as shown in Table 3, and the new signal noise is obtained as follows: Figure 12 As shown;

[0122] Frequency (Hz) Amplitude (V) phase 99974972.52 0.97 0.07° 102539062.50 0.11 -0.19° 1000976562.50 0.11 -1.71°

[0123] Table 3

[0124] (4.3.2) Using the noise floor signal Using this as a baseline, return to step (4.3.1) to continue the iterative decomposition until the noise floor signal obtained in the last round of decomposition is obtained. Once all spectral energies are less than the noise energy threshold τ, the iterative decomposition ends, and we proceed to step (5).

[0125] Assuming that after a total of K rounds of iterative decomposition, the spectral energy of the noise floor signal is always less than the noise energy threshold τ, then the ideal time-domain waveform set at each round of decomposition is represented as:

[0126]

[0127] The final noise floor signal is Where k represents the decomposition round number;

[0128] In this example, after one more iteration, the signal and noise signals meet the requirements. The decomposed signal has a frequency of 101459445.67 Hz, an amplitude of 0.12, and a phase of 2.44°. The final signal and noise spectrum is shown below. Figure 13 As shown;

[0129] (5) Obtaining the spectrum value;

[0130] (5.1) Estimation of ideal spectrum value:

[0131] For any decomposed signal component Frequency of use The local oscillator signal is digitally mixed to obtain the mixed signal. in, This represents the m-th component after mixing;

[0132] For mixing signals Perform DFT operations to extract the spectral value at zero frequency, and use it as a signal component. At frequency f n Ideal spectral value

[0133] The final decomposed frequency points and their corresponding ideal amplitude values ​​(complex numbers) are shown in Table 4.

[0134] Frequency (GHz) <![CDATA[Ideal spectral value (10 4 )]]> 0 0.0000+0.0952i 0.1020 1.5466+0.1779i 1.0000 1.5418+1.9096i 3.8000 0.8627+1.3933i 5.0000 0.0580+0.8172i 6.0000 3.2768-0.0104i 0.1000 0.7925+0.0544i 0.1025 0.0877-0.0164i 1.0010 -0.0133-0.0919i 0.1015 -0.0744+0.0629i

[0135] Table 4

[0136] (5.2) Estimation of the true spectrum value;

[0137] Similarly, the noise floor signal is obtained according to step (5.1). At frequency Noise spectrum value at Then the ideal spectrum value and Adding them together, we obtain the original time-domain signal S at the frequency point. The true spectral value at the location

[0138]

[0139] The final true spectrum values ​​(absolute values) are shown in Table 5:

[0140]

[0141]

[0142] Table 5

[0143] (6) Spectrum synthesis;

[0144] (6.1) Calculate the noise floor spectrum;

[0145] For the noise floor signal Perform FFT operation to obtain the noise floor signal spectrum S R ,like Figure 14 As shown;

[0146] Record the spectrum S of the background noise signal in sequence. R The frequency points are arranged into a frequency point sequence. Among them, the m-th frequency point

[0147] (6.2) Complete spectrum synthesis;

[0148] The spectrum of all signal components obtained in step (5) Inserting the noise signal spectrum S R In this process, the frequency sequence is arranged in ascending order based on the magnitude of the frequency values.

[0149]

[0150] in, if With a certain frequency point If they are equal, use them directly. Replace S R The corresponding spectral value;

[0151] Ultimately, a high-fidelity complete spectrum is formed:

[0152]

[0153]

[0154] Table 6

[0155] In this embodiment, based on the parameters in Table 6, the traditional method (Blackman window function method) exhibits unstable frequency error, reaching MHz levels when adjacent frequency points are close together; for example... Figure 16 As shown, the multi-stage calibration frequency method proposed in this patent can keep the frequency error within ±50KHz. Especially at adjacent frequency points, the Blackman window function method can no longer distinguish between the two frequency points (100MHz and 102MHz). The two frequencies are interfered with by each other's spectral leakage, turning into a thick spectral line. However, the method proposed in this patent can still distinguish between the two frequency points, and the spectral line of the frequency point without energy drops significantly (120dB+).

[0156] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A method of spectral leakage suppression based on multi-stage frequency correction, characterized in that, The method comprises the following steps: (1) collecting time domain signals to be analyzed; (2) performing coarse-grained spectrum sensing and component range definition on the time domain signals to obtain a plurality of initial search intervals; (3) performing frequency fine correction based on a swarm intelligence optimization algorithm for each initial search interval; (4) performing signal parameter solving and component reconstruction based on the corrected frequency value; (5) calculating spectrum values; (6) spectrum synthesis to obtain a complete spectrum with high fidelity.

2. The method of spectral leakage suppression based on multi-stage frequency correction according to claim 1, characterized in that, The method for coarse-grained spectrum sensing and component range definition in step (2) is as follows: (2.1) Let the time-domain signal being analyzed be S = [s1, s2, ..., s2]. m ,…,s M ], where s m Let m represent the m-th sampled value, and M be the total number of sampled points; perform a Fast Fourier Transform on the time-domain signal S to obtain the spectral energy distribution characteristic map; (2.2) setting a noise energy threshold τ of the frequency domain; (2.3) traversing the spectrum energy distribution feature map, counting all frequency components with spectrum energy greater than or equal to the noise energy threshold τ, and then taking a continuous frequency component as an initial search interval, a total of N initial search intervals, denoted as: where f n represents any frequency point in the nth initial search interval, [fmin n , fmax n ] represents the upper and lower limits of the nth initial search interval.

3. The method of spectral leakage suppression based on multi-stage frequency correction according to claim 1, wherein, The specific method for frequency fine correction based on the swarm intelligence optimization algorithm in step (3) is as follows: (3.1), for any one initial search interval [fmin n ,fmax n ], initialize P candidate frequencies, each of which satisfies: wherein f denotes the pth candidate frequency; (3.2) calculating a fitness function value for each candidate frequency ​ (3.2.1) randomly generating two auxiliary sequences with a length of M; wherein the mth element satisfies: F s is the sampling rate of the time-domain signal S; (3.2.2), constructing a complex sequence based on two auxiliary sequences where the mth element satisfies: (3.2.3), for each complex element modulus, and summing all the moduli as the fitness function value of the candidate frequency (3.3) from P fitness function values and the corresponding candidate frequencies iterative optimization using swarm intelligence algorithms to obtain sub-resolution level corrected frequency values 4. The method of spectral leakage suppression based on multi-stage frequency correction of claim 1, wherein, The method for signal parameter solving and component reconstruction in step (4) is as follows: (4.1) parameter estimation based on a similarity algorithm: (4.1.1) for any corrected frequency Constructing the signal model: where C n , D n , B n are the coefficients to be estimated; (4.1.2), the estimation coefficient C n , D n , B n ; Constructing the auxiliary matrix Y n : wherein the elements element (4.1.3), set vector λ = [C n ,D n ,B n ] and solve the least square problem by Moore-Penrose pseudo-inverse: solve vector λ in λ x Y n = S to get the coefficients C n ,D n ,B n to be estimated; (4.2) time domain signal reconstruction; (4.2.1) time domain signal reconstruction of a single frequency point; For any corrected frequency According to the coefficient C n , D n , B n Calculate the corresponding amplitude A n And phase According to the amplitude A n with the phase generating the ideal time-domain waveform of each frequency point wherein, (4.2.2) time domain decomposition of the noise floor; The ideal time-domain waveform sequence at N frequency points is: [X1, X2, …, XN]. n ,…,X N ] Subtracting the ideal time-domain waveforms of the components from the original time-domain signal S in turn, a bottom noise signal X is obtained R : wherein (4.3) noise floor effectiveness check; (4.3.1), the noise floor signal X R is taken as the reference, the noise floor signal X R is subjected to energy detection, if the spectral energy distribution of the noise floor signal X R is less than the noise energy threshold τ, it indicates that the noise floor signal X R is valid, the iterative decomposition ends, and step (5) is entered; otherwise, the noise floor signal X R is substituted into step (2) as the time domain signal, and N1 new initial search spaces are obtained, then N1 corrected frequency values of the sub-resolution level are obtained from the N1 search spaces according to step (3) then N1 ideal time domain waveforms are generated according to steps (4.1), (4.2) and a new noise floor signal is decomposed (4.3.2), the noise floor signal As a reference, return to step (4.3.1) to continue the iterative decomposition until the last round of decomposition of the noise floor signal meets the spectral energy threshold τ, the iterative decomposition ends, and enters step (5); Assuming that the spectrum energy of the noise floor signal satisfies the condition that all spectrum energies are less than the noise energy threshold τ after K rounds of iterative decomposition, the ideal time domain waveform set at each round of decomposition is denoted as: The final noise floor signal is where k denotes the decomposition pass number.

5. The method of spectral leakage suppression based on multi-stage frequency correction according to claim 1, wherein, The method for calculating spectrum values in step (5) is as follows: (5.1) ideal spectrum value estimation: For any decomposed signal component using a local oscillator signal with a frequency of to obtain a mixed signal wherein, denotes the mth component after mixing. DFT operation is performed on the mixed signal to extract the spectral value at zero frequency and as a signal component The ideal spectral value at frequency point ​ (5.2) real spectrum value estimation; Similarly, the noise floor signal is obtained according to step (5.1) The noise spectrum value at frequency point is obtained The ideal spectrum value is then added to to obtain the real spectrum value of the original time-domain signal S at frequency point is obtained 6. The method of spectral leakage suppression based on multi-stage frequency correction according to claim 1, wherein, The method for spectrum synthesis in step (6) is as follows: (6.1) calculating the noise floor spectrum; Noise signal FFT operation is performed to obtain noise signal spectrum S R ; sequentially recording a noise floor signal spectrum S R each of the frequency points, to form a frequency point sequence wherein the mth frequency point (6.2) complete spectrum synthesis; all the signal component spectrums obtained in step (5) inserting the noise floor signal spectrum S R In this way, the entire sequence of frequency points still conforms to the arrangement order from small to large according to the size of the frequency value: wherein, If the frequency point is equal, directly use the corresponding spectrum value in R to replace S Ultimately, a high-fidelity full spectrum is formed:

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