FID signal frequency estimation method and system based on improved interpolation DFT

Abstract

The application discloses an FID signal frequency estimation method and system based on improved interpolation DFT, and relates to the technical field of signal processing.The application adds a maximum sidelobe attenuation window to an input signal, derives an initial frequency estimation value under the condition of considering negative spectrum components, and significantly reduces the interference of negative spectrum leakage on frequency estimation on the basis of the initial frequency estimation value; on the basis, the application is no longer limited to discrete integer frequency points, but uses a discrete time Fourier transform (DTFT) to perform spectrum interpolation, thereby effectively alleviating the inherent fence effect of a fast Fourier transform (FFT), and making the frequency estimation no longer limited to the discrete interval of spectrum lines. A high-precision frequency estimation model further constructed can maintain consistent estimation performance in a full frequency band, and overcomes the defects of the existing IpDFT method that the precision fluctuates due to frequency changes. Therefore, higher estimation precision, smaller negative spectrum residual influence, and stronger robustness in a full frequency band can be realized in a complex electromagnetic environment.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and in particular relates to a method and system for estimating the frequency of FID signals based on improved interpolation DFT. Background Technology

[0002] In optically pumped atomic magnetometers, the measured magnetic field is directly related to the free induction decay (FID) signal generated in the alkali metal atom gas cell. The FID signal is a typical exponentially decaying sinusoidal signal, and its oscillation frequency (Larmer frequency) is proportional to the external magnetic field strength. Therefore, high-precision magnetic field measurement can be achieved by accurately estimating the frequency of the FID signal. However, in actual measurement environments, the FID signal is usually accompanied by strong background noise, magnetic field gradient variations, and harmonic / interharmonic interference. Furthermore, the signal itself exhibits exponential decay characteristics, and its damping factor reflects factors such as magnetic field homogeneity. This necessitates that the frequency estimation method possess strong anti-interference capabilities, insensitivity to attenuation, and stable estimation accuracy across the entire frequency band.

[0003] The Hilbert (HT) frequency meter uses a weighted linear fitting method to calculate frequency. However, this method suffers significant accuracy degradation under conditions of strong magnetic field gradients, high background noise, and signals containing harmonic and interharmonic components. This makes it difficult for the magnetometer to achieve fast and stable closed-loop control, rendering it unsuitable for complex electromagnetic environments. Therefore, this study introduces the Discrete Fourier Transform (DFT), which offers better anti-interference performance, to improve the frequency meter. However, the traditional Fourier Transform is still significantly limited in frequency estimation accuracy due to the picket fence effect and negative spectral leakage.

[0004] In addition, existing interpolation DFT (IpDFT) methods use several spectral lines from the Discrete Fourier Transform (DFT) to interpolate and estimate signal frequencies. Although the IpDFT algorithm considers the influence of negative spectral components, improving estimation accuracy to some extent, it interpolates based on integer-indexed spectral points (i.e., discrete frequency points). The positions of the spectral lines used are limited by the inherent picket-fence effect of the FFT, leading to an inherent approximation error in the interpolation model regarding the offset (i.e., fractional frequency) between the actual signal frequency and the discrete spectral lines. Furthermore, even if the model considers the negative spectrum, existing IpDFT methods struggle to completely eliminate long-range spectral leakage caused by negative frequency components, especially in short sampling sequences or low signal frequencies, where the influence of the negative spectrum remains significant. These limitations cause the estimation accuracy of the IpDFT method to fluctuate with changes in the actual signal frequency, exhibiting strong frequency dependence and making it difficult to maintain consistent performance across the entire frequency band. Therefore, existing IpDFT methods are not suitable for complex electromagnetic scenarios requiring high frequency estimation accuracy and where signal frequencies may change. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a method and system for estimating the frequency of FID signals based on improved interpolation DFT, which can achieve higher accuracy and stronger robustness in frequency estimation of FID signals under complex electromagnetic environments.

[0006] The first aspect discloses a method for estimating the frequency of an FID signal based on an improved interpolation DFT, the method comprising:

[0007] A first FID signal with N sampling points is acquired, where N is an integer greater than 1. A first maximum sidelobe attenuation window function is applied to the first FID signal and a discrete Fourier transform is performed to obtain the spectrum function of the first FID signal. The maximum spectral point of the spectrum function of the first FID signal and the spectral values ​​corresponding to its adjacent spectral points are substituted into a first preset parameter solution model to obtain an initial estimated frequency. A second maximum sidelobe attenuation window function is applied to the second FID signal and a discrete-time Fourier transform is performed to obtain the spectrum function of the second FID signal, where the second FID signal is obtained by subtracting the negative spectral leakage component from the first FID signal. The spectral points corresponding to the initial estimated frequency and the spectral values ​​corresponding to the spectral points offset by a preset spectral interval relative to the initial frequency are substituted into a second preset parameter solution model to obtain a second estimated frequency. The final signal frequency is obtained based on the second estimated frequency.

[0008] The second aspect discloses an FID signal frequency estimation system based on improved interpolation DFT, the system comprising:

[0009] The FID signal acquisition module is used to acquire a first FID signal including N sampling points, where N is an integer greater than 1; the first windowing transformation module is used to apply a first maximum sidelobe attenuation window function to the first FID signal and perform a discrete Fourier transform to obtain the spectrum function of the first FID signal; the initial estimated frequency solution module is used to substitute the maximum spectral point of the spectrum function of the first FID signal and the spectral values ​​corresponding to its adjacent spectral points into a first preset parameter solution model to obtain an initial estimated frequency; the second windowing transformation module is used to apply a second maximum sidelobe attenuation window function to the second FID signal and perform a discrete-time Fourier transform to obtain the spectrum function corresponding to the second FID signal, where the second FID signal is obtained by subtracting the negative spectral leakage component from the first FID signal; the second estimated frequency solution module is used to substitute the spectral points corresponding to the initial estimated frequency and the spectral values ​​corresponding to the spectral points offset by a preset spectral interval relative to the initial frequency into a second preset parameter solution model to obtain a second estimated frequency; and the signal frequency acquisition module is used to obtain the final signal frequency based on the second estimated frequency.

[0010] As can be seen from the above technical solutions, the present invention has the following beneficial effects:

[0011] This invention differs from the traditional IpDFT framework in principle. First, it applies a Maximum-Sidelobe-Decay (MSD) window to the input signal, deriving the initial frequency estimate while considering negative spectral components, thus significantly reducing the interference of negative spectral leakage on frequency estimation. Furthermore, it is no longer limited to discrete integer frequencies but uses Discrete-Time Fourier Transform (DTFT) for spectral interpolation, effectively mitigating the picket-fence effect inherent in Fast Fourier Transform (FFT) and freeing frequency estimation from the constraints of spectral line spacing. The further constructed high-precision frequency estimation model maintains consistent estimation performance across the entire frequency band, overcoming the accuracy fluctuations caused by frequency variations in existing IpDFT methods. Since DFT can be efficiently implemented using Fast Fourier Transform (FFT), it facilitates real-time computation on the ZYNQ embedded system platform, significantly improving the system's anti-interference capability while ensuring frequency calculation accuracy. This results in higher estimation accuracy, less residual negative spectral influence, and stronger robustness across the entire frequency band in complex electromagnetic environments. Attached Figure Description

[0012] Figure 1 The flowchart of an FID signal frequency estimation method based on improved interpolation DFT provided by the present invention is shown.

[0013] Figure 2 This is a comparison chart of the mean square error of the present invention, HT, and IpDFT at different frequencies.

[0014] Figure 3 The graph shows a comparison of the mean square error of the present invention, HT, and IpDFT under different SNRs.

[0015] Figure 4 The graph shows a comparison of the mean square error of the present invention, HT, and IpDFT under different attenuation factors.

[0016] Figure 5 This is a comparison chart of the mean square error of the present invention, HT, and IpDFT at different frequencies when harmonics are present.

[0017] Figure 6 This invention provides an architecture diagram for an FID signal frequency estimation system based on an improved interpolation DFT. Detailed Implementation

[0018] To make the objectives, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Several embodiments of the present invention are shown in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that the disclosure of the present invention will be thorough and complete.

[0019] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a particular order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0020] It should be noted that when an element is referred to as being "fixed to" another element, it can be directly on the other element or there may be an intervening element. When an element is considered to be "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "left," "right," "up," "down," and similar expressions used herein are for illustrative purposes only and are not intended to indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0021] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances. The term "and / or" as used herein includes any and all combinations of one or more of the related listed items.

[0022] In one embodiment, the present invention provides a method for estimating the frequency of an FID signal based on an improved interpolation DFT, such as... Figure 1 As shown, the specific steps include:

[0023] S101. Obtain the first FID signal including N sampling points, where N is an integer greater than 1;

[0024] First, including The first FID signal at each sampling point It can be represented as:

[0025] (1)

[0026] in, Indicates the amplitude of the first FID signal. Indicates the attenuation factor. Indicates frequency, For the initial phase, For noise, Indicates the sampling point index. It can be 2 to the power of m, where m is an integer greater than 1, for example, The value is 2048.

[0027] S102. Apply a first maximum sidelobe attenuation window function to the first FID signal and perform a discrete Fourier transform to obtain the spectrum function of the first FID signal;

[0028] Specifically, ignoring noise, a first maximum sidelobe attenuation window function is applied to the first FID signal, and the first maximum sidelobe attenuation window function is... Perform DFT transformation on each sampling point to obtain the spectrum function of the first FID signal. Specifically, it is expressed as:

[0029] (2)

[0030] in, Indicates spectrum index. This represents the spectral index corresponding to the initial frequency. Represents the imaginary unit. The first maximum sidelobe attenuation window function is shown in the formula:

[0031] (3)

[0032] in, The window function argument is represented by the window function argument. Indicates the type of the window function. This indicates that the window function is a rectangular window. This indicates that the window function is a Hanning window. The choice of window function type is directly related to the acquired FID signal, especially under white noise interference. It has advantages, especially in the presence of harmonic interference. It will have a greater advantage.

[0033] It should be noted that in actual practice, It can have many values, for example It is a Hamming window, and the type of window function can be selected according to actual needs.

[0034] In addition, the first maximum sidelobe attenuation window function with an adjacent spacing index of 1 satisfies the following relationship:

[0035] (4)

[0036] S103. Substitute the maximum spectral point of the spectral function of the first FID signal and the spectral values ​​corresponding to its adjacent spectral points into the first preset parameter solution model to obtain the initial estimated frequency.

[0037] It should be noted that the first preset parameter solution model is an estimation model for the initial estimated frequency. Specifically, the frequency solution process of the first preset parameter solution model includes:

[0038] The first correlation equation is constructed based on the maximum spectral point of the spectral function for the first FID signal and the spectral values ​​corresponding to its adjacent spectral points.

[0039] If the first correlation equation has a solution, a first correlation matrix is ​​obtained, wherein the determinant of the first correlation matrix is ​​0;

[0040] Substituting the preset relationship satisfied by the first maximum sidelobe attenuation window function into the first correlation matrix, a second correlation matrix is ​​obtained, wherein the second correlation matrix contains a first complex variable and a second complex variable; the imaginary part of the first complex variable and the second complex variable represents the attenuation factor, the real part of the first complex variable is composed of the negative of the difference between the maximum spectral point and the initial estimated frequency to be determined, and the real part of the second complex variable is composed of the negative of the sum of the maximum spectral point and the initial estimated frequency to be determined;

[0041] The initial estimated frequency is obtained by solving the second correlation matrix.

[0042] Specifically, take the maximum spectral point of formula (2). The first correlation equation is obtained by considering the adjacent spectral points, as shown in the formula:

[0043] (5)

[0044] The first correlation matrix is ​​shown in the formula:

[0045] (6)

[0046] Since the first correlation equation has a solution, the first correlation matrix satisfies:

[0047] (7)

[0048] Substituting formula (4) into formula (7) and simplifying, we obtain the second correlation matrix, as shown in the formula:

[0049] (8)

[0050] In one embodiment, the step of obtaining the initial estimated frequency based on the second correlation matrix specifically includes:

[0051] When the determinant of the second correlation matrix is ​​0, the sum and product of the complex numbers of the first and second variables can be obtained.

[0052] The attenuation factor is obtained by solving the sum of the complex numbers of the first and second variables;

[0053] The initial estimated frequency is obtained by multiplying the complex number of the first variable and the complex number of the second variable.

[0054] Specifically: Let the first variable be a complex number The second variable is a complex number. Then the second correlation matrix satisfies:

[0055] (9)

[0056] From formula (9), we can obtain:

[0057] (10)

[0058] in, , , As an intermediate variable, specifically represented as:

[0059] (11)

[0060] The attenuation factor is thus obtained by solving for it, and is expressed as follows: To distinguish it from the attenuation factor in the previous formula. and initial estimated frequency :

[0061] (12)

[0062] (13)

[0063] in, , , They represent , , . conjugate.

[0064] In one embodiment, the invention further includes:

[0065] Substituting the obtained attenuation factor, initial estimated frequency, and maximum spectral point into the first maximum sidelobe attenuation window function, we obtain the first complex constant.

[0066] Substitute the first complex constant into the spectrum function of the first FID signal, and take the conjugate of both sides of the equation to construct the second correlation equation;

[0067] The amplitude and initial phase of the first FID signal are obtained by solving the second correlation equation.

[0068] Specifically, let The above text is obtained and Substituting into formula (3) yields It is a solveable complex constant. Substituting into formula (2) and taking the conjugate of both sides of the equation, we can obtain the second correlation equation, as shown in the formula:

[0069] (14)

[0070] in, , , They represent respectively to , , Take conjugate.

[0071] The amplitude can be obtained from the above formula. and initial phase Specifically, as shown in the formula:

[0072] (15)

[0073] (16)

[0074] (17)

[0075] It should be noted that the above steps require obtaining the attenuation factor, amplitude, and initial phase of the first FID signal. Therefore, to distinguish the meaning of these three parameters in the first FID signal and their specific values ​​obtained from the final solution, they are referred to here as... This represents the attenuation factor obtained from the final solution. This indicates that the solution yields the magnitude and sum. This represents the initial phase obtained from the solution.

[0076] S104. Apply a second maximum sidelobe attenuation window function to the second FID signal and perform a discrete-time Fourier transform to obtain the spectrum function corresponding to the second FID signal, wherein the second FID signal is obtained by subtracting the negative spectrum leakage component from the first FID signal;

[0077] It should be noted that in the initial frequency estimation above, all three selected points have negative spectral leakage components, and the selection of the three points is affected by the picket fence effect. Therefore, a second-stage frequency estimation is introduced. The interference of negative spectral leakage is subtracted here, and then DTFT interpolation is performed to alleviate the picket fence effect.

[0078] Specifically, the second FID signal in this stage is represented as follows:

[0079] (18)

[0080] At this point, the second FID signal can be approximated as a complex sine wave signal, which can be expressed as:

[0081] (19)

[0082] Performing a discrete-time Fourier transform on equation (19) and then interpolating using DTFT, the spectral function corresponding to the second FID signal is obtained. Specifically, as shown in the formula:

[0083] (20)

[0084] in, Indicates the second estimated frequency index, attenuation factor and initial phase Obtained from step S103, This represents the second maximum sidelobe attenuation window function, as shown in the formula:

[0085] (twenty one)

[0086] S105. Substitute the spectrum points corresponding to the initial estimated frequency and the spectrum points offset by a preset spectrum interval relative to the initial frequency into the second preset parameter solution model to obtain the second estimated frequency.

[0087] It should be noted that the second preset parameter solution model is the estimation model for the second estimated frequency. Specifically, the frequency solution process of the second preset parameter solution model includes:

[0088] Based on the spectral points corresponding to the initial estimated frequency and the spectral points offset by a preset spectral interval relative to the initial estimated frequency, the spectral functions corresponding to the second FID signal are substituted into the first spectral point function, the second spectral point function, and the third spectral point function, respectively; wherein, the initial estimated frequency is represented by the sum of the maximum spectral point and the spectral difference;

[0089] The first ratio function is obtained based on the first spectrum point function and the second spectrum point function, and the second ratio function is obtained based on the first spectrum point function and the third spectrum point function;

[0090] The first ratio function and the second ratio function are simplified according to the first set function to obtain the third ratio function and the fourth ratio function;

[0091] A third correlation equation is constructed based on the third ratio function and the fourth ratio function, wherein the value of the third correlation equation is a preset coefficient, and the preset coefficient is obtained based on a preset spectral interval;

[0092] The third correlation equation is solved according to the type of window function to obtain the second estimated frequency.

[0093] Specifically, let: (twenty two)

[0094] in, This represents the initial estimated frequency and the spectral difference between the maximum spectral point.

[0095] Calculate the first spectral point function Second spectral point function and the third spectral point function Specifically, as shown in the formula:

[0096] (twenty three)

[0097] (twenty four)

[0098] (25)

[0099] in, This represents the preset spectral interval, typically set to 0.1 or 0.5, and its purpose is to mitigate the picket fence effect. .

[0100] Will and and The first ratio function can be obtained by dividing them respectively. Second ratio function :

[0101] (26)

[0102] (27)

[0103] Let the first set function Simplifying formulas (26) and (27) yields the third and fourth ratio functions, as shown in the formulas:

[0104] (28)

[0105] (29)

[0106] This leads to the third correlation equation:

[0107] (30)

[0108] Among them, the preset coefficient This indicates that the three spectral points mentioned above satisfy a coefficient relationship, with preset coefficients. Related to the preset spectral interval t, when t = 0.1, = -0.809016994374947 + 0.587785252292473i, at t = 0.5, =1.

[0109] In one embodiment, the step of solving the third correlation equation according to the type of the window function to obtain the second estimated frequency specifically includes:

[0110] When the type of the window function is greater than 1, the variable of the first setting function is set to the third variable complex number, wherein the real part of the third variable complex number is the attenuation factor, and the imaginary part is the difference between the initial estimated frequency and the second estimated frequency to be determined. The type of the window function greater than 1 indicates the Hanning window.

[0111] Taylor expansions are performed on the first set function and the third and fourth set functions with adjacent offset preset spectral intervals at preset positions, where the preset position indicates that the function variable is equal to the attenuation factor;

[0112] The second estimated frequency is obtained by solving the Taylor expansion formula.

[0113] Specifically, when When the window function is of type rectangular window, it is determined according to the first set function. Obtain the second set function ,at this time .

[0114] Substituting into formula (30) and solving, we get:

[0115] (31)

[0116] At this point, the second estimated frequency can be obtained. :

[0117] (32)

[0118] In one embodiment, the step of solving the third correlation equation according to the type of the window function to obtain the second estimated frequency specifically includes:

[0119] When the type of the window function is greater than 1, the variable of the first setting function is set to the third variable complex number, wherein the real part of the third variable complex number is the attenuation factor, and the imaginary part is the difference between the initial estimated frequency and the second estimated frequency to be determined. The type of the window function greater than 1 indicates the Hanning window.

[0120] Taylor expansions are performed on the first set function and the third and fourth set functions with adjacent offset preset spectral intervals at preset positions, where the preset position indicates that the function variable is equal to the attenuation factor;

[0121] The second estimated frequency is obtained by solving the Taylor expansion formula.

[0122] Specifically, when At that time, this era entered If there is no analytical solution, then the variable of the first setting function is set. Let the third variable be a complex number, that is, let ,make exist Taylor's expansion:

[0123] (33)

[0124] (34)

[0125] (35)

[0126] in, This indicates that the remainder term in the Taylor expansion is negligible. Substituting into formula (30), we get:

[0127] (36)

[0128] S106. Obtain the final signal frequency based on the second estimated frequency.

[0129] The final solution is the frequency of the N-point FID signal. Specifically, as shown in the formula:

[0130] (37)

[0131] in, Sampling rate, This is the second estimated frequency.

[0132] To better illustrate the beneficial effects achieved by the present invention, the present invention will be explained and described below through specific embodiments.

[0133] Using the frequencies in the code as the actual values, 1000 sets of frequencies were continuously calculated in MATLAB. The performance of this invention is measured by the mean squared error (MSE) of HT and IpDFT, which is expressed as follows:

[0134] (38)

[0135] in, The number of frequency groups to calculate, for example, 1000. Indicates the first The true frequency value of the group No. The predicted frequency value of the group.

[0136] Example 1: FID signal initial frequency for Attenuation factor H=1, N=2048, SNR=80dB. For example... Figure 2 As shown, the HT algorithm deviates significantly from the true value at low frequencies. In addition, the accuracy of the HT and IpDFT algorithms varies with frequency. However, the present invention maintains consistent estimation performance across the entire frequency band and is closer to the true value.

[0137] Example 2: FID signal initial frequency Attenuation factor H=1, N=2048, signal-to-noise ratio (SNR) at Change. For example... Figure 3 As shown, the HT method tends to saturate in estimation accuracy when the signal-to-noise ratio (SNR) is below 20 dB, resulting in a significant deviation from the true value. This is because under low SNR conditions, noise causes a shift in the phase difference after the HT transform, leading to a shift in frequency estimation. At high SNR conditions, the accuracy of HT is limited by the number of discrete points (i.e., the value of k), and since the number of discrete points is fixed, its accuracy cannot be further improved. In contrast, this invention exhibits stronger robustness. Furthermore, compared to the existing IpDFT method, the frequency estimation results of this invention are closer to the true value under different noise conditions.

[0138] Example 3: FID signal initial frequency Attenuation factor Changes, H=1, N=2048, SNR=80dB. For example... Figure 4 As shown, compared to HT and IpDFT, the present invention is closer to the true value under different attenuation factors.

[0139] Example 4: FID signal initial frequency Attenuation factor With H=2, N=2048, and SNR=80dB, there exists a second harmonic interharmonic with an amplitude of 0.1 times that of the original signal. Figure 5 As shown, compared to HT and IpDFT, under the condition of harmonics, the present invention has consistent estimation performance across the entire frequency band and is closer to the true value.

[0140] In summary, compared to the Hilbert algorithm, the present invention improves noise immunity by at least 20 dB and exhibits superior performance under both high and low signal-to-noise ratio conditions. Compared to IpDFT, the present invention can obtain estimation results closer to the true values ​​under the same conditions. Furthermore, the present invention demonstrates consistent estimation performance across the entire frequency band and exhibits stronger full-band robustness and higher estimation accuracy in the presence of harmonic interference. Therefore, the present invention is more suitable for FID atomic magnetic field measurement tasks in complex environments.

[0141] This application also provides an estimation system corresponding to the method embodiments described above. Since the system embodiments are basically similar to the method embodiments, the description is relatively simple. For details of the relevant technical features and their effects, please refer to the corresponding descriptions of the method embodiments provided above. This invention provides an FID signal frequency estimation system based on improved interpolation DFT, such as... Figure 6 As shown, the system specifically includes:

[0142] The FID signal acquisition module is used to acquire the first FID signal including N sampling points, where N is an integer greater than 1;

[0143] The first windowing transformation module is used to apply a first maximum sidelobe attenuation window function to the first FID signal and perform a discrete Fourier transform to obtain the spectrum function of the first FID signal.

[0144] The initial frequency estimation module is used to substitute the maximum spectral point of the spectral function of the first FID signal and the spectral values ​​corresponding to its adjacent spectral points into the first preset parameter solution model to obtain the initial estimated frequency.

[0145] The second windowing transformation module is used to apply a second maximum sidelobe attenuation window function to the second FID signal and perform a discrete-time Fourier transform to obtain the spectrum function corresponding to the second FID signal, wherein the second FID signal is obtained by subtracting the negative spectral leakage component from the first FID signal;

[0146] The second estimated frequency solution module is used to substitute the spectral points corresponding to the initial estimated frequency and the spectral values ​​corresponding to the spectral points offset by a preset spectral interval relative to the initial frequency into the second preset parameter solution model to obtain the second estimated frequency.

[0147] The signal frequency acquisition module is used to obtain the final signal frequency based on the second estimated frequency.

[0148] This application also provides an electronic device, which includes a processor and a memory. The memory stores at least one instruction or at least one program, which is loaded and executed by the processor. The method described above provides a method for estimating the frequency of an FID signal based on an improved interpolation DFT.

[0149] Furthermore, the electronic device may participate in or include the apparatus or system provided in the embodiments of this application. The electronic device may include one or more processors (processors may include, but are not limited to, processing devices such as microprocessors (MCUs) or programmable logic devices (FPGAs), memory for storing data, and transmission devices for communication functions. In addition, it may also include: a display, an input / output interface (I / O interface), a universal serial bus (USB) port (which may be included as one of the ports of the I / O interface), a network interface, a power supply, and / or a camera.

[0150] It should be noted that the aforementioned one or more processors and / or other data processing circuits are generally referred to herein as "data processing circuits". These data processing circuits can be implemented wholly or partially as software, hardware, firmware, or any other combination. Furthermore, the data processing circuits can be a single, independent processing module, or wholly or partially integrated into any other element within a device (or mobile device). As involved in the embodiments of this application, the data processing circuit serves as a processor control mechanism (e.g., selection of a variable resistor termination path connected to an interface).

[0151] The memory can be used to store software programs and modules of application software, such as the program instructions / data storage device corresponding to the method described in the embodiments of this application. The processor executes various functional applications and data processing by running the software programs and modules stored in the memory, thereby realizing the above-mentioned data processing method. The memory may include high-speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some instances, the memory may further include memory remotely located relative to the processor, and these remote memories can be connected to electronic devices via a network. Examples of the above-mentioned networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0152] The transmission device is used to receive or send data via a network. Specific examples of the network described above may include a wireless network provided by the device's communication provider. In one example, the transmission device includes a Network Interface Controller (NIC), which can connect to other network devices via a base station to communicate with the Internet. In another example, the transmission device may be a Radio Frequency (RF) module, used for wireless communication with the Internet.

[0153] The display can be, for example, a touchscreen liquid crystal display (LCD), which allows users to interact with the user interface of an electronic device (or mobile device).

[0154] This application also provides a computer storage medium storing at least one instruction or at least one program, which is loaded and executed by a processor to implement the FID signal frequency estimation method based on improved interpolation DFT provided in the above method embodiment.

[0155] Optionally, in this embodiment, the aforementioned computer storage medium may be located at at least one of the multiple network servers in a computer network. Optionally, in this embodiment, the aforementioned storage medium may include, but is not limited to, various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0156] This application also provides a computer program product or computer program that includes computer instructions stored in a computer storage medium. The processor of an electronic device reads the computer instructions from the computer storage medium and executes the computer instructions, causing the electronic device to perform the FID signal frequency estimation method based on improved interpolation DFT provided in the above-described method embodiment.

[0157] It should be noted that the order of the embodiments described above is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. Furthermore, specific embodiments have been described above. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps described in the claims can be performed in a different order than that shown in the embodiments and still achieve the desired result. Additionally, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0158] It should be understood that the above description of the preferred embodiments is quite detailed, but it should not be considered as a limitation on the scope of protection of this invention. Those skilled in the art, under the guidance of this invention, can make substitutions or modifications without departing from the scope of protection of the claims of this invention, and all such substitutions or modifications fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for estimating the frequency of an FID signal based on an improved interpolation DFT, characterized in that, The method includes: Obtain the first FID signal, which includes N sampling points, where N is an integer greater than 1; Apply a first maximum sidelobe attenuation window function to the first FID signal and perform a discrete Fourier transform to obtain the spectrum function of the first FID signal; The process involves substituting the maximum spectral point of the spectral function of the first FID signal and the spectral values ​​corresponding to its immediate and adjacent spectral points into a solution model with first preset parameters to obtain an initial estimated frequency. This process includes: constructing a first correlation equation based on the maximum spectral point of the spectral function of the first FID signal and the spectral values ​​corresponding to its immediate and adjacent spectral points; obtaining a first correlation matrix if the first correlation equation has a solution, wherein the determinant of the first correlation matrix is ​​0; substituting a preset relationship satisfied by the first maximum sidelobe attenuation window function into the first correlation matrix to obtain a second correlation matrix, wherein the second correlation matrix contains a first complex variable and a second complex variable; the imaginary parts of the first and second complex variables represent attenuation factors; the real part of the first complex variable consists of the negative of the difference between the maximum spectral point and the desired initial estimated frequency; and the real part of the second complex variable consists of the negative of the sum of the maximum spectral point and the desired initial estimated frequency; and solving the second correlation matrix to obtain the initial estimated frequency. A second maximum sidelobe attenuation window function is applied to the second FID signal and a discrete-time Fourier transform is performed to obtain the spectrum function corresponding to the second FID signal, wherein the second FID signal is obtained by subtracting the negative spectral leakage component from the first FID signal; The second estimated frequency is obtained by substituting the spectral points corresponding to the initial estimated frequency and the spectral points offset by a preset spectral interval relative to the initial frequency into the solution model with second preset parameters. This process includes substituting the spectral points corresponding to the initial estimated frequency and the spectral points offset by a preset time interval relative to the initial frequency into the solution model with second preset parameters to obtain the second estimated frequency. The initial estimated frequency is represented by the sum of the maximum spectral point and the spectral difference; a first ratio function is obtained based on the first spectral point function and the second spectral point function, and a second ratio function is obtained based on the first spectral point function and the third spectral point function; the first and second ratio functions are simplified according to a first set function to obtain a third and a fourth ratio function; a third correlation equation is constructed based on the third and fourth ratio functions, wherein the value of the third correlation equation is a preset coefficient, which is obtained based on a preset spectral interval; the third correlation equation is solved according to the type of window function to obtain the second estimated frequency; The final signal frequency is obtained based on the second estimated frequency.

2. The FID signal frequency estimation method based on improved interpolation DFT according to claim 1, characterized in that, The spectral function of the first FID signal includes: （2） in, Indicates spectrum index. This represents the spectral index corresponding to the initial estimated frequency to be determined. Represents the imaginary unit. Indicates the initial phase. Let represent the first maximum sidelobe attenuation window function, and let the first maximum sidelobe attenuation window function with an adjacent spacing index of 1 satisfy the following preset relationship: （4） in, Indicates the attenuation factor. Indicates the type of the window function.

3. The FID signal frequency estimation method based on improved interpolation DFT according to claim 1, characterized in that, The step of obtaining the initial estimated frequency based on the second correlation matrix includes: When the determinant of the second correlation matrix is ​​0, the sum and product of the complex numbers of the first and second variables can be obtained. The attenuation factor is obtained by solving the sum of the complex numbers of the first and second variables; The initial estimated frequency is obtained by multiplying the complex number of the first variable and the complex number of the second variable.

4. The FID signal frequency estimation method based on improved interpolation DFT according to claim 3, characterized in that, The method further includes: Substituting the obtained attenuation factor, initial estimated frequency, and maximum spectral point into the first maximum sidelobe attenuation window function, we obtain the first complex constant. Substitute the first complex constant into the spectrum function of the first FID signal, and take the conjugate of both sides of the equation to construct the second correlation equation; The amplitude and initial phase of the first FID signal are obtained by solving the second correlation equation.

5. The FID signal frequency estimation method based on improved interpolation DFT according to claim 1, characterized in that, Solving the third correlation equation according to the type of window function to obtain the second estimated frequency includes: When the type of the window function is equal to 1, the second setting function is obtained according to the first setting function, wherein the type of the window function equal to 1 indicates a rectangular window; Substituting the second set function into the third correlation equation and solving it, we obtain the second estimated frequency.

6. The FID signal frequency estimation method based on improved interpolation DFT according to claim 1, characterized in that, Solving the third correlation equation according to the type of window function to obtain the second estimated frequency includes: When the type of the window function is greater than 1, the variable of the first setting function is set to the third variable complex number, wherein the real part of the third variable complex number is the attenuation factor, and the imaginary part is the difference between the initial estimated frequency and the second estimated frequency to be determined. The type of the window function greater than 1 indicates the Hanning window. Taylor expansions are performed on the first set function and the third and fourth set functions with adjacent offset preset spectral intervals at preset positions, where the preset position indicates that the function variable is equal to the attenuation factor; The second estimated frequency is obtained by solving the Taylor expansion formula.

7. The FID signal frequency estimation method based on improved interpolation DFT according to claim 1, characterized in that, The final signal frequency is obtained based on the second estimated frequency, including: The final signal frequency is obtained based on the ratio of the sampling rate to the number of sampling points N and the second estimated frequency.

8. A frequency estimation system for FID signals based on improved interpolation DFT, characterized in that, The system includes: The FID signal acquisition module is used to acquire the first FID signal including N sampling points, where N is an integer greater than 1; The first windowing transformation module is used to apply a first maximum sidelobe attenuation window function to the first FID signal and perform a discrete Fourier transform to obtain the spectrum function of the first FID signal. The initial frequency estimation module is used to substitute the maximum spectral point of the spectral function of the first FID signal and the spectral values ​​corresponding to its immediate and adjacent spectral points into a first preset parameter solution model to obtain the initial estimated frequency. The process of substituting the maximum spectral point of the spectral function of the first FID signal and the spectral values ​​corresponding to its immediate and adjacent spectral points into the first preset parameter solution model to obtain the initial estimated frequency includes: constructing a first correlation equation based on the maximum spectral point of the spectral function of the first FID signal and the spectral values ​​corresponding to its immediate and adjacent spectral points; and, if the first correlation equation has a solution, obtaining the initial estimated frequency. An correlation matrix is ​​generated, wherein the determinant of the first correlation matrix is ​​0. A second correlation matrix is ​​obtained by substituting the preset relationship satisfied by the first maximum sidelobe attenuation window function into the first correlation matrix, wherein the second correlation matrix contains a first complex variable and a second complex variable. The imaginary parts of the first and second complex variables represent attenuation factors, the real part of the first complex variable consists of the negative of the difference between the maximum spectral point and the initial estimated frequency to be determined, and the real part of the second complex variable consists of the negative of the sum of the maximum spectral point and the initial estimated frequency to be determined. The initial estimated frequency is obtained by solving the second correlation matrix. The second windowing transformation module is used to apply a second maximum sidelobe attenuation window function to the second FID signal and perform a discrete-time Fourier transform to obtain the spectrum function corresponding to the second FID signal, wherein the second FID signal is obtained by subtracting the negative spectral leakage component from the first FID signal; The second frequency estimation module is used to substitute the spectral points corresponding to the initial estimated frequency and the spectral values ​​corresponding to spectral points offset by a preset spectral interval relative to the initial frequency into the second preset parameter solution model to obtain the second estimated frequency. The step of substituting the spectral points corresponding to the initial estimated frequency and the spectral values ​​corresponding to spectral points offset by a preset time relative to the initial frequency into the second preset parameter solution model to obtain the second estimated frequency includes: substituting the spectral points corresponding to the initial estimated frequency and the spectral points offset by a preset spectral interval relative to the initial estimated frequency into the spectral function corresponding to the second FID signal to obtain the first spectral point function, the second spectral point function, and the third spectral function, respectively. The method involves using point functions; where the initial estimated frequency is represented by the sum of the maximum spectral point and the spectral difference; obtaining a first ratio function based on the first and second spectral point functions, and a second ratio function based on the first and third spectral point functions; simplifying the first and second ratio functions according to a first set function to obtain a third and a fourth ratio function; constructing a third correlation equation based on the third and fourth ratio functions, where the values ​​of the third correlation equation are preset coefficients, obtained according to a preset spectral interval; and solving the third correlation equation according to the type of window function to obtain the second estimated frequency. The signal frequency acquisition module is used to obtain the final signal frequency based on the second estimated frequency.

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