A high-stability frequency estimation method suitable for free induction decay signals
Patent Information
- Application Number
- CN202610616949.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-05-07
- Publication Date
- 2026-09-29
AI Technical Summary
[0005]本发明的目的在于：为了解决现有方法在有限时间内存在频率估计误差较大且估计结果稳定度较差的技术问题，提供一种适用于自由感应衰减信号的高稳定度频率估计方法
（1）提出了一种基于对数谱线插值的非整数频点频谱提取方法。利用频谱峰值及其左右相邻谱线构建对数幅度谱模型，通过局部二次拟合实现对连续频谱的近似拟合，从而在非整数频点处获取信号的频谱信息。该方法有效减小了栅栏效应引起的频率估计误差。
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Abstract
Description
Technical Field
[0001] This application relates to the field of nuclear magnetic resonance signal processing technology, and in particular to a high-stability frequency estimation method suitable for freely inductively decaying signals. Background Technology
[0002] The free induction decay (FID) signal output by a proton magnetoresistive magnetometer has an amplitude in the microvolt range and typically decays rapidly within one second. Given that the sensor and amplification circuitry are fixed, the magnetometer's measurement accuracy depends solely on the accuracy of frequency estimation of the FID signal over a finite time period.
[0003] Currently, frequency estimation methods used in proton magnetoresistive magnetometers are mainly divided into two categories: direct frequency estimation methods and indirect frequency estimation methods. Direct frequency estimation methods, such as multi-cycle synchronous frequency measurement and equal-precision frequency measurement, are essentially based on the principle of zero-crossing counting. They have advantages such as simple computation and ease of hardware implementation, and have been widely used in engineering practice. However, these methods have limited frequency estimation accuracy and require extending the measurement time to improve accuracy. They are also sensitive to noise and signal attenuation, leading to large fluctuations in the estimation results and poor frequency estimation stability. Indirect frequency estimation methods mainly utilize modern signal processing methods to estimate the signal frequency by analyzing the characteristics of the FID signal in the time or frequency domain. Examples include time-domain autocorrelation methods, parameter fitting methods, and spectral interpolation. These algorithms can theoretically achieve high frequency estimation accuracy, but they have high computational complexity and also suffer from large frequency estimation deviations and poor stability over short periods.
[0004] In summary, existing methods suffer from significant frequency estimation errors within a limited timeframe, along with noticeable fluctuations and poor stability in the estimation results. Therefore, achieving high-precision and high-stability frequency estimation of FID signals within a short timeframe is a key technical challenge for improving the performance of proton magnetoresistive magnetometers. Summary of the Invention
[0005] The purpose of this invention is to provide a highly stable frequency estimation method suitable for freely inductively decaying signals, in order to solve the technical problems of large frequency estimation errors and poor stability of estimation results in existing methods within a limited time.
[0006] The above-mentioned objective of this application is achieved through the following technical solution: Step S1: Sample and segment the free induction attenuation signal to be tested using a sliding window to obtain several sub-signals; Step S2: Perform logarithmic spectral interpolation on each sub-signal to obtain the initial frequency estimate of each sub-signal, and then perform median statistics on the initial frequency estimates of all sub-signals to obtain the global frequency estimate. Step S3: Using the global frequency estimate as the reference frequency, calculate the complex spectrum value of each sub-signal at the reference frequency, and extract the phase of each sub-signal; Step S4: Unwrap the phases of all sub-signals to eliminate phase jumps and obtain a continuous phase sequence; Step S5: Perform first-order difference on the continuous phase sequence and statistically average the obtained difference phases; Step S6: Based on the linear relationship between phase difference and signal frequency, the accurate frequency estimate is obtained by calculating the differential phase after statistical averaging.
[0007] Optionally, step S1 includes: The free-inductance attenuated signal to be tested is sampled to obtain a discrete signal sequence. ,in Here is the sampling point number, and the total number of sampling points is... N The sampling frequency is ; The discrete signal sequence is segmented using a sliding window, with a window length of [value missing]. M The sliding step size is L Multiple sub-signals were obtained:
[0008] in, m This is the index of local sampling points within the window. , The total number of segments, and The sliding segmentation process is equivalent to applying a length of [missing information] to the original free-induction attenuated signal. A rectangular window; Indicates the first Joke signal.
[0009] Optionally, step S2 includes: For the Joke signal M Point discrete Fourier transform and extraction of peak spectral line indexes. and the logarithmic magnitudes of the left and right adjacent spectral lines, i.e. , , ; The initial frequency estimates of each sub-signal are obtained by fitting the local spectrum using the logarithmic spectral interpolation method. ,as follows:
[0010] in Indicates the first Peak spectral index of segment signals; Logarithmic spectral interpolation is performed on all segmented sub-signals to obtain K A rough estimate of the frequency ; Median statistical processing is performed on the initial frequency estimates of all sub-signals to obtain the global frequency estimate: .
[0011] Optionally, step S3 includes: Based on the above global frequency estimates Using the reference value, the spectrum of each sub-signal at this frequency is calculated to obtain the corresponding complex spectrum value:
[0012] in, The sampling interval; In complex spectral values Based on this, each sub-signal is in The phase at that point is represented as:
[0013] in, This indicates the argument of a complex number. The phase sequence is unwrapped to obtain a continuous phase sequence:
[0014] in This indicates the unwinding process.
[0015] Optionally, step S5 includes: The unwound phase sequence with respect to the segment index The relationship is approximately linear, expressed as:
[0016] in, The phase term is a constant. For phase sequence Performing a first-order difference yields the difference phase:
[0017] in This indicates the number of sampling points between the starting points of two adjacent sub-signals.
[0018] Optionally, step S6 includes: By statistically averaging the first-order phase difference components and based on the linear relationship between the phase difference and the signal frequency, the precise frequency estimate of the signal is further obtained:
[0019] in This indicates the number of sampling points between the starting points of two adjacent sub-signals.
[0020] An electronic device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to enable the electronic device to perform a high-stability frequency estimation method suitable for freely inductively attenuated signals.
[0021] A computer-readable storage medium storing instructions that, when executed, perform a highly stable frequency estimation method suitable for freely inductively decaying signals.
[0022] The beneficial effects of the technical solution provided in this application are: (1) A method for extracting the spectrum of non-integer frequencies based on logarithmic spectral line interpolation is proposed. A logarithmic amplitude spectrum model is constructed using the spectral peak and its left and right adjacent spectral lines. Approximate fitting of the continuous spectrum is achieved through local quadratic fitting, thereby obtaining the spectral information of the signal at non-integer frequencies. This method effectively reduces the frequency estimation error caused by the picket fence effect.
[0023] (2) A phase recursive modeling method based on sliding segmentation was constructed. The phase recursive relationship between sub-signals was obtained by using the sliding segmentation strategy. On this basis, the phase information of each segment signal at the global frequency was extracted, and a linear model of phase change with segment index was established, thereby avoiding the estimation bias caused by spectral asymmetry.
[0024] (3) Based on the above phase recursion model, a precise frequency estimation method based on differential phase averaging is proposed. By performing differential operations on the phases of adjacent signal segments and then statistically averaging them, a highly stable estimation of the phase change rate is achieved. On this basis, a phase difference-signal frequency linear fitting model is constructed to obtain the precise value of the signal frequency. Attached Figure Description
[0025] The present application will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a flowchart of an embodiment of this application; Figure 2 This is a comparison chart of frequency estimation RMSE under different signal-to-noise ratio conditions in the embodiments of this application; Figure 3 This is a schematic diagram of the electronic device structure in the embodiments of this application. Detailed Implementation
[0026] To provide a clearer understanding of the technical features, objectives, and effects of this application, the specific embodiments of this application will now be described in detail with reference to the accompanying drawings.
[0027] The embodiments of this application provide a high-stability frequency estimation method suitable for freely inductively decaying signals.
[0028] Please refer to Figure 1 , Figure 1 This is a flowchart of a highly stable frequency estimation method for freely inductively decaying signals, as described in an embodiment of this application, including: Step S1: Sample and segment the free induction attenuation signal to be tested using a sliding window to obtain several sub-signals; Step S2: Perform logarithmic spectral interpolation on each sub-signal to obtain the initial frequency estimate of each sub-signal, and then perform median statistics on the initial frequency estimates of all sub-signals to obtain the global frequency estimate. Step S3: Using the global frequency estimate as the reference frequency, calculate the complex spectrum value of each sub-signal at the reference frequency, and extract the phase of each sub-signal; Step S4: Unwrap the phases of all sub-signals to eliminate phase jumps and obtain a continuous phase sequence; Step S5: Perform first-order difference on the continuous phase sequence and statistically average the obtained difference phases; Step S6: Based on the linear relationship between phase difference and signal frequency, the accurate frequency estimate is obtained by calculating the differential phase after statistical averaging.
[0029] By adopting the above technical solutions, (1) the present invention realizes frequency estimation of non-integer spectral lines through logarithmic spectral line interpolation method, avoiding the influence of the picket fence effect on the frequency estimation accuracy in traditional discrete Fourier transform; (2) the present invention uses the signal sliding segmentation method to introduce a phase difference-signal frequency linear fitting model, effectively avoiding the frequency estimation deviation caused by spectral asymmetry to the interpolation method; (3) the present invention can realize high-precision and high-stability frequency estimation of FID signals in a short time, effectively improving measurement efficiency. The implementation steps of the frequency estimation method described in this invention are as follows: Figure 1As shown, the FID signal is first segmented using a sliding window, and logarithmic spectral interpolation is performed on each segment to obtain the corresponding initial frequency estimate. Based on the frequency estimates of all sub-signals, a median statistical method is used to determine the global frequency estimate. Then, using the global frequency as a reference frequency, the spectrum of each sub-signal at this frequency is calculated to obtain its complex spectrum value, and the phase of each sub-signal segment is extracted. Further, all sub-phases are unwrapped to eliminate phase mode jumps, resulting in a continuous phase sequence. Subsequently, the obtained phase sequence is subjected to first-order difference, and the differential phases are statistically averaged. Finally, based on the linear relationship between phase difference and signal frequency, a linear fitting model is constructed to achieve accurate estimation of the signal frequency, thereby obtaining a high-precision frequency estimation result.
[0030] Step S1 includes: The free-inductance attenuated signal to be tested is sampled to obtain a discrete signal sequence. ,in Here is the sampling point number, and the total number of sampling points is... N The sampling frequency is ; The discrete signal sequence is segmented using a sliding window, with a window length of [value missing]. M The sliding step size is L Multiple sub-signals were obtained:
[0031] in, m This is the index of local sampling points within the window. , The total number of segments, and The sliding segmentation process is equivalent to applying a length of [missing information] to the original free-induction attenuated signal. A rectangular window; Indicates the first Joke signal.
[0032] As one example, coarse frequency estimation of the signal based on logarithmic spectral line interpolation: In order to obtain the signal frequency from each segmented sub-signal, it is necessary to perform spectral analysis on each segment of the signal.
[0033] Step S2 includes: For the Joke signal M Point discrete Fourier transform and extraction of peak spectral line indexes. and the logarithmic magnitudes of the left and right adjacent spectral lines, i.e. , , ; The initial frequency estimates of each sub-signal are obtained by fitting the local spectrum using the logarithmic spectral interpolation method. ,as follows:
[0034] in Indicates the first Peak spectral index of segment signals; Logarithmic spectral interpolation is performed on all segmented sub-signals to obtain K A rough estimate of the frequency ; Median statistical processing is performed on the initial frequency estimates of all sub-signals to obtain the global frequency estimate: .
[0035] Step S3 includes: Based on the above global frequency estimates Using the reference value, the spectrum of each sub-signal at this frequency is calculated to obtain the corresponding complex spectrum value:
[0036] in, The sampling interval; In complex spectral values Based on this, each sub-signal is in The phase at that point is represented as:
[0037] in, This indicates the argument of a complex number. As one embodiment, since the range of phase values is The phase sequence obtained directly has abrupt changes. Therefore, the phase sequence is unwound to obtain a continuous phase sequence.
[0038] The phase sequence is unwrapped to obtain a continuous phase sequence:
[0039] in This indicates the unwinding process.
[0040] Step S5 includes: The unwound phase sequence with respect to the segment index The relationship is approximately linear, expressed as:
[0041] in, The phase term is a constant. For phase sequence Performing a first-order difference yields the difference phase:
[0042] in This indicates the number of sampling points between the starting points of two adjacent sub-signals.
[0043] Step S6 includes: By statistically averaging the first-order phase difference components and based on the linear relationship between the phase difference and the signal frequency, the precise frequency estimate of the signal is further obtained:
[0044] in This indicates the number of sampling points between the starting points of two adjacent sub-signals.
[0045] In one embodiment, the frequency estimation performance of the proposed method is verified through simulation experiments, and the root mean square error is used to reflect the performance of the method. In the simulation experiment, the initial amplitude of the FID signal is set to 5uV, the frequency to 2100Hz, the transverse relaxation time to 200ms, the sampling frequency to 10kHz, the number of sampling points to 2048, the sliding window length to 1292, the total number of segments to 680, and the sliding step size to 1.
[0046] In the simulation scheme, the initial signal-to-noise ratio (SNR) was set to SNR = -15dB:5dB:20dB, and 100 Monte Carlo experiments were performed under each SNR condition. To highlight the accuracy of the method of this invention, it is compared with the traditional FFT method. Figure 2 This is a schematic diagram showing the frequency estimation RMSE of the two methods under different signal-to-noise ratio conditions.
[0047] Depend on Figure 2 It can be seen that, under the condition of a signal-to-noise ratio of -15dB:5dB:20dB, the frequency estimation error of the method proposed in this invention is smaller than that of the traditional FFT method, exhibiting higher frequency estimation accuracy and stability. Furthermore, the RMSE of the method proposed in this invention gradually decreases with increasing signal-to-noise ratio. In contrast, the traditional FFT method is affected by factors such as the picket fence effect, resulting in a larger overall estimation error that does not change significantly with the signal-to-noise ratio. Compared with commercial magnetometers, taking the GSM-19 Overhauser magnetometer as an example, its technical parameters show a minimum sampling interval of 0.2s, corresponding to an overall frequency measurement rate of approximately 5Hz. In comparison, the single frequency estimation time of the method proposed in this invention is approximately 20ms, corresponding to a frequency measurement output rate of approximately 50Hz, significantly shortening the single estimation time while maintaining high stability in frequency estimation. It should be noted that the frequency measurement output rate is the frequency estimation rate at the algorithm level, used to characterize the computational efficiency of the method of this invention, and is not equivalent to the hardware sampling rate.
[0048] This application also discloses an electronic device. (See reference...) Figure 3 , Figure 3This is a schematic diagram of the structure of an electronic device disclosed in an embodiment of this application. The electronic device 500 may include: at least one processor 501, at least one network interface 504, a user interface 503, a memory 505, and at least one communication bus 502.
[0049] The communication bus 502 is used to enable communication between these components.
[0050] The user interface 503 may include a display screen, and optionally, the user interface 503 may also include a standard wired interface or a wireless interface.
[0051] The network interface 504 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).
[0052] This application also discloses a computer-readable storage medium storing a plurality of instructions adapted for loading by a processor to execute the above-described high-stability frequency estimation method for freely inductively decaying signals.
[0053] The above are merely exemplary embodiments of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure.
[0054] This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.
Claims
1. A high-stability frequency estimation method suitable for freely inductively attenuated signals, characterized in that, The method includes the following steps: Step S1: Sample and segment the free induction attenuation signal to be tested using a sliding window to obtain several sub-signals; Step S2: Perform logarithmic spectral interpolation on each sub-signal to obtain the initial frequency estimate of each sub-signal, and then perform median statistics on the initial frequency estimates of all sub-signals to obtain the global frequency estimate. Step S3: Using the global frequency estimate as the reference frequency, calculate the complex spectrum value of each sub-signal at the reference frequency, and extract the phase of each sub-signal; Step S4: Unwrap the phases of all sub-signals to eliminate phase jumps and obtain a continuous phase sequence; Step S5: Perform first-order difference on the continuous phase sequence and statistically average the obtained difference phases; Step S6: Based on the linear relationship between phase difference and signal frequency, the accurate frequency estimate is obtained by calculating the differential phase after statistical averaging.
2. The high-stability frequency estimation method for freely inductively attenuated signals as described in claim 1, characterized in that, Step S1 includes: The free-inductance attenuated signal to be tested is sampled to obtain a discrete signal sequence. ,in Here is the sampling point number, and the total number of sampling points is... N The sampling frequency is ; The discrete signal sequence is segmented using a sliding window, with a window length of [value missing]. M The sliding step size is L Multiple sub-signals were obtained: in, m This is the index of local sampling points within the window. , The total number of segments, and The sliding segmentation process is equivalent to applying a length of [missing information] to the original free-induction attenuated signal. A rectangular window; Indicates the first Joke signal.
3. The high-stability frequency estimation method for freely inductively attenuated signals as described in claim 2, characterized in that, Step S2 includes: For the Joke signal M Point discrete Fourier transform and extraction of peak spectral line indexes. and the logarithmic magnitudes of the left and right adjacent spectral lines, i.e. , , ; The initial frequency estimates of each sub-signal are obtained by fitting the local spectrum using the logarithmic spectral interpolation method. ,as follows: in Indicates the first Peak spectral index of segment signals; Logarithmic spectral interpolation is performed on all segmented sub-signals to obtain K A rough estimate of the frequency ; Median statistical processing is performed on the initial frequency estimates of all sub-signals to obtain the global frequency estimate: .
4. The high-stability frequency estimation method for freely inductively attenuated signals as described in claim 3, characterized in that, Step S3 includes: Based on the above global frequency estimates Using the reference value, the spectrum of each sub-signal at this frequency is calculated to obtain the corresponding complex spectrum value: in, The sampling interval; In complex spectral values Based on this, each sub-signal is in The phase at that point is represented as: in, This indicates the argument of a complex number. The phase sequence is unwrapped to obtain a continuous phase sequence: in This indicates the unwinding process.
5. The high-stability frequency estimation method for freely inductively attenuated signals as described in claim 4, characterized in that, Step S5 includes: The unwound phase sequence with respect to the segment index The relationship is approximately linear, expressed as: in, The phase term is a constant. For phase sequence Performing a first-order difference yields the difference phase: in This indicates the number of sampling points between the starting points of two adjacent sub-signals.
6. The high-stability frequency estimation method for freely inductively attenuated signals as described in claim 5, characterized in that, Step S6 includes: By statistically averaging the first-order phase difference components and based on the linear relationship between the phase difference and the signal frequency, the precise frequency estimate of the signal is further obtained: in This indicates the number of sampling points between the starting points of two adjacent sub-signals.
7. An electronic device, characterized in that, The device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to enable the electronic device to perform the high-stability frequency estimation method for freely inductively attenuated signals as described in any one of claims 1-6.
8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed by a computer, perform the high-stability frequency estimation method for freely inductively decaying signals as described in any one of claims 1-6.