A method, system and device for sensitively detecting free decay signals

Abstract

A method for sensitively sensing freely decaying signals is disclosed. This method first performs a standard time-frequency transform on the freely decaying signal to obtain its standard time-frequency structure and establishes a corresponding standard time-frequency structure library. Then, based on the standard time-frequency structure of the freely decaying signal and the established standard time-frequency structure library, the cumulative harmony of the signal at each time step is obtained through similarity theory, generating a cumulative harmony spectrum. This invention significantly improves the sensing sensitivity and resolution of freely decaying signals.

Description

Technical Field

[0001] This invention belongs to the field of signal processing, and specifically relates to a method, system and device for sensitively detecting freely decaying signals. Background Technology

[0002] For harmonic signals in time series, current techniques primarily rely on Fourier transform analysis. If a harmonic signal exists in the time series, a corresponding spectral line will appear in its Fourier spectrum, and the height of the spectral line roughly reflects the strength of the harmonic signal. If a harmonic signal is very weak, the spectral line in the Fourier spectrum will be very short, potentially obscured by noise. Therefore, it is difficult to detect weak harmonic signals using Fourier transform. For example, in... Figure 1 In the Fourier spectrum of the nuclear magnetic resonance FID (free induced decay signal) data shown, the spectral lines of some weak harmonic signals are masked by the giant peak at 1150 Hz, making it impossible to perceive the existence of these harmonic signals. Summary of the Invention

[0003] The purpose of this invention is to address the aforementioned problems in the prior art by providing a method, system, and device capable of sensitively detecting freely decaying signals.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows:

[0005] A method for sensitively detecting freely decaying signals includes the following steps:

[0006] Step A: Perform standard time-frequency transformation on the free decay signal to obtain the standard time-frequency structure of the signal, and establish the corresponding standard time-frequency structure library;

[0007] Step B: Based on the standard time-frequency structure of the free decay signal and the established standard time-frequency structure library, the cumulative harmony of the signal at each time moment is obtained through similarity theory, thereby generating the cumulative harmony spectrum.

[0008] Step B calculates the cumulative harmony degree based on the following formula:

[0009]

[0010] In the above formula, Frequency at time s The corresponding cumulative harmony degree, Let f(t) be the standard time-frequency structure of a freely decaying signal f(t), where f(t)∈C, C is a complex number, τ is time, Φ(τ) is the standard time-frequency structure library, and R is the real number domain.

[0011] Step A involves standard time-frequency transformation according to the following formula:

[0012]

[0013]

[0014] In the above formula, Let f(t) be the standard time frequency of the freely decaying signal, f(t)∈C, where C is a complex number. For kernel function Shift to the right by time τ, the underscore - indicates conjugate, and R is the real number field. Regarding frequency The real function is w(·), which is the standard window function, and i represents the imaginary number.

[0015] In step A, before performing standard time-frequency conversion, the free attenuation signal is divided into frequency bands.

[0016] In step A, the standard time-frequency structure library Φ(τ) is calculated using the following formula:

[0017]

[0018]

[0019] In the above formula, The j-th frequency at time τ The corresponding standard time-frequency structure, j = 1, 2, ..., K, where K is the number of frequencies divided and i represents an imaginary number.

[0020] A system for sensitively detecting freely decaying signals includes a standard time-frequency transformation module, a standard time-frequency structure library establishment module, and a cumulative harmonic spectrum generation module;

[0021] The standard time-frequency transformation module is used to perform standard time-frequency transformation on the free decay signal to obtain the standard time-frequency structure of the signal.

[0022] The standard time-frequency structure library creation module is used to create a standard time-frequency structure library;

[0023] The cumulative harmonicity spectrum generation module is used to obtain the cumulative harmonicity of the signal at each time step based on the standard time-frequency structure of the free decaying signal and the established standard time-frequency structure library, and generate the cumulative harmonicity spectrum.

[0024] A device for sensitively detecting freely decaying signals, including a processor and a memory;

[0025] The memory is used to store computer program code and to transmit the computer program code to the processor;

[0026] The processor is used to execute the aforementioned method for sensing freely decaying signals according to instructions in the computer program code.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0028] This invention provides a method for sensitively detecting freely decaying signals. First, a standard time-frequency transform is performed on the freely decaying signal to obtain its standard time-frequency structure, and a corresponding standard time-frequency structure library is established. Then, based on the standard time-frequency structure of the freely decaying signal and the established library, the cumulative harmonicity of the signal at each time step is obtained through similarity theory, thereby generating a cumulative harmonicity spectrum. This method, based on standard time-frequency transform and combined with similarity theory to generate a harmonicity spectrum, fully highlights the harmonicity of the time series, thus sensitively detecting the presence of harmonic signals, especially weak harmonic signals, in the time series. This harmonicity spectrum is far superior to the traditional Fourier spectrum in terms of sensing sensitivity and resolution. Therefore, this invention significantly improves the sensing sensitivity and resolution of freely decaying signals. Attached Figure Description

[0029] Figure 1 The Fourier spectrum of the nuclear magnetic resonance FID signal.

[0030] Figure 2 This is a flowchart of the present invention.

[0031] Figure 3 The cumulative harmony spectrum generated in Example 1.

[0032] Figure 4 This is a framework diagram of the system described in Example 3.

[0033] Figure 5 This is a structural diagram of the device described in Example 4. Detailed Implementation

[0034] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0035] Example 1:

[0036] See Figure 2 A method for sensitively detecting free decay signals, specifically for nuclear magnetic resonance (FID) signals, is performed in the following steps:

[0037] 1. For nuclear magnetic resonance FID signals, frequency band division settings are set. If it is necessary to analyze the 1-100Hz frequency band, the frequency band can be divided into multiple frequencies, and the difference between each adjacent frequency is 0.5Hz.

[0038] 2. Perform a standard time-frequency transformation on the FID signal according to the following formula to obtain the standard time-frequency structure of the signal:

[0039]

[0040]

[0041] In the above formula, Let f(t) be the standard time-frequency transform of the FID signal, where f(t) ∈ C, and C is a complex number. For kernel function Shift to the right by time τ, the underscore - indicates conjugate, and R is the real number field. Regarding frequency The real function, in this embodiment, That is, the standard time-frequency transform adopts the standard wavelet transform, and the basic wavelet is φ(t) = w(t)exp(it), where w(·) is the standard window function. In this embodiment, the standard Gauss window is used. i represents an imaginary number.

[0042] Simultaneously, a corresponding standard time-frequency structure library is established based on the frequency parameters in the standard time-frequency structure. The standard time-frequency structure library Φ(τ) is calculated using the following formula:

[0043]

[0044]

[0045] In the above formula, The j-th frequency at time τ The corresponding standard time-frequency structure, j = 1, 2, ..., K, where K is the number of frequencies divided.

[0046] 3. Based on the following similarity theory, the cumulative harmony of the signal at each time step is obtained, generating a signal as follows: Figure 3 The cumulative harmony spectrum shown:

[0047]

[0048] In the above formula, Frequency at time s The corresponding cumulative harmony level.

[0049] By comparison Figure 1 and Figure 3 It can be observed that the cumulative harmonic spectrum generated in this embodiment not only displays all identifiable signal peaks in the Fourier spectrum, but also clearly shows the signal located at 1155Hz, which is masked by the giant peak at 1150Hz in the Fourier spectrum, resulting in better signal amplification. This also demonstrates that the method described in this invention is far superior to the traditional Fourier spectrum in terms of sensing sensitivity and resolution.

[0050] Example 2:

[0051] This embodiment is for the following single-frequency free attenuation signal:

[0052]

[0053] In the above formula, Angular frequency, For the initial phase,

[0054] The standard time-frequency transformation of the above signal is performed using the method described in Example 1, resulting in the following standard time-frequency structure:

[0055]

[0056] At the same time, a standard time-frequency structure library with the following structure will be established:

[0057]

[0058] Based on the similarity theory used in Example 1, the cumulative harmony ρ(τ) of the signal at each time point is obtained.

[0059] For the integration region D∈{t|0≤t≤τ,τ≤X}, according to the inner product principle, let:

[0060]

[0061] W1(τ)=∫ D |z1(t)| 2 dt,

[0062] W2(τ)=∫ D |z2(t)| 2 dt,

[0063] Therefore:

[0064]

[0065]

[0066]

[0067] Based on the formula for calculating cumulative harmony, we have:

[0068]

[0069] Right now

[0070]

[0071] Since ρ(τ) and τ are both known, the numerical solution for a can be obtained.

[0072] Example 3:

[0073] See Figure 4 A system for sensitively detecting freely decaying signals includes a standard time-frequency transformation module 1, a standard time-frequency structure library establishment module 2, and a cumulative harmonic spectrum generation module 3.

[0074] The standard time-frequency transformation module 1 is used to perform standard time-frequency transformation on the free decay signal to obtain the standard time-frequency structure of the signal.

[0075] The standard time-frequency structure library creation module 2 is used to create a standard time-frequency structure library;

[0076] The cumulative harmonicity spectrum generation module 3 is used to obtain the cumulative harmonicity of the signal at each time step based on the standard time-frequency structure of the free decaying signal and the established standard time-frequency structure library, and to generate the cumulative harmonicity spectrum by means of the following similarity theory:

[0077]

[0078] In the above formula, Frequency at time s The corresponding cumulative harmony degree, Φ(τ) is the standard time-frequency transform of a freely decaying signal, and Φ(τ) is the standard time-frequency structure library.

[0079] Example 4:

[0080] See Figure 5 A device for sensitively sensing a free decaying signal includes a processor 41 and a memory 42, wherein the memory 42 is used to store computer program code 43 and transmit the computer program code 43 to the processor 41; the processor 41 is used to execute the method for sensitively sensing a free decaying signal as described in Embodiment 1 according to the instructions in the computer program code 43.

Claims

1. A method for sensitively detecting freely decaying signals, characterized in that: The method includes the following steps in sequence: Step A: Perform standard time-frequency transformation on the free decay signal to obtain the standard time-frequency structure of the signal, and establish the corresponding standard time-frequency structure library; Perform the standard time-frequency transformation according to the following formula: ； ； In the above formula, Free decay signal Standard time frequency, , It is a complex number. For kernel function Shift to the right , underline Indicates conjugate. For the real number field, Regarding frequency real functions, For standard window functions, represents an imaginary number; The standard time-frequency structure library The following formula is used to calculate: ； ； In the above formula, for The frequency at time j The corresponding standard time-frequency structure, K is the frequency of the division. represents an imaginary number; Step B: Based on the standard time-frequency structure of the freely decaying signal and the established standard time-frequency structure library, the cumulative harmony of the signal at each time step is obtained through the following similarity theory, thereby generating the cumulative harmony spectrum: ； In the above formula, for Time Frequency The corresponding cumulative harmony degree, Free decay signal The standard time-frequency structure, , It is a complex number. For time, It is a standard time-frequency structure library. It is the field of real numbers.

2. The method for sensitively detecting a freely decaying signal according to claim 1, characterized in that: In step A, before performing standard time-frequency conversion, the free attenuation signal is divided into frequency bands.

3. A system for sensitively detecting freely decaying signals, characterized in that: The system includes a standard time-frequency transformation module (1), a standard time-frequency structure library establishment module (2), and a cumulative harmonic spectrum generation module (3). The standard time-frequency transformation module (1) is used to perform the following standard time-frequency transformation on the free decay signal to obtain the standard time-frequency structure of the signal: ； ； In the above formula, Free decay signal Standard time frequency, , It is a complex number. For kernel function Shift to the right , underline Indicates conjugate. For the real number field, Regarding frequency real functions, For standard window functions, represents an imaginary number; The standard time-frequency structure library creation module (2) is used to create the following standard time-frequency structure library. : ； ； In the above formula, for The frequency at time j The corresponding standard time-frequency structure, K is the frequency of the division. represents an imaginary number; The cumulative harmonicity spectrum generation module (3) is used to obtain the cumulative harmonicity of the signal at each time step based on the standard time-frequency structure of the free decaying signal and the established standard time-frequency structure library, and to generate the cumulative harmonicity spectrum by means of the following similarity theory: ； In the above formula, for Time Frequency The corresponding cumulative harmony degree, Free decay signal The standard time-frequency structure, , It is a complex number. For time, It is a standard time-frequency structure library. It is the field of real numbers.

4. A device for sensitively detecting free-attenuating signals, characterized in that: Includes a processor (41) and a memory (42); The memory (42) is used to store computer program code (43) and transmit the computer program code (43) to the processor (41). The processor (41) is configured to execute the method for sensing a freely decaying signal according to any one of claims 1-2 according to instructions in the computer program code (43).

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