CN104655929A - Measuring method for digital time frequency of time domain signal and corresponding target identification method - Google Patents
Measuring method for digital time frequency of time domain signal and corresponding target identification method Download PDFInfo
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Abstract
The invention provides a measuring method for digital time frequency of a time domain signal. The measuring method comprises the following steps: (1) setting time window length delta t according to the sampling rate v of a to-be-detected signal; confirming frequency spectrum range of temporal frequency measurement, wherein the frequency spectrum ranges form 1/delta T to v/2; (2) intercepting the to-be-detected signal through the time window; (3) setting discrete frequency points sequence in the certain frequency spectrum range; equaling frequency value to current frequency points towards each frequency point; taking two sinusoidal signals of which the phase difference is 90 degrees constantly; conducting related calculation on the current to-be-processed signal slices respectively; taking two related calculation results as real part and imaginary part calculation mould and argument respectively to obtain spectrum value and phase position value of a current time point and a current frequency point; (4) actuating the step (2) and the step (3) repeatedly until obtaining corresponding spectrum values and phase position values of the time point and frequency point combination of the to-be-texted signal. The measuring method can accurately measure phase position time-frequency spectrum while accurately measuring spectrum time-frequency spectrum , and is high in noise resisting capability , response speed and time resolving power.
Description
Technical Field
The invention relates to the technical field of electronics and time-frequency measurement, in particular to a digital time-frequency measurement method of a time-domain signal.
Background
The spectrometer is a typical spectrum measuring device and is widely applied to the fields of electrics and electronics, physical chemistry, biomedicine, national defense safety and the like. With the increasing application level and requirements, people have higher and higher requirements on the functions of the frequency spectrograph. For example, for applications in ultrasonography, electrocardiography, and pulse radar, the spectrometer should have not only excellent spectral resolution but also excellent time resolution.
At present, a frequency spectrograph popular in domestic and foreign markets is a Fourier transform-based frequency spectrograph, and for an amplitude spectrum, the frequency spectrograph has good frequency spectrum resolution capability and time resolution capability and can process the evolution of complex transient response signals and derivative signals thereof to a certain extent. However, the fourier transform has a window truncation effect in the time domain, which requires approximating an infinitely long signal with a signal within a finite time window, which causes a significant deviation of the phase measurement from the amplitude measurement. Namely, the existing frequency spectrograph based on Fourier transform can accurately measure the amplitude spectrum of a signal, and simultaneously, the measured phase spectrum has larger deviation and even errors. The phase spectrum can reflect a large number of characteristics of the measured signal, and if the amplitude spectrum and the phase spectrum cannot be accurately and synchronously measured, the information carried in the signal (especially a signal with complex transient response and a derivative signal thereof) is difficult to completely analyze.
In order to overcome the above defects, chinese patent application CN 101308175a proposes an improved scheme based on fourier transform, which introduces some parameters to modify its phase spectrum during fourier transform, thereby reducing the phase deviation to some extent. However, the scheme cannot fundamentally change the time domain window truncation effect in the fourier transform, and the scheme may bring extra deviation due to artificially introduced parameters, so the accuracy of the phase spectrum still has a deficiency and needs to be improved.
Therefore, there is a need for a solution that can accurately measure the amplitude spectrum and the phase spectrum of the time domain signal simultaneously.
Disclosure of Invention
The invention aims to provide a solution which can accurately and synchronously measure the amplitude spectrum and the phase spectrum of a time domain signal.
In order to achieve the above object, the present invention provides a digital time-frequency measuring method, comprising the following steps:
1) setting a time window length delta T, and determining a measurable frequency spectrum range according to the set time window length delta T and the sampling rate v of the signal to be measured, wherein the frequency spectrum range is as follows: 1/Δ T to v/2;
2) intercepting a signal to be detected by using a time window to obtain a signal fragment to be processed corresponding to the current time point;
3) setting a discrete frequency point sequence in the range determined in the step 1), and respectively carrying out related calculation on current signal slices to be processed by using two sinusoidal reference signals with frequency values equal to the current frequency point and constant phase difference of 90 degrees for each frequency point in the frequency point sequence; respectively taking correlation calculation results corresponding to the two reference signals as a real part and an imaginary part to form complex numbers, calculating a module and an argument of the formed complex numbers, and respectively taking the module and the argument as an amplitude value and a phase value of a current time point and a current frequency point;
4) and setting the next time point as the current time point, and repeatedly executing the steps 2) to 3) until obtaining the amplitude value and the phase value corresponding to each time point and frequency point combination of the detected signal.
Wherein, in the step 1), the determined spectrum range is: 2/delta T to v/5.
Wherein the step 3) further comprises: for each current frequency point f, calculating a corresponding current period k/f, and discarding a section of data at the tail of the signal fragment to be processed from the current signal fragment to be processed to ensure that the time length of the signal to be processed participating in the relevant calculation is an integral multiple of the period length 1/f corresponding to the current frequency point; and the time length of each reference signal is consistent with the time length of the signal to be processed participating in the correlation calculation.
Wherein the step 3) further comprises: setting the discrete frequency point sequence by linear point taking or nonlinear point taking in the range determined in the step 1).
Wherein, in the step 3), the nonlinear point taking comprises: and (4) uniformly taking points by using a logarithm, and uniformly taking points by using a polynomial function or uniformly taking points by using a reciprocal. In the range determined in the step 1), points are uniformly taken on the abscissa axis along the logarithm, polynomial or reciprocal function, and the ordinate of the taken point is the taken frequency point value, so that the obtained discrete frequency point sequence is arranged along the logarithm, polynomial or reciprocal function, and the required time frequency spectrum is more flexibly obtained.
In step 3), when the discrete frequency point sequence is set to adopt linear point taking, for any frequency point f in the discrete frequency point sequence, the time window length Δ T is an integral multiple of the cycle length 1/f corresponding to the frequency point f.
Compared with the prior art, the invention has the following technical effects:
1. the phase time frequency spectrum can be accurately measured while the amplitude time frequency spectrum is accurately measured.
2. The noise resistance is strong.
3. The response speed is high.
4. The time resolution is high.
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FIG. 1 shows a schematic diagram of the principles of the present technology;
FIG. 2 shows a flow diagram of one embodiment of the present invention;
FIG. 3 illustrates a time domain waveform of a signal to be analyzed in one embodiment of the present invention;
FIG. 4 shows a comparison of the measured amplitude and phase spectra (represented by the grey lines) of the signal under analysis of FIG. 3 with those of a conventional Fourier transform scheme (represented by the black box lines), according to one embodiment of the present invention;
FIG. 5 illustrates a time domain waveform of another signal to be analyzed in an embodiment of the present invention;
FIG. 6 shows a measured amplitude spectrum for the analyzed signal of FIG. 5, in accordance with one embodiment of the present invention;
FIG. 7 illustrates a time-frequency joint analysis magnitude spectrogram measured for the analyzed signal of FIG. 5, in accordance with one embodiment of the present invention;
FIG. 8 illustrates a time-frequency joint analysis phase spectrogram measured for the analyzed signal of FIG. 5, in accordance with one embodiment of the present invention;
FIG. 9 illustrates a time domain waveform of yet another signal to be analyzed in an embodiment of the present invention;
FIG. 10 illustrates an amplitude spectrum measured in accordance with one embodiment of the present invention for the analyzed signal of FIG. 9;
fig. 11 shows the time-domain profile and the spectral profile of a signal sliced between 116 microseconds and 124 microseconds measured under a relatively strong noise condition for the analyzed signal of fig. 9 according to one embodiment of the present invention.
Wherein a) b) are respectively time domain and frequency domain spectra of background noise when the target signal is not contained; c) d) time domain and frequency domain spectra of the target signal with noise, which are measured once respectively; e) f) average time domain and frequency domain spectra of 10 times of measurement of the target signal with noise respectively; g) h) average time domain and frequency domain spectra of 100 measurements of the noisy target signal, respectively; i) j) are the average time domain and frequency domain spectra of 1000 noisy target signal measurements, respectively.
Detailed Description
The invention is further described below with reference to the figures and examples.
For ease of understanding, the measurement principle of the present invention will be described first. Fig. 1 shows a schematic diagram of the technical principle of the present invention, and the present invention provides a method of combining a phase-locked loop and a correlator to achieve fast and accurate measurement of the amplitude and phase of a high-density spectrum, where the measurement of the phase is directly obtained by correlating two paths of signals of the phase-locked loop with a measured signal respectively, without repeatedly scanning the phase, thereby greatly saving the processing time. Specifically, the basic principle of the phase-locked time-frequency measurement used by the invention is as follows: firstly, setting the frequency omega to be measured to be 2 pi f, and generating two paths of sine wave signals with constant phase difference of 90 degrees, such as cos (omega t) and sin (omega t), namely a complex signal e by a phase-locked loopiωt(ii) a And then, the two signals with the locked phases are respectively subjected to correlation operation with the measured signal according to the formula (1a) or (1b) to obtain complex numbers (a real part and an imaginary part, or amplitude and phase) of the signals at the set frequency. The principle formula is expressed as follows:
It is noted that the basic principle used in the present invention, i.e. equations (1a) and (1b), is formally very similar to the integration or summation of the fourier transform, since the equations of the present invention have the characteristics common to time-domain to frequency-domain or real-space to density-space transforms. In fact, the time-resolved phase-locking principle used by the present invention is different from the fourier transform in nature. Specifically, the fourier transform assumes that the original signal is in a positive and negative infinite interval, and the orthogonality between any two frequencies can be ensured only when the ideal assumption is satisfied, so that the spectrum accuracy can be ensured. However, this ideal situation does not exist in practical applications, because the time window of the signal is not infinite in practical applications, and this deviation results in the fact that the actual fourier transform spectrum cannot guarantee continuous orthogonality, and its accuracy at some frequency points is partially or even completely lost, which is especially true in the phase spectrum. The invention relates to a method for processing a real signal with a limited time length, which comprises the following steps: for any frequency point in the frequency spectrum, a sufficient time length of natural number times (for example, 2 times, 3 times, etc.) is taken from an original signal (i.e., a signal to be measured) according to a corresponding period, and then correlation is performed on a pair of orthogonal signals with a phase difference locked at 90 degrees with the frequency point, for example, by obtaining a real part and an imaginary part of the signal at the frequency point through formulas (2b) and (3b), respectively, amplitude values and phase values of the corresponding time slices of the original signal at the corresponding frequency point can be obtained. Moreover, the scheme avoids the interference of signal energy of other frequencies on the measurement of the frequency point to a great extent, so that the continuity of the frequency point and the measurement accuracy of each frequency point can be ensured simultaneously.
Based on the above analysis, fig. 2 shows a flow chart of a digital time-frequency measurement method provided in an embodiment of the present invention, which includes the following steps:
step 101: a time domain digital signal is acquired. The time domain digital signal may be a directly received digital signal or a digital signal obtained by sampling an analog signal.
Step 102: initializing, setting a variable Ti of a time point to be scanned, setting a starting time point to be T0 (i is 0 at this time), setting a time window length Δ T, moving a step dt of the time point, determining a measurable spectrum range according to a sampling rate v of the acquired time domain digital signal, wherein the spectrum range is between 1/Δ T and v/2, wherein 1/Δ T is a low frequency boundary, a significant decrease in measurement accuracy occurs at too low frequencies, and v/2 is a high frequency limit according to shannon's sampling theorem. Preferably, the spectral range is between 2/Δ T and v/5, which can increase a certain engineering margin, for example, when the upper limit is v/5, the upper frequency limit is increased by 2.5 times of the engineering margin.
Generating a frequency point sequence according to the determined frequency spectrum range, wherein each frequency point f in the frequency point sequence meets the conditions: the number of sampling points of the time window length delta T is integral multiple of the number of sampling points corresponding to the period length (namely 1/f) of the frequency point f. For example: the frequency points taken may be: 2/Δ T, 3/Δ T, …, n/Δ T. Where n may be chosen as desired, for example in the range of tens to hundreds, care should be taken to ensure that n/Δ T is less than the upper limit of the determined spectral range, for example less than v/5.
For convenience of description, the frequency points are denoted as Fj, j is a natural number from 1 to N, the initial value of j is 1, and N is the number of frequency points constituting the frequency point sequence.
Step 103: and extracting the time domain digital signal to be detected from Ti to the time period of Ti + delta T to obtain a time domain digital signal segment corresponding to the current time point Ti.
Step 104: and generating a phase-locked loop corresponding to the Fj frequency point, namely generating two reference signals cos (ω t) and sin (ω t) with a constant phase difference of 90 degrees, wherein ω is the angular frequency corresponding to the Fj frequency point, and ω is 2 pi Fj. Step 103 and step 104 may be performed in parallel.
Step 105: and respectively carrying out correlation operation on the two reference signals cos (ω t) and sin (ω t) and the time domain signal in the current time window to obtain two correlation results.
Step 106: and (3) respectively taking the two correlation results in the step 105 as a real part and an imaginary part to form a complex number, then calculating a modulus and an argument of the complex number, taking the modulus as a time point Ti, the amplitude value of a frequency point Fj as A (Ti, Fj), taking the argument as the time point Ti, and the phase value of the frequency point Fj as psi (Ti, Fj), and then increasing j by 1.
Step 107: and judging whether j is larger than N, if not, returning to the step 104, generating a next frequency point, continuing to perform related processing on the time domain digital signal segment corresponding to the current time point Ti, and if so, entering the step 108.
Step 108: i is self-incremented by 1 and j is reset to 1. Since the time point moving step dt has been set at initialization, in this step, Ti increases by itself dt when i increases by 1.
Step 109: and judging whether the current Ti + delta T exceeds the range of the time domain digital signal to be detected, if so, entering the step 110, otherwise, returning to the step 103, generating the next time domain digital signal segment and carrying out correlation operation on the next time domain digital signal segment and the phase-locked loop corresponding to the current frequency point Fj.
Step 110: and outputting the time-frequency amplitude value a (Ti, Fj) and the time-frequency phase value Ψ (Ti, Fj) corresponding to Ti and Fj to form a two-dimensional time-frequency amplitude spectrum (e.g., the two-dimensional spectrogram shown in fig. 7) and a time-frequency phase spectrum (e.g., the two-dimensional spectrogram shown in fig. 8).
Referring to fig. 1 again, the signal flow direction of the present invention can be seen, and the processing conditions of the digital time domain signal to be measured at each stage are more intuitively shown. The digital time domain signal to be measured is firstly cut into time domain signal segments, then the time domain signal segments and the digital frequency conversion phase-locked loop are subjected to correlation operation to obtain two paths of correlation results, the two paths of correlation results are respectively used as a real part and an imaginary part of a complex number, and thus, an amplitude time frequency spectrum and a phase time frequency spectrum can be obtained by calculating a mode and an amplitude angle of the complex number.
Further, in step 102, when the frequency spectrum range is set, the number of sampling points within the time window length Δ T is 2 times the number of sampling points corresponding to the minimum frequency point of the determined frequency spectrum range. At this time, the uncertainty of the measurement of frequency, amplitude and phase can be controlled within 10%. In another embodiment, the number of sampling points of the time window length Δ T is a multiple of the number of sampling points corresponding to the minimum frequency point of the determined frequency spectrum range, and the value may also be 3, at this time, the uncertainty of the measurement of the frequency, the amplitude, and the phase may be reduced to within 2%, but the computational complexity may be increased. Of course, the above-mentioned multiple can also be an integer of 3 or more, which is easily understood by those skilled in the art.
In step 102, the frequency bin sequence is obtained by performing linear point extraction in the determined spectrum range. In another embodiment of the present invention, the frequency point sequence may also be obtained by a non-linear point-taking strategy, such as a logarithmic uniform point-taking, a polynomial function uniform point-taking, a reciprocal uniform point-taking, and the like. This point-taking strategy can more flexibly obtain a spectrum with a required resolution. Meanwhile, when a nonlinear point-taking strategy is adopted, a section of data at the end of a time window with the length of delta T can be omitted to ensure that the number of sampling points of the time window participating in the correlation calculation is integral multiple of the number of sampling points corresponding to the period length (namely 1/f) of the frequency point f, thereby ensuring the accuracy of the phase spectrum.
The effect of the above embodiment is further illustrated by three specific signal measurements.
Example 1: measuring the frequency, amplitude and phase of each frequency component in the unknown signal
A signal is set, which is additively synthesized by three sinusoidal signals having frequencies of 2.3kHz, 37.7kHz and 397.3kHz, amplitudes of 1.1V, 0.2V and 0.7V, and phases of 30 degrees, 60 degrees and 120 degrees, respectively, without direct frequency multiplication, and the expression thereof is shown in formula (4):
the time domain waveform of this signal is shown in fig. 3. Fig. 4 shows a comparison of the amplitude and phase spectra measured according to the present invention (represented by the grey lines) with those measured by a conventional discrete fourier transform scheme (represented by the black boxed lines) for the signal under analysis of fig. 3. Referring to fig. 4, it can be seen that in logarithmic coordinates, the coordinate points obtained by fourier transform are much more sparse at low frequencies than at high frequencies, and the spectrum obtained by using the method can be uniformly sampled in both linear and logarithmic coordinates. In addition, the inventor also carries out comparison examination on the window effect of the two, and the frequency spectrum obtained by Fourier transform has obvious change, but the invention has no obvious change. The comparison of the results of the measurement of the unknown signal with the set values by two spectrum analysis methods, as shown in table 1, can be seen that the spectrum obtained by the present invention and the spectrum obtained by the fourier transform spectrum have significant advantages in the measurement of frequency points, amplitudes and phases, wherein the last three rows of data are the average of the measurement uncertainties of the differences between the measured values and the set values of the three frequency points, the measurement uncertainties of the fourier transform on the frequency, amplitude and phase are 3.9%, 5.5% and 98.8%, respectively, while the uncertainties measured by the present invention are only 0.17%, 1.1% and 6.7%, respectively. Table 1 shows the comparison of the unknown signal measurements of example 1 using the invention with the usual discrete Fourier transform spectra
TABLE 1
Example 2: joint time-frequency analysis of pulses and their derived signals
Designing three pulses P according to the sine function combination simulation pulse waveform P (t) shown in formula (5)1(t)、P2(t)、P3(t) and applying a white noise interference w (t) with a voltage varying randomly between-1 and 1, and combining the four weights according to equation (6) to obtain a simulated waveform of the experimental pulse and its derived signal, wherein the time domain waveform diagram is shown in fig. 5, and fig. 6 shows the amplitude spectrum measured according to an embodiment of the present invention for the analyzed signal of fig. 5. Wherein,
P(t)＝sinc(2πt×300000)-2×sinc(2πt×600000)
W(t)＝Random(-1,1)
S2(t)＝P1(t)+0.5P2(t)+0.2P3(t)+0.005W(t) (6)
it can be seen from fig. 6 that the energy of the detected signal is mainly distributed between 100kHz and 1MHz, and in order to comprehensively express the time-frequency characteristics contained in the signal, the time-frequency joint amplitude spectrogram and the phase spectrogram of the signal obtained by the invention are respectively shown in fig. 7 and fig. 8, from which the evolution of the frequency spectrums of the pulse signal and the derived signal thereof along with time can be clearly seen.
Example 3: anti-noise analysis of a target signal swamped by noise during a specified time period
The signal generation process is similar to example 2, but simulates a more demanding practical application, i.e. for some reason, P3(t) the pulse signal is highly suppressed and reduced to 5% of the original signal, and the background noise is enhanced to 100 times of the original signal, and the synthesis process is as in equation 7:
S3(t)＝P1(t)+0.5P2(t)+0.01P3(t)+0.5W(t) (7)
the time domain waveform corresponding to the example signal is shown in fig. 9, and fig. 10 shows that for the analyzed signal of fig. 9, although the overall frequency spectrum of the analyzed signal has no obvious difference from fig. 10 to fig. 6 of example 2, namely the frequency spectrum energy is still mainly distributed between 100kHz and 1MHz, the pulse three P3(t) can hardly be compared with fig. 5And (4) distinguishing. In order to accurately judge whether the time period signal exists or not and the spectrum intensity, the time period is subjected to focusing analysis. Fig. 11 shows the time-domain profile and the spectral profile of a signal sliced between 116 microseconds and 124 microseconds measured under a relatively strong noise condition for the analyzed signal of fig. 9 according to one embodiment of the present invention. Wherein a) b) are respectively time domain and frequency domain spectra of background noise when the target signal is not contained; c) d) time domain and frequency domain spectra of the target signal with noise, which are measured once respectively; e) f) average time domain and frequency domain spectra of 10 times of measurement of the target signal with noise respectively; g) h) average time domain and frequency domain spectra of 100 measurements of the noisy target signal, respectively; i) j) are the average time domain and frequency domain spectra of 1000 noisy target signal measurements, respectively. As shown in FIG. 11, by comprehensively comparing the background in the absence of pulses and using the method of multiple synchronous cumulative averaging, it can be seen that although P is not seen from the time domain3(t) pulse, but through the technology of the invention, the signal can be judged to exist from one measurement of the time interval frequency spectrum, and the frequency spectrum can be accurately measured at 500-700kHz and the amplitude is about 0.01V through 10 measurements and cumulative average.
In an actual test, a certain radar is used for receiving a reflected signal of a known target, then the reflected signal is analyzed according to the method of the invention to obtain a time frequency spectrum of the signal (namely, an amplitude value and a phase value of each frequency point of the reflected signal in each set time window), then the azimuth and the speed of the target are calculated according to the amplitude spectrum and the phase spectrum information obtained by the time frequency spectrum, and the obtained result is consistent with the actual azimuth and the speed of the known target.
Finally, it should be noted that the above examples are only intended to describe the technical solutions of the present invention and not to limit the technical methods, the present invention can be extended in application to other modifications, variations, applications and embodiments, and therefore all such modifications, variations, applications, embodiments are considered to be within the spirit and teaching scope of the present invention.
Claims (9)
1. A digital time-frequency measuring method of time-domain signals comprises the following steps:
1) receiving a digital signal to be measured, setting a time window length delta T according to a sampling rate v of the signal to be measured, and determining a frequency spectrum range of time frequency measurement, wherein the frequency spectrum range is between 1/delta T and v/2, and 1/delta T is less than v/2;
2) intercepting a signal to be detected by using a time window to obtain a signal fragment to be processed corresponding to the current time point;
3) setting a discrete frequency point sequence in the range determined in the step 1), and regarding each frequency point in the discrete frequency point sequence, using two sinusoidal signals with frequency values equal to the current frequency point and constant phase difference of 90 degrees as reference signals, and respectively carrying out related calculation on current signal slices to be processed; respectively taking correlation calculation results corresponding to the two reference signals as a real part and an imaginary part of a complex number, then calculating a modulus and an argument of the complex number, and respectively taking the modulus and the argument as an amplitude value and a phase value of a current time point and a current frequency point;
4) and setting the next time point as the current time point, and repeatedly executing the steps 2) to 3) until obtaining the amplitude value and the phase value corresponding to each time point and frequency point combination of the detected signal.
2. The method for digital time-frequency measurement of a time-domain signal according to claim 1, wherein the determined spectral range in step 1) is: 2/delta T to v/5.
3. The method for digital time-frequency measurement of time-domain signals according to claim 2, wherein said step 3) further comprises: and for each current frequency point f, calculating a current period k/f corresponding to the current frequency point f, and discarding a section of data at the tail of the signal slice to be processed from the current signal slice to be processed so as to ensure that the time length of the signal to be processed participating in the related calculation is integral multiple of the period length 1/f corresponding to the current frequency point.
4. The method for digital time-frequency measurement of time-domain signals according to claim 3, wherein said step 3) further comprises: the time length of each reference signal is consistent with the time length of the signal to be processed participating in the correlation calculation.
5. The method for digital time-frequency measurement of time-domain signals according to claim 3, wherein said step 3) further comprises: setting the discrete frequency point sequence by linear point taking or nonlinear point taking in the frequency spectrum range determined in the step 1).
6. The method according to claim 5, wherein the non-linear point taking in step 3) comprises: and (4) uniformly taking points by using a logarithm, and uniformly taking points by using a polynomial function or uniformly taking points by using a reciprocal.
7. The digital time-frequency measurement method of time-domain signals according to claim 3, wherein in step 3), when the discrete frequency point sequence is set to adopt linear point taking, for any frequency point f in the discrete frequency point sequence, the time window length Δ T is an integer multiple of the period length 1/f corresponding to the frequency point f.
8. The method for digital time-frequency measurement of time-domain signals according to claim 1, wherein in step 3), the two reference signals are: cos (ω t) and sin (ω t), t represents time, and ω represents angular frequency corresponding to the current frequency point.
9. A method of object recognition, comprising the steps of:
1) detecting a target to obtain a reflected signal of the target;
2) acquiring an amplitude-time frequency spectrum and a phase-time frequency spectrum of the reflection signal by using the digital time-frequency measurement method of the time-domain signal according to any one of claims 1 to 6;
3) and calculating the azimuth and the speed of the target according to the amplitude time frequency spectrum and the phase time frequency spectrum obtained in the step 2).
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| CN107328993A (en) * | 2017-08-17 | 2017-11-07 | 北京研创达科技有限公司 | Frequency measuring equipment and frequency measurement method |
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| CN107037247A (en) * | 2016-11-14 | 2017-08-11 | 丁大良 | A kind of recognition methods of data signal |
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| CN107328993B (en) * | 2017-08-17 | 2020-07-24 | 中国科学院物理研究所 | Frequency measuring device and frequency measuring method |
| WO2020177647A1 (en) * | 2019-03-01 | 2020-09-10 | 华为技术有限公司 | Method using radio signal to probe target entity, and related device |
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