CN117997455A - Method and system for calculating group delay measurement phase - Google Patents
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Abstract
The invention relates to a method and a system for calculating a group delay measurement phase, belonging to the technical field of spectrum analysis, wherein the method comprises the following steps: s1, connecting tested equipment, calculating a set frequency, performing spectral peak search, frequency offset calculation and compensation on a received multi-carrier baseband IQ signal, and intercepting the multi-carrier baseband IQ signal; s2, processing the intercepted multicarrier baseband IQ signal through fast Fourier transformation, and calculating a measurement phase connected with the tested equipment in a mode of unwinding and inverse unwinding; s3, calculating a calibration phase when the tested device is not connected, and calculating group delay by combining the measurement phase when the tested device is connected. The invention can rapidly and accurately calculate the real measurement phase, thereby calculating the accurate group delay.
Description
Technical Field
The present invention relates to the field of spectrum analysis technologies, and in particular, to a method and a system for calculating a group delay measurement phase.
Background
Delays occur when all frequency components of the signal propagate through devices such as amplifiers, speakers, or in a medium such as air; the delay of all frequencies together is called the group delay, which can be used to describe the transmission quality of certain elements, and the group delay can also measure the time required for a signal to propagate in a channel or device under test.
In a spectrum analyzer, a signal source generally transmits a multi-carrier signal to measure group delay, wherein the multi-carrier signal consists of a plurality of unmodulated carriers with fixed step sizes and can be used as an input signal, so that quick broadband measurement is realized; under the condition that the tested equipment is not measured, the existing method carries out preliminary reference measurement on an input signal, calculates a calibration measurement phase, stores a measurement result in an analyzer, carries out reference for group delay calculation in the measurement of the subsequent tested equipment, is connected with the tested equipment, uses a signal source to send the same signal for measurement, and calculates the measurement phase; however, the conventional method directly calculates the measured phase by using the input signal data, and there is a time difference between the measured calibration phase and the original measured phase, so that the calculated group delay error is large, even erroneous, and therefore, it is difficult to accurately calculate the group delay by using the conventional method.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a method and a system for calculating the group delay measurement phase, and solves the defects of the traditional method.
The aim of the invention is achieved by the following technical scheme: a method of calculating a group delay measurement phase, the method comprising:
s1, connecting tested equipment, calculating a set frequency, performing spectral peak search, frequency offset calculation and compensation on a received multi-carrier baseband IQ signal, and intercepting the multi-carrier baseband IQ signal;
S2, processing the intercepted multicarrier baseband IQ signal through fast Fourier transformation, and calculating a measurement phase connected with the tested equipment in a mode of unwinding and inverse unwinding;
s3, calculating a calibration phase when the tested device is not connected, and calculating group delay by combining the measurement phase when the tested device is connected.
The step of S1 specifically comprises the following steps:
S101, calculating a first root carrier frequency according to the number CarrierNum of carriers and the carrier interval CARRIERSPACING set by user input And the last carrier frequencyThereby obtaining the frequency group transmitted by the signal source；
S102, receiving the multi-carrier signal through a spectrum analyzer, down-converting the multi-carrier signal to a baseband to obtain a multi-carrier baseband IQ signal, and inputting the multi-carrier baseband IQ signalPerforming fast Fourier transform, moving the zero frequency component to the spectrum center fftshift, and performing spectrum peak search to obtain a received frequency group/>；
S103, calculating multi-carrier baseband IQ signalsIs then calculated as the fast fourier transform length/>And rounding down, n represents the total degree of the multi-carrier baseband IQ signal;
s104, calculating through a discrete Fourier transform frequency offset estimation algorithm And/>Frequency offset between/>Obtaining the non-frequency offset multi-carrier baseband IQ signal/>；
S105, for non-frequency offset multi-carrier baseband IQ signalIntercepting, namely intercepting a signal with the length of FFTLen, and calculating to obtain an intercepted non-frequency offset multi-carrier baseband IQ signal/>Wherein/>，m＜n。
The zero frequency component is moved to the spectrum center fftshift and the spectrum peak search is carried out to obtain the received frequency groupThe method specifically comprises the following steps:
front is put forward Location and back of the individual points/>Position substitution of individual points to obtain frequency spectrum/>；
Searching spectral peaks to find outThe maximum spectral line yfftMax in (a) and the frequency index maxIdx corresponding to that spectral line are set to be 0.3, and the threshold thd is set to be/>All less than/>Is set to zero;
the current point is considered as a spectral peak when the frequency spectrum value of the current point is larger than that of the adjacent points on the left and right sides, all the spectral peaks are found out, the frequency where the spectral peaks are positioned is the carrier frequency, and a received frequency group is obtained 。
The step of S104 specifically includes the following:
for multi-carrier baseband IQ signals Intercepting to obtain intercepted multi-carrier baseband IQ signal/>Calculate search step/>And/>Corresponding frequency bin/>Calculating the discrete Fourier transform value/>, corresponding to fPeakSum power value/>Wherein, the method comprises the steps of, wherein,Abs represents a modulus, j represents an imaginary number, and e represents a base of a natural logarithm;
According to steps Calculating fPeak discrete Fourier transform values and power values of the left frequency point and the right frequency point to respectively obtain left frequency point/>Corresponding discrete Fourier transform values/>And right frequency point/>Corresponding discrete Fourier transform values/>And its corresponding power value/>And/>And find/>、/>And/>Maximum value/>Update fPeak to the value/>Corresponding frequency point values and updating search steps/>This step is repeated untilLess than a preset value;
Final end Corresponding frequency/>I.e. the estimated frequency of a received carrier wave, isFind and/>The frequency with the closest value is subtracted to obtain the frequency deviation/>Then compensating to obtain non-frequency offset multi-carrier baseband IQ signal/>。
The step of S2 specifically comprises the following steps:
S201, intercepting the non-frequency offset multi-carrier baseband IQ signal Performing fast Fourier transform and moving the zero frequency component to the center fftshift of the spectrum, i.e./>Location and back of the individual points/>The positions of the points are replaced to obtain FFTSig, then spectrum peak searching is carried out, and frequency indexes PeakIndex corresponding to the spectrum peaks are calculated;
S202, calculating the original measurement phase Imag represents taking the imaginary part and real represents taking the real part;
S203, will Is converted into degrees to obtain the initial measured phase/>；
S204, throughCalculating the difference between the calibration phase and the initial phase,/>Representing a calibration phase, f representing each frequency point of the carrier wave;
S205, pair Unwrapping to obtain a first temporary phase variable/>，Indicating unwinding;
s206, judging If there is a peak, then pair alone/>And/>Unwind and update the difference/>If there is no peak value, thenThe value of (2) remains unchanged;
S207, solution matrix Obtain/>Calculated out， />，/>For stepping, start represents the starting point;
s208, calculating a second temporary phase variable ，Representation/>A value after unwinding;
S209, pair Performing inverse winding until the phase value after inverse winding is within +/-180 DEG to obtain the measured phase/>, which is connected with the tested equipment。
By passing throughGroup delay is calculated, where F represents each frequency of the multi-carrier,Representing the unwrapped values of the measured phase and the calibrated phase difference values.
A system for calculating group delay measurement phase comprises a signal preprocessing module, a calculation measurement phase module and a group delay calculation module;
The signal preprocessing module is used for: the method comprises the steps of calculating a set frequency after connecting tested equipment, performing spectral peak search, frequency offset calculation and compensation on a received multi-carrier baseband IQ signal, and intercepting the multi-carrier baseband IQ signal;
the calculation and measurement phase module: the method is used for processing the intercepted multicarrier baseband IQ signals through fast Fourier transformation, and calculating the measurement phase of the connected tested equipment through the mode of unwrapping and inverse unwrapping.
The group delay calculation module: for calculating a group delay in combination with the measured phase when the device under test is connected after calculating the calibration phase when the device under test is not connected.
The signal preprocessing module specifically realizes the following contents:
According to the number CarrierNum of carriers and the carrier interval CARRIERSPACING set by user input, a first root carrier frequency is calculated And the last carrier frequencyThereby obtaining the frequency group transmitted by the signal source；
Receiving multi-carrier signals through a spectrum analyzer, down-converting the multi-carrier signals to a baseband to obtain multi-carrier baseband IQ signals, and inputting the multi-carrier baseband IQ signalsPerforming fast Fourier transform, moving the zero frequency component to the spectrum center fftshift, and performing spectrum peak search to obtain a received frequency group/>；
Calculating multi-carrier baseband IQ signalIs then used to calculate the length of the fast Fourier transformAnd rounding down;
calculation of frequency offset estimation algorithm by discrete Fourier transform And/>Frequency offset betweenObtaining the non-frequency offset multi-carrier baseband IQ signal/>；
For non-frequency offset multi-carrier baseband IQ signalIntercepting, namely intercepting a signal with the length of FFTLen, and calculating to obtain an intercepted non-frequency offset multi-carrier baseband IQ signal/>Wherein/>。
The calculation and measurement phase module specifically realizes the following contents:
for intercepted non-frequency offset multi-carrier baseband IQ signal Performing fast Fourier transform and moving the zero frequency component to the center fftshift of the spectrum, i.e./>Location and back of the individual points/>The positions of the points are replaced to obtain FFTSig, then spectrum peak searching is carried out, and frequency indexes PeakIndex corresponding to the spectrum peaks are calculated;
Calculating the original measured phase Imag represents taking the imaginary part and real represents taking the real part;
Will be Is converted into degrees to obtain the initial measured phase/>；
By passing throughCalculating the difference between the calibration phase and the initial phase,/>Representing a calibration phase, f representing each frequency point of the carrier wave;
For a pair of Unwrapping to obtain a first temporary phase variable/>， Indicating unwinding;
Judging If there is a peak, then pair alone/>And/>Unwind and update the difference/>If there is no peak value, thenThe value of (2) remains unchanged;
Solution matrix Obtain/>. Calculating， />， />For stepping, start represents the starting point;
Calculating a second temporary phase variable ， />Representation/>A value after unwinding;
For a pair of Performing inverse winding until the phase value after inverse winding is within +/-180 DEG to obtain the measured phase/>, which is connected with the tested equipment。
The invention has the following advantages: a method and a system for calculating group delay measurement phase can rapidly and accurately calculate real measurement phase, thereby calculating accurate group delay.
Drawings
FIG. 1 is a schematic flow chart of the present invention;
FIG. 2 is a schematic flow chart of signal preprocessing;
Fig. 3 is a flow chart of calculating a group delay measurement phase.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are only some embodiments of the present application, not all embodiments. The components of the embodiments of the present application generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Accordingly, the following detailed description of the embodiments of the application, as presented in conjunction with the accompanying drawings, is not intended to limit the scope of the application as claimed, but is merely representative of selected embodiments of the application. All other embodiments, which can be made by a person skilled in the art without making any inventive effort, are intended to be within the scope of the present application. The application is further described below with reference to the accompanying drawings.
As shown in fig. 1 and 2, the present invention relates to a method for calculating a group delay measurement phase, which specifically includes the following steps:
1. Preprocessing signals;
Step 1-1: the set frequency is calculated. When the signal source transmits the multi-carrier signal, the user is required to input the set carrier number CarrierNum and carrier interval CARRIERSPACING, the first carrier frequency Last root carrier frequencyThe transmitted frequency group can then be calculated. Since the spectrum analyzer will down-convert the received signal to baseband, the default center frequency/>。
Step 1-2: the spectrum analyzer receives the multi-carrier signal, down-converts the signal to baseband, and then outputs the IQ signal to the input multi-carrier basebandPerforming fast Fourier transform FFT and moving the zero frequency component to the center fftshift of the spectrum, i.e./>Location of the individual points and back/>Position replacement of the points, n represents the total number of the multi-carrier baseband IQ signals, and frequency spectrum/>, is obtained. Then searching spectrum peak, finding out/>Maximum spectral line yfftMax in (a) and the frequency index/>, to which that spectral line correspondsLet the threshold thd be 0.3, will/>All less than/>The spectrum values of the current point are set to be zero, the spectrum peaks are searched for in order to eliminate interference of background noise, namely, the current point is larger than the spectrum values of the left and right adjacent points, the current point is regarded as the spectrum peak, all the spectrum peaks are found out, the frequency where the spectrum peaks are located is the carrier frequency, and the received frequency group/>。
Step 1-3: calculating multi-carrier baseband IQ signalIs then calculated to be the FFT lengthAnd rounded down. 10000 is chosen as the upper limit of the FFT length to improve the calculation speed and reduce the memory occupation.
Step 1-4: the signal sent by the signal source and the signal received by the frequency spectrograph have certain frequency offset, so as to calculate the frequency offsetA DFT (discrete fourier transform) frequency offset estimation algorithm is employed. To reduce the computational complexity, use is made ofData points are calculated, and the multi-carrier baseband IQ signal/>Intercepting to obtain intercepted multi-carrier baseband IQ signal/>Wherein/>M < n recalculates search step/>And/>Corresponding frequency bin/>Then calculate/>Corresponding DFT values/>Sum power value/>Where abs represents the modulo value. Then according to step/>Calculation/>DFT values and power values of the left frequency point and the right frequency point are respectively obtained to obtain left frequency point/>Corresponding DFT values/>And right frequency point/>Corresponding DFT values/>And its corresponding power value/>And/>And find/>、/>And/>Maximum value/>Update/>The value of (2) isCorresponding frequency point values and updating search steps/>This process is repeated untilThe loop is terminated, wherein the accuracy of the frequency offset estimate may be adjusted by adjusting the value of the terminated loop.
At this time, the finalCorresponding frequency/>I.e. the estimated frequency of a received certain root carrier. At the position ofFind and/>The frequency with the closest value is subtracted to obtain the frequency deviation/> 。
Then compensating to obtain non-frequency offset multi-carrier baseband IQ signalI.e./>Wherein/>For the sampling rate, j represents the imaginary number and e represents the base of the natural logarithm.
Step 1-5: for non-frequency offset multi-carrier baseband IQ signalIntercepting. Cut-out length is/>The next calculation is carried out on the signals of the (4) to obtain intercepted non-frequency offset multi-carrier baseband IQ signals/>Wherein/>
2. Calculating phase；
As shown in fig. 3, step 2-1: for intercepted non-frequency offset multi-carrier baseband IQ signalPerforming fast Fourier transform FFT and moving the zero frequency component to the center fftshift of the spectrum, i.e./>Location of the individual points and back/>The positions of the points are replaced to obtain FFTSig, then spectrum peak searching is carried out (the specific flow steps are the same as those of the step 1-2), and the frequency index/>, corresponding to the spectrum peak, is calculated。
Step 2-2: calculating the original measured phaseThe imag and real are the common descriptions in matlab software, imag represents the imaginary part and real represents the real part. At this time/>The measured phase of the group delay cannot be directly considered, otherwise the calculated group delay result is very erroneous or even erroneous.
Step 2-3: conversion ofUnit to degree of (a) to obtain an initial measured phase/>。
Step 2-4: by passing through， />Calculating the difference between the calibration phase and the original measurement phase, wherein f represents each frequency point of the carrier wave, and the value is 1,2, …,/>When the DUT (device under test) is not connected to calibration, steps 1-1, 1-2, 1-3, 1-4, 1-5, 2-1, 2-2 are performed, and the calculated phase/>I.e. calibration phase。
Step 2-5: for a pair ofUnwinding to obtain a temporary phase variableWherein/>The unwind is represented as a common function in matlab software.
Step 2-6: judgingIf there is a peak, if there is a peak whose value is greater than the values of both the left and right sides, there is a peak, if there is a peak, then the pair/>, aloneAnd/>Unwind and update the difference. If there is no peak value, < >The value of (2) remains unchanged.
Step 2-7: solution matrixObtain/>. Calculating，/>， />For stepping, start represents the starting point.
Step 2-8: calculating a temporary phase variableAt this time/>Is/>Values after unwinding.
Step 2-9: for a pair ofPerforming inverse winding until the phase value after inverse winding is within + -180 DEG, and solving to obtain/>。
3. Calculating group delay;
step 3-1: group delay Wherein F is each frequency of the multi-carrier,The unwrapped values representing the measured phase and the calibrated phase difference values.
The foregoing is merely a preferred embodiment of the invention, and it is to be understood that the invention is not limited to the form disclosed herein but is not to be construed as excluding other embodiments, but is capable of numerous other combinations, modifications and adaptations, and of being modified within the scope of the inventive concept described herein, by the foregoing teachings or by the skilled person or knowledge of the relevant art. And that modifications and variations which do not depart from the spirit and scope of the invention are intended to be within the scope of the appended claims.
Claims (9)
1. A method of calculating a group delay measurement phase, comprising: the method comprises the following steps:
s1, connecting tested equipment, calculating a set frequency, performing spectral peak search, frequency offset calculation and compensation on a received multi-carrier baseband IQ signal, and intercepting the multi-carrier baseband IQ signal;
S2, processing the intercepted multicarrier baseband IQ signal through fast Fourier transformation, and calculating a measurement phase connected with the tested equipment in a mode of unwinding and inverse unwinding;
s3, calculating a calibration phase when the tested device is not connected, and calculating group delay by combining the measurement phase when the tested device is connected.
2. A method of computing group delay measurement phases according to claim 1, wherein: the step of S1 specifically comprises the following steps:
S101, calculating a first root carrier frequency according to the number CarrierNum of carriers and the carrier interval CARRIERSPACING set by user input And the last carrier frequencyThereby obtaining the frequency group transmitted by the signal source；
S102, receiving the multi-carrier signal through a spectrum analyzer, down-converting the multi-carrier signal to a baseband to obtain a multi-carrier baseband IQ signal, and inputting the multi-carrier baseband IQ signalPerforming fast Fourier transform, moving the zero frequency component to the spectrum center fftshift, and performing spectrum peak search to obtain a received frequency group/>；
S103, calculating multi-carrier baseband IQ signalsIs then used to calculate the length of the fast Fourier transformAnd rounding down, n represents the total degree of the multi-carrier baseband IQ signal;
s104, calculating through a discrete Fourier transform frequency offset estimation algorithm And/>Frequency offset betweenObtaining the non-frequency offset multi-carrier baseband IQ signal/>；
S105, for non-frequency offset multi-carrier baseband IQ signalIntercepting, namely intercepting a signal with the length of FFTLen, and calculating to obtain an intercepted non-frequency offset multi-carrier baseband IQ signal/>Wherein/>，/>。
3. A method of calculating a group delay measurement phase according to claim 2, wherein: the zero frequency component is moved to the spectrum center fftshift and the spectrum peak search is carried out to obtain the received frequency groupThe method specifically comprises the following steps:
front is put forward Location and back of the individual points/>Position substitution of individual points to obtain frequency spectrum/>；
Searching spectral peaks to find outThe maximum spectral line yfftMax in (a) and the frequency index maxIdx corresponding to that spectral line are set to be 0.3, and the threshold thd is set to be/>All less than/>Is set to zero;
the current point is considered as a spectral peak when the frequency spectrum value of the current point is larger than that of the adjacent points on the left and right sides, all the spectral peaks are found out, the frequency where the spectral peaks are positioned is the carrier frequency, and a received frequency group is obtained 。
4. A method of calculating a group delay measurement phase according to claim 2, wherein: the step of S104 specifically includes the following:
for multi-carrier baseband IQ signals Intercepting to obtain intercepted multi-carrier baseband IQ signal/>Calculate search step/>And/>Corresponding frequency bin/>Calculating the discrete Fourier transform value/>, corresponding to fPeakSum power value/>Wherein, the method comprises the steps of, wherein,Abs represents a modulus, j represents an imaginary number, and e represents a base of a natural logarithm;
According to steps Calculating fPeak discrete Fourier transform values and power values of the left frequency point and the right frequency point to respectively obtain left frequency point/>Corresponding discrete Fourier transform values/>And right frequency point/>Corresponding discrete Fourier transform values/>And its corresponding power value/>And/>And find/>、/>And/>Maximum value/>Update fPeak to the value/>Corresponding frequency point values and updating search steps/>This step is repeated untilLess than a preset value;
Final end Corresponding frequency/>I.e. the estimated frequency of a received root carrier is equal to the frequency of the received root carrier at/>Find and/>The frequency with the closest value is subtracted to obtain the frequency deviation/>Then compensating to obtain non-frequency offset multi-carrier baseband IQ signal/>。
5. A method of calculating a group delay measurement phase according to claim 2, wherein: the step of S2 specifically comprises the following steps:
s201, intercepting the non-frequency offset multi-carrier baseband IQ signal Performing fast Fourier transform and moving the zero frequency component to the center fftshift of the spectrum, i.e./>Location and back of the individual points/>The positions of the points are replaced to obtain FFTSig, then spectrum peak searching is carried out, and frequency indexes PeakIndex corresponding to the spectrum peaks are calculated;
s202, calculating the original measurement phase Imag represents taking the imaginary part and real represents taking the real part;
S203, will Is converted into degrees to obtain the initial measured phase/>；
S204, throughCalculating the difference between the calibration phase and the initial phase,/>Representing a calibration phase, f representing each frequency point of the carrier wave;
S205, pair Unwrapping to obtain a first temporary phase variable/>，Indicating unwinding;
s206, judging If there is a peak, then pair alone/>And/>Unwind and update the difference/>If there is no peak value, thenThe value of (2) remains unchanged;
S207, solution matrix Obtain/>Calculated out，/>，/>For stepping, start represents the starting point;
s208, calculating a second temporary phase variable ，/>Representation/>A value after unwinding;
S209, pair Performing inverse winding until the phase value after inverse winding is within +/-180 DEG to obtain the measured phase/>, which is connected with the tested equipment。
6. A method of computing group delay measurement phases according to claim 5, wherein: the step of S3 specifically includes the following:
By passing through Group delay is calculated, where F represents each frequency of the multi-carrier,Representing the unwrapped values of the measured phase and the calibrated phase difference values.
7. A system for computing group delay measurement phases, comprising: the system comprises a signal preprocessing module, a calculation and measurement phase module and a group delay calculation module;
The signal preprocessing module is used for: the method comprises the steps of calculating a set frequency after connecting tested equipment, performing spectral peak search, frequency offset calculation and compensation on a received multi-carrier baseband IQ signal, and intercepting the multi-carrier baseband IQ signal;
the calculation and measurement phase module: the method comprises the steps of processing intercepted multicarrier baseband IQ signals through fast Fourier transformation, and calculating measurement phases connected with tested equipment through a mode of unwinding and inverse unwinding;
the group delay calculation module: for calculating a group delay in combination with the measured phase when the device under test is connected after calculating the calibration phase when the device under test is not connected.
8. A system for computing group delay measurement phases according to claim 7, wherein: the signal preprocessing module specifically realizes the following contents:
According to the number CarrierNum of carriers and the carrier interval CARRIERSPACING set by user input, a first root carrier frequency is calculated And the last carrier frequencyThereby obtaining the frequency group transmitted by the signal source；
Receiving multi-carrier signals through a spectrum analyzer, down-converting the multi-carrier signals to a baseband to obtain multi-carrier baseband IQ signals, and inputting the multi-carrier baseband IQ signalsPerforming fast Fourier transform, moving the zero frequency component to the spectrum center fftshift, and performing spectrum peak search to obtain a received frequency group/>；
Calculating multi-carrier baseband IQ signalIs then used to calculate the length of the fast Fourier transformAnd rounding down, n represents the total degree of the multi-carrier baseband IQ signal;
calculation of frequency offset estimation algorithm by discrete Fourier transform And/>Frequency offset betweenObtaining the non-frequency offset multi-carrier baseband IQ signal/>；
For non-frequency offset multi-carrier baseband IQ signalIntercepting, namely intercepting a signal with the length of FFTLen, and calculating to obtain an intercepted non-frequency offset multi-carrier baseband IQ signal/>Wherein/>，/>。
9. A system for computing group delay measurement phases according to claim 7, wherein: the calculation and measurement phase module specifically realizes the following contents:
for intercepted non-frequency offset multi-carrier baseband IQ signal Performing fast Fourier transform and moving the zero frequency component to the center fftshift of the spectrum, i.e./>Location and back of the individual points/>The positions of the points are replaced to obtain FFTSig, then spectrum peak searching is carried out, the frequency index PeakIndex corresponding to the spectrum peak is calculated, and n represents the total degree of the multi-carrier baseband IQ signal;
Calculating the original measured phase Imag represents taking the imaginary part and real represents taking the real part;
Will be Is converted into degrees to obtain the initial measured phase/>；
By passing throughCalculating the difference between the calibration phase and the initial phase,/>Representing a calibration phase, f representing each frequency point of the carrier wave;
For a pair of Unwrapping to obtain a first temporary phase variable/>，/>Indicating unwinding;
Judging If there is a peak, then pair alone/>And/>Unwind and update the difference/>If there is no peak value, then/>The value of (2) remains unchanged;
Solution matrix Obtain/>，
Calculating，/>，/>For stepping, start represents the starting point;
Calculating a second temporary phase variable ，/>Representation ofA value after unwinding;
For a pair of Performing inverse winding until the phase value after inverse winding is within +/-180 DEG to obtain the measured phase/>, which is connected with the tested equipment。
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| CN114448500A (en) * | 2020-11-03 | 2022-05-06 | 富士通株式会社 | Phase frequency response measuring method and device |
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| CN111856401A (en) * | 2020-07-02 | 2020-10-30 | 南京大学 | Time delay estimation method based on cross-spectrum phase fitting |
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