CN108362939B - Frequency domain parameter measuring method of linear frequency modulation signal - Google Patents
Frequency domain parameter measuring method of linear frequency modulation signal Download PDFInfo
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- CN108362939B CN108362939B CN201810098772.1A CN201810098772A CN108362939B CN 108362939 B CN108362939 B CN 108362939B CN 201810098772 A CN201810098772 A CN 201810098772A CN 108362939 B CN108362939 B CN 108362939B
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Abstract
The invention discloses a frequency domain parameter measuring method of a linear frequency modulation signal, which comprises the following steps: s1, acquiring time domain data: performing time domain windowing on the signal, and dividing the signal into a plurality of data segments; s2, data transformation: performing discrete Fourier transform on each data segment to obtain a sub-band frequency spectrum corresponding to each data segment; s3, frequency spectrum interpolation: interpolating each sub-band frequency spectrum to obtain a frequency spectrum signal after point expansion corresponding to each data segment; s4, frequency spectrum time delay: adding time domain delay information on the frequency spectrum signal after point number expansion; s5, frequency spectrum synthesis: performing spectrum synthesis on all spectrum signals with time domain delay information to recover the complete spectrum of the original signal; s6, frequency domain parameter measurement: and measuring frequency domain parameters by using the recovered complete frequency spectrum. The invention comprehensively recovers the original signal frequency spectrum by using the short-time frequency spectrum, fits more frequency spectrum information of the original signal, improves the frequency resolution and further improves the measurement precision of the bandwidth and the initial frequency.
Description
Technical Field
The invention relates to frequency domain parameter measurement, in particular to a frequency domain parameter measurement method of a linear frequency modulation signal.
Background
In the process of detecting the space domain signal, Short Time Fourier Transform (STFT) is a commonly used processing method for timely obtaining frequency domain parameters such as bandwidth, initial frequency or center frequency in the captured signal pulse description word; the signal is divided into data segments with short time by sliding a window in a time domain, then each short-time signal is subjected to DFT (discrete Fourier transform) to obtain a sub-band spectrum, and corresponding frequency domain information is analyzed, but for a modulated signal such as a linear frequency modulation signal (LFM), the frequency spectrum of each short-time data segment cannot accurately reflect the frequency domain information of an original complete signal, FIG. 1 is a schematic diagram (short-time signal spectrum) for performing spectrum analysis on the signal in a narrow data window, FIG. 2 is an original signal spectrum, and it can be seen by comparing the two diagrams that each segment of spectrum only reflects part of the spectrum information of the original signal, and measurement on each sub-band spectrum parameter is affected by frequency resolution and the like, a frequency measurement error is large, and further obtaining parameters such as bandwidth, center frequency and the like of the original signal by each sub-band measurement parameter necessarily brings a large error.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a frequency domain parameter measuring method of a linear frequency modulation signal, which comprehensively recovers the frequency spectrum of an original signal by using a short-time frequency spectrum, fits more frequency spectrum information of the original signal, improves the frequency resolution and further improves the measuring precision of the bandwidth and the initial frequency.
The purpose of the invention is realized by the following technical scheme: a frequency domain parameter measurement method of a linear frequency modulation signal comprises the following steps:
s1, acquiring time domain data: performing time domain windowing on the signal, and dividing the signal into a plurality of time domain data segments x (N), wherein N is 0, 1, …, and N-1, and each data segment contains N discrete data;
s2, data transformation: performing discrete fourier transform on each data segment to obtain a subband spectrum x (k) corresponding to each data segment:
s3, frequency spectrum interpolation: interpolating a sub-band spectrum X (k) corresponding to each data segment to obtain a spectrum signal X '(k) with spread points corresponding to each data segment, where the spectrum signal X' (k) is a frequency domain signal including r × N data, and r is a positive integer;
s4, frequency spectrum time delay: adding time domain delay information on the frequency spectrum signal X' (k) corresponding to each data segment by utilizing the time domain delay property of Fourier transform;
s5, frequency spectrum synthesis: carrying out spectrum synthesis on all spectrum signals X' (k) with time domain delay information to recover the complete spectrum of the original signal;
s6, frequency domain parameter measurement: and measuring frequency domain parameters of the original signal by using the recovered complete frequency spectrum.
Wherein the step S3 includes the following substeps:
and S301, if (r-1) N zeros are complemented in X (N), and r is a positive integer, obtaining a new sequence X ' (N) of r points N, and deriving a frequency spectrum signal X ' (k) corresponding to X ' (N) through discrete Fourier transform:
as can be seen, X' (k) is a linear weighting of X (k);
s302, according to the derivation result, interpolating X (k) in the frequency domain to obtain a required frequency spectrum signal X '(k), wherein the frequency spectrum signal X' (k) is a frequency domain signal containing r × N data.
Wherein the step S4 includes the following substeps: for each data segment, adding time domain delay information to the corresponding frequency spectrum signal X' (k) by using the time domain delay property of Fourier transform to obtain:
DFT { } represents discrete Fourier transform, t represents the t-th data segment selected by a time domain window, q represents the time interval of selecting the data segment by the time domain window, and (t-1) q is the delay information of each data segment; in the formula (I), the compound is shown in the specification,
The invention has the beneficial effects that: the invention comprehensively recovers the original signal frequency spectrum by using the short-time frequency spectrum, fits more frequency spectrum information of the original signal, improves the frequency resolution and further improves the measurement precision of the bandwidth and the initial frequency.
Drawings
FIG. 1 is a schematic diagram of signal spectrum analysis within a narrow data window;
FIG. 2 is a diagram of a raw signal spectrum;
FIG. 3 is a flow chart of a method of the present invention;
fig. 4 is a diagram illustrating spectrum recovery according to an embodiment of the present invention.
Detailed Description
The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the following.
As shown in fig. 3, a method for measuring frequency domain parameters of a chirp signal includes the following steps:
s1, acquiring time domain data: performing time domain windowing on the signal, and dividing the signal into a plurality of time domain data segments x (N), wherein N is 0, 1, …, and N-1, and each data segment contains N discrete data;
s2, data transformation: performing discrete fourier transform on each data segment to obtain a subband spectrum x (k) corresponding to each data segment:
s3, frequency spectrum interpolation: interpolating a sub-band spectrum X (k) corresponding to each data segment to obtain a spectrum signal X '(k) with spread points corresponding to each data segment, where the spectrum signal X' (k) is a frequency domain signal including r × N data, and r is a positive integer;
s4, frequency spectrum time delay: adding time domain delay information on the frequency spectrum signal X' (k) corresponding to each data segment by utilizing the time domain delay property of Fourier transform;
s5, frequency spectrum synthesis: carrying out spectrum synthesis on all spectrum signals X' (k) with time domain delay information, and fitting to recover the complete spectrum of the original signal;
s6, frequency domain parameter measurement: and measuring frequency domain parameters of the original signal by using the recovered complete frequency spectrum.
Wherein the step S3 includes the following substeps:
and S301, if (r-1) N zeros are complemented in X (N), and r is a positive integer, obtaining a new sequence X ' (N) of r points N, and deriving a frequency spectrum signal X ' (k) corresponding to X ' (N) through discrete Fourier transform:
it is understood that when k is m, X' (k) is a linear weight of X (k), which can be further simplified to
When k ≠ m, X' (k) is still linear weighting of X (k), but the weighting is rather complicated.
S302, according to the derivation result, interpolating X (k) in the frequency domain to obtain a required frequency spectrum signal X '(k), wherein the frequency spectrum signal X' (k) is a frequency domain signal containing r × N data.
The step S4 includes the following sub-steps:
for each data segment, adding time domain delay information to the corresponding frequency spectrum signal X' (k) by using the time domain delay property of Fourier transform to obtain:
DFT { } represents discrete Fourier transform, t represents the t-th data segment selected by a time domain window, q represents the time interval of selecting the data segment by the time domain window, and (t-1) q is the delay information of each data segment; in the formula (I), the compound is shown in the specification,
In the embodiment of the present application, the method of the present application is used to comprehensively recover a complete signal spectrum from an LFM signal with a bandwidth of 40MHz, and the obtained result is as shown in fig. 4, as can be known from comparing fig. 2, the recovered spectrum is approximately consistent with the original spectrum, so that parameters of bandwidth and initial frequency can be accurately measured.
In conclusion, the invention comprehensively recovers the original signal spectrum by using the short-time spectrum, fits more spectrum information of the original signal, improves the frequency resolution, and further improves the measurement precision of the bandwidth and the initial frequency.
Claims (2)
1. A frequency domain parameter measurement method of a linear frequency modulation signal is characterized in that: the method comprises the following steps:
s1, acquiring time domain data: performing time domain windowing on the signal, and dividing the signal into a plurality of time domain data segments x (N), wherein N is 0, 1, …, and N-1, and each data segment contains N discrete data;
s2, data transformation: performing discrete fourier transform on each data segment to obtain a subband spectrum x (k) corresponding to each data segment:
s3, frequency spectrum interpolation: interpolating a sub-band spectrum X (k) corresponding to each data segment to obtain a spectrum signal X '(k) with spread points corresponding to each data segment, where the spectrum signal X' (k) is a frequency domain signal including r × N data, and r is a positive integer;
the step S3 includes the following sub-steps:
and S301, if (r-1) N zeros are complemented in X (N), and r is a positive integer, obtaining a new sequence X ' (N) of r points N, and deriving a frequency spectrum signal X ' (k) corresponding to X ' (N) through discrete Fourier transform:
as can be seen, X' (k) is a linear weighting of X (k);
s302, interpolating X (k) in a frequency domain according to a derivation result to obtain a required frequency spectrum signal X '(k), wherein the frequency spectrum signal X' (k) is a frequency domain signal containing r × N data;
s4, frequency spectrum time delay: adding time domain delay information on the frequency spectrum signal X' (k) corresponding to each data segment by utilizing the time domain delay property of Fourier transform;
s5, frequency spectrum synthesis: carrying out spectrum synthesis on all spectrum signals X' (k) with time domain delay information to recover the complete spectrum of the original signal;
s6, frequency domain parameter measurement: and measuring frequency domain parameters of the original signal by using the recovered complete frequency spectrum.
2. The method of claim 1, wherein the frequency domain parameter measurement is performed by: the step S4 includes the following sub-steps:
for each data segment, adding time domain delay information to the corresponding frequency spectrum signal X' (k) by using the time domain delay property of Fourier transform to obtain:
DFT { } represents discrete Fourier transform, t represents the t-th data segment selected by a time domain window, q represents the time interval of selecting the data segment by the time domain window, and (t-1) q is the delay information of each data segment; in the formula (I), the compound is shown in the specification,
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| CN117118536B (en) * | 2023-10-25 | 2023-12-19 | 南京派格测控科技有限公司 | Method, device, equipment and storage medium for determining frequency modulation stability |
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