CN115840080A - Frequency spectrum analysis technology based on Chirp transformation architecture and rapid digital pulse pressure algorithm - Google Patents

Frequency spectrum analysis technology based on Chirp transformation architecture and rapid digital pulse pressure algorithm Download PDF

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CN115840080A
CN115840080A CN202211554277.XA CN202211554277A CN115840080A CN 115840080 A CN115840080 A CN 115840080A CN 202211554277 A CN202211554277 A CN 202211554277A CN 115840080 A CN115840080 A CN 115840080A
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signal
chirp
frequency
intermediate frequency
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李大帅
童玲
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Yangtze River Delta Research Institute of UESTC Huzhou
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Yangtze River Delta Research Institute of UESTC Huzhou
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Abstract

The invention relates to a signal spectrum analysis technology based on linear frequency modulation transformation, which comprises a linear frequency modulation signal processing circuit system, a linear phase discrete point time domain distribution function algorithm and a digital pulse compression part. The Chirp signal processing circuit mixes the generated Chirp signal (i.e. an intra-pulse Chirp repetition signal) with a signal to be detected as a local oscillation signal to obtain a Chirp signal, i.e. a modulation Chirp signal, modulated by the signal to be detected. And inputting the modulated chirp signal into a band-pass filter to obtain an intermediate frequency chirp signal and outputting the intermediate frequency chirp signal. ADC is used for carrying out A/D conversion on the intermediate frequency chirp signal, and a digital signal is output. The digital signal is composed of a series of intermediate frequency chirp signals with the same initial frequency, termination frequency and chirp rate but different initial time, and the initial time of each chirp signal component corresponds to the frequency contained in the signal to be measured. And calculating a linear phase discrete sampling point time distribution function meeting the secondary phase characteristic of the intermediate frequency chirp signal output by the filter. And extracting the intermediate frequency chirp signal according to a time distribution function to obtain two groups of linear phase orthogonal sampling points, and performing superposition calculation to obtain signal spectrum information. The invention organically combines a hardware circuit signal processing system and a software algorithm, and realizes rapid and high-resolution spectrum analysis and measurement.

Description

Frequency spectrum analysis technology based on Chirp transformation architecture and rapid digital pulse pressure algorithm
Technical Field
The invention belongs to the field of signal processing, and particularly relates to a spectrum analysis method of a fast digital pulse pressure algorithm based on a Chirp Transform spectrum analyzer (Chirp Transform Spectrometer-CTS) architecture.
Background
The spectrum analyzer is used as a main instrument for detecting the signal spectrum, and has various principles. The classic heterodyne frequency-sweeping spectrum analyzer is the earliest, the system has certain frequency-sweeping time, the scanning time is long when a broadband signal is measured, and real-time spectrum analysis cannot be achieved. With the advent of high-speed ADCs, the increase in chip computing power, and the development of high-speed bus technology, fourier transform spectrometers based on digital signal processing technology have been developed. The Fourier transform spectrometer is mainly based on a Fast Fourier Transform (FFT) algorithm, i.e., the frequency spectrum characteristic of a measured signal is obtained through the FFT algorithm after analog-to-digital conversion. The Fourier transform spectrometer can realize real-time analysis of broadband and high-resolution signals, and meanwhile, the process is fully digital processing, so that remote control and spectrum reconstruction are easy, and the system integration level is high. However, the FFT architecture has some disadvantages, the thermal power consumption is large, and the increase of the resolution results in a large increase of the FFT computation.
In recent years, a linear frequency modulation transform spectrum analyzer (CTS) based on a radar pulse compression technology is widely applied to the fields of spaceflight and deep space exploration. The basic principle of the CTS is to mix a signal to be measured with a Chirp signal having known characteristics, the intermediate frequency signal output by the mixing is subjected to band-pass filtering to form an intermediate frequency Chirp signal having a specific Chirp rate and a fixed frequency band, the intermediate frequency Chirp signal is subjected to pulse compression by using a surface acoustic wave filter, and the frequency spectrum information of the signal to be measured can be obtained according to the time domain distribution and the envelope information of the output pulse pressure signal. The method can realize broadband high-resolution real-time spectrum analysis and has the advantages of small volume, light weight, low power consumption and the like. However, the physical pulse compression mode based on the surface acoustic wave filter has the problems of large attenuation, non-ideal dispersion characteristics and the like, and influences the system spectral resolution and the measurement dynamic range. In addition, the bandwidth of the saw filter is limited, and a parallel processing of a multi-path structure is often required when processing a broadband signal.
The invention uses digital pulse compression technology to replace surface wave filter, solving the problem existing in CTS spectrum analysis technology.
Disclosure of Invention
The invention aims to solve the problems of great signal attenuation and non-ideal dispersion characteristics of a surface acoustic wave filter in a CTS system, and provides a real-time spectrum analysis method based on a digital pulse compression technology.
In order to achieve the above purpose, the invention designs a fast digital pulse compression algorithm. The method can realize the rapid pulse compression of the intermediate frequency Chirp signal and solve the problems of attenuation, non-ideal dispersion and the like of the surface acoustic wave filter. The method specifically comprises the following steps:
(1) Spectral modulation of a signal under test
Let the input signal contain m spectral components, and its time domain mathematical model is as follows:
Figure BDA0003979026210000021
wherein, a i 、f i And
Figure BDA0003979026210000022
respectively representing the amplitude, frequency and initial phase of the ith spectral component. />
Chirp signal s ec (t) is a chirp signal that can be expressed as:
Figure BDA0003979026210000023
the subscript "ec" indicates the Chirp signal. a is ec 、f ec0 And
Figure BDA0003979026210000024
respectively representing the amplitude, initial frequency and initial phase of the Chirp signal, k representing the Chirp rate of the Chirp signal, and T 0 The Chirp signal has bandwidth of B = kT representing the duration of one period 0 。
Mixing the input signal with a Chirp signal to obtain a modulated Chirp signal:
Figure BDA0003979026210000025
the subscript "mc" denotes the modulation Chirp. l m Representing the mixing coefficients of the mixer, in the subsequent derivation,/ m The ideal value is 1. When the input signal and the Chirp signal meet the linear working range of the mixer, the amplitude of the modulated Chirp signal output by the intermediate frequency end of the mixer and the amplitude of the input signal at the radio frequency end are in a linear relation. The output difference frequency signal of the modulated Chirp signal after passing through the low-pass filter is:
Figure BDA0003979026210000031
the subscript "mcdf" denotes the difference frequency component in the modulated Chirp signal.
(2) Modulated Chirp signal bandpass filtering
As shown in equation (4), the initial and final frequencies of the modulated Chirp signal vary with the frequency of the signal to be measured. And inputting the modulated Chirp signal into an intermediate frequency filter to obtain an intermediate frequency Chirp output signal with the same initial frequency and termination frequency and different initial time, thereby realizing the conversion from frequency to time.
The modulated Chirp signal is filtered by an intermediate frequency band-pass filter, and the output intermediate frequency Chirp signal is represented as follows:
Figure BDA0003979026210000032
Figure BDA0003979026210000033
in the formula (5), the subscript "if" represents an intermediate frequency Chirp signal, l f Representing filter coefficients, in subsequent derivation f The ideal value is 1. In the formula (6) f bpfstart And f bpfstop Respectively representing the start and end frequencies of the if bandpass filter. As can be seen from equations (5) and (6), the intermediate frequency Chirp signal contains m Chirp components, and the start frequency, the end frequency and the duration of each Chirp component are the same, but the start frequency, the end frequency and the duration of each Chirp component are the sameThe start and end times of each Chirp component are different. According to the equation (6), the start and end times of the Chirp signal are related to the frequency of the input signal. Let B bpf Represents the passband of the bandpass filter, let t i As the initial time of the ith intermediate frequency Chirp component:
Figure BDA0003979026210000034
formula (5) can be further expressed as:
Figure BDA0003979026210000035
/>
Figure BDA0003979026210000036
the intermediate frequency Chirp signal of equation (8) contains amplitude and frequency information of each input signal component.
(3) Orthogonal decimation time series
The first step in digital pulse compression of the intermediate frequency Chirp signal is to determine two sets of orthogonal sampling points. Aiming at the characteristics of the intermediate frequency Chirp signal expressed by the formula (8), such as phase, chirp rate, initial termination frequency and the like, two groups of discrete sampling time sequences are designed
Figure BDA0003979026210000041
And &>
Figure BDA0003979026210000042
(superscripts 1 and 2 represent two mutually orthogonal sample point sequences), the phases and the corresponding time distributions of the two sets of sample points satisfy the following relationship:
Figure BDA0003979026210000043
Figure BDA0003979026210000044
wherein the content of the first and second substances,
Figure BDA0003979026210000045
is an arbitrary constant and is set to 0. Aiming at the ith intermediate frequency Chirp signal component, two groups of orthogonal sampling point time sequences->
Figure BDA0003979026210000046
And &>
Figure BDA0003979026210000047
Has a value range of t i ～t i +B bpf And N is a positive integer from 1 to N. Since discrete sampling times do not guarantee that the two completely ideal sets of orthogonal sampling points are obtained, a phase deviation measure is introduced into equation (11)>
Figure BDA0003979026210000048
And N represents the number of sampling points of the two groups of time sequences and is determined by the bandwidth, the frequency range and the Chirp rate of the intermediate frequency Chirp signal. Ideally the value of N is:
Figure BDA0003979026210000049
from equations (10) and (11), a time series can be derived
Figure BDA00039790262100000410
And &>
Figure BDA00039790262100000411
The values of (A) are as follows:
Figure BDA00039790262100000412
Figure BDA00039790262100000413
according to the formula (13) and the formula (14), two sets of time series
Figure BDA00039790262100000414
And &>
Figure BDA00039790262100000415
The difference between the values of adjacent elements in (a) varies with n.
(4) Digital pulse compression
After two groups of orthogonal sampling point time sequences are obtained, equations (13) and (14) are respectively processed from t j And extracting the intermediate frequency Chirp signal at any moment, accumulating and summing the sequence values of the two groups of extracted orthogonal sampling points, and squaring and adding to obtain information related to the ith frequency component power of the input signal. The orthogonal sampling point sequences at different initial moments change t after the calculation j And obtaining power information of different frequency components.
The intermediate frequency Chirp signal of the formula (8) is processed according to a time sequence
Figure BDA0003979026210000051
And &>
Figure BDA0003979026210000052
From t j The sampling accumulation is started at the moment, and the obtained result can be represented as:
Figure BDA0003979026210000053
/>
Figure BDA0003979026210000054
wherein the time sequence of the samples
Figure BDA0003979026210000055
And &>
Figure BDA0003979026210000056
Satisfies the following conditionsConditions are as follows:
Figure BDA0003979026210000057
let Δ t ji ＝t i -t j Equation (17) can be expressed as:
Figure BDA0003979026210000058
Figure BDA0003979026210000059
according to equations (18) and (19), when i = j, equations (15) and (16) will become: (changing i to j)
Figure BDA00039790262100000510
Figure BDA00039790262100000511
Correspondingly, the input signal amplitude a corresponding to the jth intermediate frequency Chirp component j Can be expressed as:
Figure BDA00039790262100000512
for other intermediate frequency Chirp components (i.e., i ≠ j), equation (15) is:
Figure BDA0003979026210000061
order to
Figure BDA0003979026210000062
Δf ji ＝kΔt ji Equation (23) can be simplified as:
Figure BDA0003979026210000063
similarly, equation (16) can be expressed as:
Figure BDA0003979026210000064
equations (24) and (25) show that the final accumulation result of the fast digital pulse compression algorithm is equivalent to the discrete value accumulation of a cosine signal. When N is large enough, the accumulated result goes to zero.
(5) Frequency resolution and noise floor
For a fixed compression duration T c By comparing equation (20) with equation (24), the frequency resolution f can be calculated by finding the 3dB bandwidth r The relationship with the compression duration is:
Figure BDA0003979026210000065
/>
wherein the content of the first and second substances,
Figure BDA0003979026210000066
and &>
Figure BDA0003979026210000067
Respectively correspond to Δ t ji < 0 and Δ t ji Frequency resolution in the case of > 0. As can be seen from equation (26), the frequency resolution is mainly related to the compression duration and the Chirp rate k. When the Chirp rate k is determined, the frequency resolution of the system is only related to the compression duration. Different frequency resolutions can be achieved by varying the compression duration. When +>
Figure BDA0003979026210000068
The influence of the Chirp rate k on the frequency resolution is negligible, i.e. only in systems with lower frequency resolution the influence of the Chirp rate is taken into account.
The pulse compression process can be divided into spectral detection at low frequency resolution and spectral detection at high frequency resolution. Under the low frequency resolution, the frequency spectrum detection realizes quick frequency spectrum rough separation by using shorter compression time length, and determines the approximate distribution of the frequency spectrum; the spectrum detection under the high frequency resolution is realized by utilizing a longer compression time length to realize high-resolution spectrum subdivision under the condition that the approximate distribution of the spectrum is known.
The purpose of the invention is realized as follows:
the invention relates to a software and hardware combined spectrum analysis method based on linear frequency modulation conversion and a rapid digital pulse pressure algorithm. And mixing and filtering the detected signal and a local oscillator Chirp signal to obtain a band-pass filtering output Chirp signal containing the characteristics of the detected signal. Calculating a periodic equiphase discrete point array time distribution function satisfying quadratic phase characteristics according to characteristics of a Chirp signal output by band-pass filtering
Figure BDA0003979026210000071
From t according to the law of the time distribution function 1 Sequentially extracting corresponding equal-phase sampling point values from the Chirp signal output by the band-pass filter at the moment, accumulating and summing to calculate the root mean square, namely the Chirp signal at the initial moment is t 1 And the corresponding band-pass filtering outputs the amplitude of the Chirp component, namely the amplitude of a certain frequency component of the detected signal. Changing t 1 The amplitude information of other frequency components of the detected signal can be obtained.
The invention uses the periodic equiphase superposition algorithm to replace the original surface acoustic wave filter to realize rapid pulse compression, solves the matching problem between devices and links, and simultaneously avoids the problems of large signal attenuation, link matching, difficult device processing and the like of the surface acoustic wave filter. Compared with the traditional digital pulse compression algorithm, the method greatly reduces the calculation amount aiming at the sparse spectrum under the condition of ensuring the sufficient signal amplitude accuracy.
Drawings
FIG. 1: a flow chart of a digital frequency spectrum calculation method based on linear frequency modulation transformation and a rapid digital pulse pressure algorithm;
FIG. 2 is a schematic diagram: and the tested signal and the Chirp signal are mixed and stretched schematically.
Detailed Description
The following description of specific embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It should be particularly noted that in the following description, a detailed description of known functions and designs will be omitted herein when it may obscure the subject matter of the present invention.
Examples
FIG. 1 is a flow chart of a digital spectrum calculation method based on chirp conversion and fast digital pulse pressure according to the present invention.
In this embodiment, as shown in fig. 1, the method for calculating a digital spectrum based on chirp transform and fast digital pulse pressure according to the present invention includes the following steps:
1. frequency mixing output modulation Chirp signal of detected signal and local oscillator Chirp signal
The invention needs to mix the tested signal with the local oscillator Chirp signal with known characteristics to obtain the modulated spectrum broadening Chirp signal s mc (t) correlating the frequency components of the signal under test with the initial frequency of the mixed output modulated Chirp signal, as shown in fig. 2. In the embodiment, the initial frequency of the local oscillator Chirp signal is 3.4GHz, the termination frequency is 5.4GHz, and the Chirp rate is 100MHz/us. The signal to be measured contained 11 dot frequency signals, the frequencies of which were 5.6GHz,5.7GHz,5.9GHz,5.999GHz,6.0GHz,6.01GHz,6.03GHz,6.06GHz,6.1GHz,6.3GHz and 6.4GHz, the signal amplitude was set to 0.14V, and the initial phase was 0.
2. Modulated Chirp signal bandpass filtering
Inputting the modulated Chirp signal into a band-pass filter to obtain an intermediate frequency Chirp output signal s with the same initial frequency, termination frequency and different initial time ifc (t) of (d). Signal s ifc And (t) is composed of a plurality of Chirp signal components, as shown in the formula (5). The Chirp signal components have the same start frequency, end frequency and Chirp rate but different initial times. The Chirp signal components at different initial times correspond to different frequency components of the signal under test, as shown in fig. 2.
In this embodiment, the modulated Chirp signal passes through a band-pass filter with a center frequency of 1.6GHz and a passband width of 1GHz, and an intermediate frequency Chirp signal with a bandwidth of 1GHz is output. The filtering output signal consists of 11 Chirp signal components with initial frequency of 1.1GHz, end frequency of 2.1GHz and Chirp rate of 100MHz/us, and the initial time of the 11 Chirp signals in the time domain corresponds to the frequency of the signal to be measured.
3. Linear phase quadrature sampling point sequence
In order to detect each Chirp signal component in the intermediate frequency Chirp signal, two groups of mutually orthogonal discrete sampling point sequences are calculated according to the formula (10) and the formula (11), and the time rule is adopted
Figure BDA0003979026210000081
The formula (17) is satisfied. In this embodiment, the value of the phase approximation factor is p = (-3%). 2 π, and the sampling rate is 5GSPS.
4. Intermediate frequency Chirp signal digital pulse compression
At a sampling rate of 5G, s is matched from zero time according to equation (5) ifc (t) performing linear phase orthogonal sampling point extraction to obtain two orthogonal sampling point arrays
Figure BDA0003979026210000082
Respectively superposing all elements in the sampling point array to obtain->
Figure BDA0003979026210000083
Calculating the amplitude of the corresponding frequency point as: />
Figure BDA0003979026210000084
5. Spectral information extraction of a signal under test
Since different frequency information of the detected signal is reflected on the intermediate frequency Chirp signal components with different initial moments, in order to obtain each frequency component of the detected signal, the initial moments of the orthogonal sampling point sequences need to be changed in sequence, that is, the time distribution function in step 4 is used
Figure BDA0003979026210000085
And (4) performing translation on the whole time axis to detect and compress intermediate frequency Chirp signal components at different initial moments.
In the embodiment, when the frequency resolution is set to 100kHz and the Chirp rate is 100MHz/us, the corresponding time resolution Δ t is 1ns. For intermediate frequency Chirp signal s ifc And (t), calculating once according to the step 4 at intervals of 1ns (corresponding to 5 discrete sampling points under the sampling rate of 5 GSPS) and obtaining the amplitude information of the corresponding frequency components. And calculating the frequency spectrum information of the whole frequency band in sequence. For comparison, the embodiment also adopts a classic time domain pulse compression algorithm to the intermediate frequency Chirp signal s ifc (t) calculating.

Claims (4)

1. The patent relates to a spectrum analysis technology based on a linear frequency modulation conversion framework and a rapid pulse compression algorithm, the characteristics of which depend on a signal spectrum analysis technology combining hardware signal modulation and a digital pulse compression algorithm, and the spectrum analysis technology mainly comprises the following steps:
1) Modulating the measured signal and the local oscillator broadening linear frequency modulation signal;
2) Band-pass filtering of the modulated chirp signal;
3) Outputting the digital sampling of the intermediate frequency linear frequency modulation signal;
4) Extracting the quadrature phase of the sampling signal, and performing pulse compression operation and spectrum detection based on a digital pulse compression algorithm;
5) The time domain window function translation enables spectral scanning within the entire bandwidth.
2. According to the spectral analysis technique mentioned in claim 1, the specific method of linear phase quadrature extraction described in step 4) is expressed as follows: according to the initial frequency, the termination frequency and the Chirp rate of the intermediate frequency linear frequency modulation signal, two groups of mutually orthogonal sampling time sequence sequences can be calculated, and the two groups of time sequence sequences can be regarded as the same phase basis function of the intermediate frequency linear frequency modulation signal.
3. According to the spectrum analysis technique of claim 1, the specific detection and compression method of the if chirp signal described in step 4) can be expressed as follows: firstly, two groups of extracted orthogonal digital signal sequences are respectively accumulated, the root mean square operation is carried out on the result, and the obtained root mean square value is the amplitude value of the corresponding frequency, so that the digital pulse compression of the intermediate frequency linear frequency modulation signal is realized.
4. According to the spectrum analysis technique mentioned in claim 1, the specific signal spectrum measurement method based on the linear phase and time shift characteristic time series described in step 5) can be expressed as follows: the linear frequency modulation of the signal to be measured is realized by a hardware modulation method, an intermediate frequency linear frequency modulation signal with a specific bandwidth is obtained through a band-pass filter, the linear component of each different time reference in the intermediate frequency linear frequency modulation signal is realized by digital pulse compression through the linear phase time sequence method mentioned in the step 4), and the frequency and amplitude information of the signal to be measured is calculated according to the pulse envelope and time distribution information obtained by the pulse compression.
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