CN106817130A - Burst signal lack sampling system and method based on the limited new fixed rate of interest - Google Patents

Burst signal lack sampling system and method based on the limited new fixed rate of interest Download PDF

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CN106817130A
CN106817130A CN201710029078.XA CN201710029078A CN106817130A CN 106817130 A CN106817130 A CN 106817130A CN 201710029078 A CN201710029078 A CN 201710029078A CN 106817130 A CN106817130 A CN 106817130A
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burst signal
signal
lack sampling
sampled
fixed rate
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付宁
黄国兴
乔立岩
范传智
曹杰
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Harbin Institute of Technology
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Harbin Institute of Technology
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    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03MCODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M1/00Analogue/digital conversion; Digital/analogue conversion
    • H03M1/12Analogue/digital converters
    • H03M1/124Sampling or signal conditioning arrangements specially adapted for A/D converters
    • H03M1/1245Details of sampling arrangements or methods

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  • Theoretical Computer Science (AREA)
  • Digital Transmission Methods That Use Modulated Carrier Waves (AREA)

Abstract

Burst signal lack sampling system and method based on the limited new fixed rate of interest, is related to signal processing technology field.The present invention is modulated by four-way, amplified and LPF and lack sampling treatment using the parametrization characteristic of burst signal, obtains the fourier coefficient of discrete distribution in burst signal frequency spectrum.The a small amount of fourier coefficient by getting reconstructs unknown amplitude and delay parameter again.Time delay reconstruction accuracy of the invention is very high, and amplitude Estimation only has the error of very little.

Description

Burst signal lack sampling system and method based on the limited new fixed rate of interest
Technical field
The present invention relates to signal processing technology field, more particularly to a kind of burst signal based on the limited new fixed rate of interest is owed to adopt Sample system and method.
Background technology
Burst signal is widely present in the fields such as radio communication, medical imaging and radar.For the sampling of such signal, Traditional nyquist sampling theorem requirement sample rate is greater than the twice of signal highest frequency.With the hair of wireless communication technique Exhibition, the time width of pulse is more and more narrow, and corresponding bandwidth is more and more wider, causes Nyquist sample rate also more and more higher, and this undoubtedly gives Sampling System Design based on nyquist sampling theorem brings stern challenge.Sample frequency requirement ADC devices higher With analog bandwidth and sample rate wider, meanwhile, high sampling rate will produce substantial amounts of sampled data, this to system storage and Transfer resource also increases extra burden.Thus, nyquist sampling theorem is increasingly becoming burst signal sampling system and sets The bottleneck of meter, governs the development of signal processing technology.
2002, Vetterli et al. proposed that a kind of lack sampling of utilization signal parameter characteristic is theoretical --- limited new breath Rate (Finite Rate of Innovation, abbreviation FRI) is sampled.The theory is different from nyquist sampling theorem, and it refers to Go out:For the parameter sparse signal that some can be completely represented by a limited number of free parameter, such as burst signal, as long as choosing After checking its filtering with suitable sampling, and uniform sampling is carried out with the speed greater than or equal to the new fixed rate of interest of signal, it is possible to profit Go out unknown parameter with the sample Perfect Reconstruction for collecting.The sampling rate of FRI sampling theories is only by the new fixed rate of interest of signal, i.e. unit Free parameter number decision in time, will generally be much smaller than the nyquist sampling rate of signal, so as to greatly drop Low sampling rate.
It is using Sinc samplings core (i.e. perfect low pass filter that the simplest method of Fourier coefficients is obtained to burst signal Ripple device), however, the method is merely able to obtain one section of continuous fourier coefficient subset, quality reconstruction is poor;Tur et al. is introduced A kind of single channel pre-sampling filtering obtains any discrete fourier coefficient, but this filter response exists It is difficult in practical application;Gedalyahu et al. is directly acquire inputted signal using multichannel mixing integration structure Fourier coefficient, each passage can only gather a fourier coefficient in this structure, and hardware system is in large scale, and each logical Synchronization between road is a very big problem;One kind is devised in order to obtain the fourier coefficient of discrete distribution, Eldar et al. Multichannel lack sampling radar receiver, however, in order to avoid spectral aliasing, the structure employs a kind of complicated and simulation of redundancy Preprocessing process.So far, under limited new fixed rate of interest theoretical frame, the discrete distribution of burst signal how is efficiently obtained Fourier coefficient, is still a key issue.
The content of the invention
For above-mentioned deficiency, the present invention provides a kind of burst signal lack sampling system and side based on the limited new fixed rate of interest Method.
Burst signal lack sampling system based on the limited new fixed rate of interest of the invention, the system is generated including modulated signal Module, four-way lack sampling module and reconstructed module;
Modulated signal generation module, for generating 4 tunnel modulated signals;
Four-way lack sampling module, after burst signal to be sampled is split into 4 tunnels, respectively with 4 tunnel modulated signals Be modulated, to modulation after 4 road signals be amplified successively and filter, intercept discrete point in burst signal frequency spectrum to be sampled Four sub- bands are carried out lack sampling by four subbands of cloth;
Reconstructed module, for the sample according to sampling, obtains fourier coefficient, using restructing algorithm from fourier coefficient Estimate the amplitude and delay parameter of burst signal to be sampled.
Preferably, the lack sampling module of each passage in the four-way lack sampling module includes multiplier, amplifies Device, wave filter and ADC sampler;
Burst signal to be sampled is input into multiplier simultaneously with modulated signal all the way, is input into after being multiplied through multiplier to putting Big device, amplified device is input into wave filter after amplifying, and after filtered device LPF, obtains discrete distribution in shunting signal frequency spectrum A subband;ADC sampler carries out lack sampling with the speed higher than 2 times of low pass filter cutoff frequency to the subband.
Preferably, the modulated signal generation module, the cosine signal different for generating 4 tunnel frequencies.
Preferably, the multiplication factor of the amplifier is 10 times.
Preferably, the system, also including display module, the width for showing the burst signal to be sampled for estimating Value and delay parameter.
The present invention provides the burst signal lack sampling method based on the limited new fixed rate of interest, and methods described includes:
Step one:Generate 4 tunnel modulated signals;
Step 2:It is modulated with 4 tunnel modulated signals respectively after burst signal to be sampled is split into 4 tunnels, after modulation 4 road signals be amplified successively and LPF, the subband of discrete distribution in the signal spectrum of filtered 4 road is intercepted respectively, Lack sampling is carried out to the four sub- bands for intercepting with the speed higher than 2 times of low pass filter cutoff frequency;
Step 3:Sample to sampling carries out DFT, fourier coefficient is obtained, using restructing algorithm from Fu The amplitude and delay parameter of burst signal to be sampled are estimated in vertical leaf system number.
Preferably, in the step one, the frequency of modulated signal is ωi, i=1 ..., 4;
Wherein, N represent on sampling time axle interval [0, T) grid number that is divided, m represents arbitrarily selected integer, ωmaxIt is the highest frequency of burst signal to be sampled.
Preferably, the modulated signal is the different cosine signal of 4 tunnel frequencies.
Preferably, the step 2 comprises the following steps:
Step 2 one:After burst signal to be sampled is split into 4 tunnels, it is modulated with 4 tunnel modulated signals respectively;
Step 2 two:Signal after each channel modulation is amplified 10 times;
Step 2 three:LPF is carried out to the signal after amplification using low pass filter, by four filtering of passage It is truncated to four subbands of discrete distribution in burst signal frequency spectrum to be sampled;
Step 2 four:Low speed sampling is carried out with the speed higher than 2 times of low pass filter cutoff frequency, lack sampling is realized.
Preferably, the step 3 comprises the following steps:
Step 3 one:Sample is yi[n], n represents sample number, and its continuous time Fourier transform is Yi(ω),K=1,2 ..., K;K represents the quantity of fourier coefficient;
Step 3 two:Delay parameter tl=nl△, △=T/N, wherein nl∈ { 0,1 ..., N-1 }, train of pulse letter to be sampled The continuous time Fourier transform of number x (t) is:
alIt is the amplitude of burst signal to be sampled, j refers to imaginary part, and L represents the quantity of delay parameter;
Step 3 three:According to formula two and formula three, the continuous time Fourier transform of signal is after modulation:
Wherein, HmK () is known complex exponential sequence;
Step 3 four:Obtain K >=2L non-zero fourier coefficientUsing OMP algorithms from these Fourier leaf systems Parameter is estimated in numberLast delay parameter estimate
The beneficial effects of the present invention are the present invention is modulated using the parametrization characteristic of burst signal by multichannel With the simulation preprocessing means such as LPF, the fourier coefficient of discrete distribution in input signal spectrum is obtained.Again by obtaining To a small amount of fourier coefficient reconstruct unknown amplitude and delay parameter.Due to unknown in the unit interval in burst signal Number of parameters will be much smaller than its signal bandwidth, therefore, it is possible to greatly reduce sampling rate.Experimental verification, time delay weight of the invention Structure precision is very high, and amplitude Estimation only has the error of very little.
Above-mentioned technical characteristic can in any suitable manner be combined or substituted by equivalent technical characteristic, as long as can reach To the purpose of the present invention.
Brief description of the drawings
Fig. 1 is the principle schematic of the burst signal lack sampling system based on the limited new fixed rate of interest in implementation method one.
Fig. 2 is that the principle of the burst signal lack sampling system based on the limited new fixed rate of interest realized using specific chip is illustrated Figure.
Fig. 3 is the principle schematic of four-way lack sampling module in implementation method one.
Fig. 4 is the primary signal in experimental verification;
Fig. 5 is the signal in experimental verification using method of the present invention sample reconstruction;
Fig. 6 is the quality reconstruction figure of different Sub-nyquist sampling methods.
Specific embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than whole embodiments.It is based on Embodiment in the present invention, those of ordinary skill in the art obtained on the premise of creative work is not made it is all its His embodiment, belongs to the scope of protection of the invention.
It should be noted that in the case where not conflicting, the embodiment in the present invention and the feature in embodiment can phases Mutually combination.
The invention will be further described with specific embodiment below in conjunction with the accompanying drawings, but not as limiting to the invention.
Implementation method one:The burst signal lack sampling system based on the limited new fixed rate of interest described in present embodiment, such as Fig. 1 It is shown, including modulated signal generation module, four-way lack sampling module and reconstructed module;
Modulated signal generation module, for generating 4 tunnel modulated signals;
Four-way lack sampling module, after burst signal to be sampled is split into 4 tunnels, respectively with 4 tunnel modulated signals Be modulated, to modulation after 4 road signals be amplified successively and filter, intercept discrete point in burst signal frequency spectrum to be sampled Four sub- bands are carried out lack sampling by four subbands of cloth;
Reconstructed module, for the sample according to sampling, obtains fourier coefficient, using restructing algorithm from fourier coefficient Estimate the amplitude and delay parameter of burst signal to be sampled.
Present embodiment also includes burst signal generation module to be sampled, for generating burst signal to be sampled;
As shown in Fig. 2 the burst signal generation module to be sampled of present embodiment uses AWG NI PXIe-5442 is realized.
The modulated signal generation module of present embodiment is realized using multifunctional data acquisition card NI PXIe-6368.
Present embodiment is embedded into PXle-1082 cabinets using host computer Labview softwares, control modulated signal generation Module and burst signal generation module to be sampled work, while being additionally operable to realize the function of reconstructed module.
Burst signal to be sampled is split into 4 tunnels, and 4 tunnel modulated signals are input to four-way lack sampling module simultaneously, Be modulated and amplify and low-pass filtering treatment after, then carry out lack sampling.
As shown in figure 3, the four-way lack sampling module of present embodiment adopts module including module pretreatment module sum;
Module pretreatment module includes four multipliers, four amplifiers and four wave filters;
The multiplier of present embodiment realizes that the amplifier of present embodiment uses chip LT1101 using chip AD633 Realize, the wave filter of present embodiment is realized using chip MAX275.
Number adopts module includes four ADC samplers;
The ADC sampler of present embodiment is realized using multi-functional DAQ boards NI PXI-6255.
Burst signal to be sampled is modulated with 1 tunnel modulated signal through multiplier all the way, amplifies through amplifier after modulation, The filtered device of signal of amplification carries out LPF, obtains a subband of discrete distribution in shunting signal frequency spectrum;ADC sampler Lack sampling is carried out to the subband with the speed higher than 2 times of low pass filter cutoff frequency.
In preferred embodiment, the modulated signal in present embodiment is the different cosine signal of 4 tunnel frequencies.
In preferred embodiment, the multiplication factor of the amplifier of present embodiment is 10 times.
In preferred embodiment, present embodiment also includes display module, for showing the train of pulse to be sampled for estimating letter Number amplitude and delay parameter.
Implementation method two:The burst signal lack sampling method based on the limited new fixed rate of interest of present embodiment, including:
Step one, generates burst signal to be measured, and signal form is represented byWherein, t ∈ [0, T) it is observation time,It is unknown parameter.
Step 2:4 tunnel modulated signals are generated, signal form is expressed as pi(t)=cos (ωiT), i=1 ..., 4.Wherein, ωiIt is modulating frequency.
Wherein, N represent on time shaft interval [0, T) grid number that is divided, m represents arbitrarily selected integer, ωmax It is the highest frequency of burst signal to be sampled.
Step 3:Simulation preprocessing process:Burst signal to be sampled is modulated with 4 tunnel modulated signals respectively, is adjusted Signal after system is amplified and LPF successively, intercepts four sons of discrete distribution in burst signal frequency spectrum to be sampled Four sub- bands are carried out lack sampling by band, specifically include following steps:
Step 3 one:Stage of modulating:It is different with 4 tunnel frequencies respectively after burst signal to be sampled is split into 4 tunnels Cosine signal be modulated;
Step 3 two:Amplification stage:For the loss that Compensation Modulation process is brought, the signal after each channel modulation is amplified 10 times;
Step 3 four:LPF is carried out to the signal after amplification, arteries and veins to be sampled is truncated to by the filtering of four passages Rush four subbands of discrete distribution in string signal frequency spectrum;
Step 3 five:Low speed sampling is carried out with the speed higher than 2 times of low pass filter cutoff frequency, lack sampling is realized.Adopt Collect the Fourier coefficients of the DFT as input pulse string signal of sample.
Step 4:DFT is carried out to the signal that sampling is obtained, fourier coefficient is obtained, using restructing algorithm The amplitude and delay parameter of burst signal to be sampled are estimated from fourier coefficient, following steps are specifically included:
Step 4 one:Sample is yi[n], n represents sample number, and its continuous time Fourier transform is Yi(ω),K=1,2 ..., K;K represents the quantity of fourier coefficient;
Step 4 two:Delay parameter tl=nl△, △=T/N, wherein nl∈ { 0,1 ..., N-1 }, train of pulse letter to be sampled The continuous time Fourier transform of number x (t) is:
alIt is the amplitude of burst signal to be sampled, j refers to imaginary part, and L represents the quantity of delay parameter;
Step 3 three:According to formula two and formula three, the continuous time Fourier transform of signal is after modulation:
Wherein,Because m and impulse waveform h (t) are priori , it is known that HmK () is known complex exponential sequence;Unknown parameter in formula four is onlyTherefore only need obtain K >= 2L non-zero fourier coefficientK=1,2 ..., K can estimate all of unknown parameter, and then reconstruct input Pulse signal.
Step 4 four:Obtain K >=2L non-zero fourier coefficientUsing OMP (Orthogonal Matching Pursuit, orthogonal matching pursuit) algorithm estimates parameter from these fourier coefficientsWhen last Prolong estimates of parameters
Experimental verification:In order to verify performance of the invention, hardware experiments checking has been carried out.Using AWG NI PXIe-5442 generates burst signal to be measured, it is assumed that the burst signal is represented byIts middle arteries Waveform h (t)=sinc (2Bt) is rushed for known a priori, the peak frequency of signal is B=200kHz.Observation interval t ∈ [0, T) Inside there are L=8 pulse, T=1s.Delay parameter is set to tl=[0.1,0.15,0.3,0.4,0.5,0.6,0.8,0.9], width Degree parameter is set to al=[8,6,6.5,7,5,9,6.5,8.5].Modulated signal is produced by DAQ equipment NI PXIe-6368, shape Formula is pi(t)=cos (2 π fiT), modulating frequency fi=[10,50,70,80] kHz.In stage of modulating, test signal enters 4 Passage is mixed with 4 modulated signals respectively.Signal after filtering stage, modulation is cut off the analog low-pass that frequency is 1KHz and filters Ripple device MAX275 is filtered.
Experiment one, under noise-free case, is sampled simultaneously with the sample rate of 5KHz using PXIe-6368 to filtering signal It is transferred to reconstructed module.Therefore, total sampling rate is 5*4=20KHz, is reduced compared to Nyquist Nyquist frequencies 400KHz 20 times.Reconstruction result is as shown in figure 5, primary signal is as shown in Figure 4.By experimental result as can be seen that time delay of the invention is reconstructed Precision is very high, and amplitude Estimation has the error of very little.
Experiment two, white Gaussian noise is superimposed by test signal, and signal to noise ratio increases to 50dB from 0dB.Using the present invention and base Compare in single pass LPF method, the quality reconstruction of different Sub-nyquist sampling methods is as shown in fig. 6, wherein single The LPF method of passage includes the reconstruct filtered using OMP and incidental expenses.Test result indicate that in low signal-to-noise ratio, this hair It is bright to have preferably performance than the method based on low pass filter, because Fourier coefficients aperture is very crucial in a noisy environment.And As signal to noise ratio increases, aperture becomes no longer so important, and at this time total hits determines quality reconstruction.
Although describing the present invention herein with reference to specific implementation method, it should be understood that, these realities Apply the example of example only principles and applications.It should therefore be understood that can be carried out to exemplary embodiment Many modifications, and other arrangements are can be designed that, without departing from the spirit of the invention that appended claims are limited And scope.It should be understood that can be by way of different from described by original claim come with reference to different appurtenances Profit is required and feature specifically described herein.It will also be appreciated that the feature with reference to described by separate embodiments can be used In other described embodiments.

Claims (10)

1. a kind of burst signal lack sampling system based on the limited new fixed rate of interest, it is characterised in that the system includes that modulation is believed Number generation module, four-way lack sampling module and reconstructed module;
Modulated signal generation module, for generating 4 tunnel modulated signals;
Four-way lack sampling module, after burst signal to be sampled is split into 4 tunnels, is carried out with 4 tunnel modulated signals respectively Modulation, to modulation after 4 road signals be amplified successively and filter, intercept discrete distribution in burst signal frequency spectrum to be sampled Four sub- bands are carried out lack sampling by four subbands;
Reconstructed module, for the sample according to sampling, obtains fourier coefficient, is estimated from fourier coefficient using restructing algorithm Go out the amplitude and delay parameter of burst signal to be sampled.
2. the burst signal lack sampling system based on the limited new fixed rate of interest according to claim 1, it is characterised in that described The lack sampling module of each passage in four-way lack sampling module includes multiplier, amplifier, wave filter and ADC sampler;
Burst signal to be sampled is with modulated signal all the way while input is input into amplification to multiplier after multiplier multiplication Device, amplified device is input into wave filter after amplifying, after filtered device LPF, discrete distribution in acquisition shunting signal frequency spectrum One subband;ADC sampler carries out lack sampling with the speed higher than 2 times of low pass filter cutoff frequency to the subband.
3. the burst signal lack sampling system based on the limited new fixed rate of interest according to claim 2, it is characterised in that described Modulated signal generation module, the cosine signal different for generating 4 tunnel frequencies.
4. the burst signal lack sampling system based on the limited new fixed rate of interest according to claim 3, it is characterised in that described The multiplication factor of amplifier is 10 times.
5. the burst signal lack sampling system based on the limited new fixed rate of interest according to claim 4, it is characterised in that described System, also including display module, amplitude and delay parameter for showing the burst signal to be sampled for estimating.
6. a kind of burst signal lack sampling method based on the limited new fixed rate of interest, it is characterised in that methods described includes:
Step one:Generate 4 tunnel modulated signals;
Step 2:It is modulated with 4 tunnel modulated signals respectively after burst signal to be sampled is split into 4 tunnels, 4 tunnels after modulation Signal is amplified and LPF successively, the subband of discrete distribution in the signal spectrum of filtered 4 road is intercepted respectively, to be higher than The speed that 2 times of low pass filter cutoff frequency carries out lack sampling to the four sub- bands for intercepting;
Step 3:Sample to sampling carries out DFT, fourier coefficient is obtained, using restructing algorithm from Fourier The amplitude and delay parameter of burst signal to be sampled are estimated in coefficient.
7. the burst signal lack sampling method based on the limited new fixed rate of interest according to claim 6, it is characterised in that described In step one, the frequency of modulated signal is ωi, i=1 ..., 4;
Wherein, N represent on sampling time axle interval [0, T) grid number that is divided, m represents arbitrarily selected integer, ωmax It is the highest frequency of burst signal to be sampled.
8. the burst signal lack sampling method based on the limited new fixed rate of interest according to claim 7, it is characterised in that described Modulated signal is the different cosine signal of 4 tunnel frequencies.
9. the burst signal lack sampling method based on the limited new fixed rate of interest according to claim 8, it is characterised in that described Step 2 comprises the following steps:
Step 2 one:After burst signal to be sampled is split into 4 tunnels, it is modulated with 4 tunnel modulated signals respectively;
Step 2 two:Signal after each channel modulation is amplified 10 times;
Step 2 three:LPF is carried out to the signal after amplification using low pass filter, is intercepted by four filtering of passage Four subbands of discrete distribution in burst signal frequency spectrum to be sampled;
Step 2 four:Low speed sampling is carried out with the speed higher than 2 times of low pass filter cutoff frequency, lack sampling is realized.
10. the burst signal lack sampling method based on the limited new fixed rate of interest according to claim 6, it is characterised in that institute Step 3 is stated to comprise the following steps:
Step 3 one:Sample is yi[n], n represents sample number, and its continuous time Fourier transform is Yi(ω),K=1,2 ..., K;K represents the quantity of fourier coefficient;
Step 3 two:Delay parameter tl=nl△, △=T/N, wherein nl∈ { 0,1 ..., N-1 }, burst signal x to be sampled T the continuous time Fourier transform of () is:
alIt is the amplitude of burst signal to be sampled, j refers to imaginary part, and L represents the quantity of delay parameter;
Step 3 three:According to formula two and formula three, the continuous time Fourier transform of signal is after modulation:
Wherein, HmK () is known complex exponential sequence;
Step 3 four:Obtain K >=2L non-zero fourier coefficientUsing orthogonal matching pursuit algorithm from these Fouriers Parameter is estimated in leaf system numberLast delay parameter estimate
CN201710029078.XA 2017-01-16 2017-01-16 Burst signal lack sampling system and method based on the limited new fixed rate of interest Pending CN106817130A (en)

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CN108984474A (en) * 2018-06-04 2018-12-11 哈尔滨工业大学 A kind of lack sampling method of non-ideal piecewise polynomial signal
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CN111224672A (en) * 2020-01-16 2020-06-02 哈尔滨工业大学 Multi-harmonic signal undersampling method based on multi-channel time delay
CN111830477A (en) * 2020-06-16 2020-10-27 哈尔滨工业大学 Time delay Doppler parameter joint estimation method based on FRI sampling

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CN108337205B (en) * 2018-03-21 2020-10-02 哈尔滨工业大学 BPSK signal undersampling parameter estimation method based on multi-channel feedback structure
CN108337205A (en) * 2018-03-21 2018-07-27 哈尔滨工业大学 A kind of lack sampling method for parameter estimation of the bpsk signal based on multi-channel feedback structure
CN108572352A (en) * 2018-04-25 2018-09-25 哈尔滨工业大学 A kind of method for parameter estimation of the phase-coded signal based on lack sampling
CN108572352B (en) * 2018-04-25 2021-05-28 哈尔滨工业大学 Parameter estimation method of phase coding signal based on undersampling
CN108984474A (en) * 2018-06-04 2018-12-11 哈尔滨工业大学 A kind of lack sampling method of non-ideal piecewise polynomial signal
CN108984474B (en) * 2018-06-04 2022-07-15 哈尔滨工业大学 Under-sampling method of non-ideal piecewise polynomial signal
CN109889231A (en) * 2019-02-01 2019-06-14 哈尔滨工业大学 Burst signal lack sampling method based on random demodulation and the limited new fixed rate of interest
CN110944336A (en) * 2019-10-18 2020-03-31 浙江工业大学 Time-frequency spectrum sensing method based on limited new information rate
CN110944336B (en) * 2019-10-18 2023-06-09 浙江工业大学 Time spectrum sensing method based on limited new information rate
CN110808929A (en) * 2019-10-23 2020-02-18 中国人民解放军陆军勤务学院 Real-complex conversion type signal-to-noise ratio estimation algorithm of subtraction strategy
CN111224672A (en) * 2020-01-16 2020-06-02 哈尔滨工业大学 Multi-harmonic signal undersampling method based on multi-channel time delay
CN111224672B (en) * 2020-01-16 2023-07-21 哈尔滨工业大学 Multi-channel delay-based multi-harmonic signal undersampling method
CN111830477A (en) * 2020-06-16 2020-10-27 哈尔滨工业大学 Time delay Doppler parameter joint estimation method based on FRI sampling

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Application publication date: 20170609