The Research Of Parameter Estimation Based On All Phase And Reconstruction Algorithm For Short-sample Signals

Signal parameter estimation and reconstruction is essential in the fields of radarcommunications, voice processing, fault diagnosis and even medical clinics.However,when sample is insufficient, the performance of the existing signal parameterestimation and reconstruction methods will be in serious decline. For example,sinusoidal signal composed of two conjugate complex exponential frequencycomponents, when the sample holds too short support interval, two conjugatedcomponents become near thereby introducing ignorable spectral interference, directlycausing a sharp decline in the performance of frequency estimation. Moreover, shortsamples reduce spectral resolution, and the concentrated distribution of the frequencycomponents become higher, it similarly produces spectral interference, reduces thefrequency, phase and amplitude estimation accuracy. Recently, compressed sensingsignal reconstruction becomes a research hotspot, its reconstruction error will bebigger when sample length is too short. In the light of the above signal processingproblems caused by short sample, this thesis presents a parameter estimation based onall phase and reconstruction algorithm for short sample signals.To make high precision parameter measurement for short sample signal, allphase FFT spectrum analysis is extended to all phase DTFT in the thesis, and basedon this, to estimate parameters of short support interval and intensive spectrum signal.All phase DTFT is a continuous spectrum, it’s not only with good spectrum leakageinhibition performance, but its phase spectrum contains more parameter informations.When used for a short interval sinusoidal signal, we can estimate its frequencyparameter through all phase DTFT amplitude spectrum search to obtain a higherprecision than traditional DTFT, and also can pass through extreme point scanning ofphase spectrum to further improve the precision. When used for short sample doubleintensive frequencies signal, this thesis has proved when each amplitude spectrumpeak cannot be identified (even though the spectral interval is less than1frequencyresolution), with the help of all phase DTFT phase spectrum, we still can achieve highprecision of frequency, phase and amplitude s. Experimental results show that thealgorithms consume less samples, have high estimation accuracy and anti-noiseability. Signal reconstruction is a core of compressed sensing system, however theexisting reconstruction algorithms ignore the orthogonal property of transformationmatrix, therefore spend a very long sample. Therefore, this thesis proposes spectralcorrection to reduce sample consumption. Spectrum correction theory is quite mature,but the existing ones are not suitable for direct DFT to original signal in compressedsensing system (cannot do orthogonal transformation with window).The thesis takesDFT matrix as orthogonal transform matrix, Fourier spectrum as observation sample,based on this it proposes a compressed sensing reconstruction algorithm to processDFT spectral line without window. The algorithm only needs the amplitude ratio ofpeak spectrum and sub-peak spectrum lines, it can achieve high reconstructionprecision, reduce the RIP requirement, it is also characterized with high stability andmin error in noisy situation.