All-Phase Digital Discontinuous Signal Processing

This dissertation deals with processing discontinuous signal by the method of All Phase including All Phase truncating of continuous signal, All Phase processing to the signal with discontinues point, All Phase processing to the truncation caused by the boundary of finite frequency filter, and All Phase designing of the filter with discontinuous frequency characteristic. First, the paper introduces All Phase truncation considering all kinds of truncation situations, which can make the truncation error less. The signal is analyzed through All Phase spectrum analysis. It can be verified by experimental results that All Phase spectrum analysis has good characters which can reduce leakage and distinguish the spectrum of a small signal beside a big signal, and the reason of which is interpreted deeply. And All phase DFT frequency amplitude phase correction is put forward which has higher precision. All Phase least square approximation to the discontinuous signal is also introduced with less error than the traditional method.Secondly, two kinds of All Phase frequency sampling method are deduced, which are especially suitable for designing filters with discontinuous frequency characteristic. This method not only can assure the expect response of sampling points, but also improve the character between sampling points. The dissertation researches All Phase FIR filter deeply and four kinds of All Phase linear filters are designed which make the theory of All Phase more integrity. Additionally, the problem of controlling cut-off frequency can be resolved through the combination of the two kinds of All Phase sampling method and through the shift and compensation. Some examples are given in the paper. Some researches were also accomplished on the designing of sharp-pass band filters by the All phase FRM method, which requairs few arithmetic operations.Thirdly, this paper proposes a new design method of All Phase half band filte with no transition point, small overshooting, small pass and stop band ripple, sharp transition band. It can be implemented spectrum factorization to get QMF, which can get perfect reconstruction signal with error is only 5×10^-13, while traditional error is 5×10^-4.Finally, the All Phase power spetrum estimation and All Phase color noise are researched. The color noise is analyzed by using Welch method and All Phase power spectrum method seperatly, of which the test result shows that our method can detect...