Spectrum analysis and synthesis of relaxation signals

Abstract The paper is devoted to spectrum analysis and synthesis of monotonie long-time-interval and wide-frequency-band relaxation signals by nonlinear phase FIR digital filters with the logarithmic sampling (Shtrauss, 1995). Expressions for frequency responses and filter algorithms are derived for the basic integral transforms related to spectrum analysis and synthesis. It is shown that most of the problems of spectrum analysis and synthesis may be solved by the filters designed for the Fourier and Heviside-Carson sine transforms, or by using coefficients from these filters. Peculiarities of filter design by the identification method are considered. A complex optimization criterion is proposed minimizing the square error of output signal and controlling over the filter coefficients. In order to expand the argument range and the sampling rate of output sequence, filter banks with filters having the shifted impulse responses are built up for the Fourier and Heviside-Carson sine transforms. Performance of the designed filters is evaluated. Simulation results with noisy and noise-free signals are presented.