Exact Short-Time Identification of Rational or Polynomial Exponent Signals

Abstract

This paper describes a novel model and short-time estimation method of nonstationary or generalized sinusoids and their parameters. The model expresses the time derivative of log-amplitude and phase (complex exponent) with a rational function of time. When all poles of the rational function are simple, it is integrated to obtain the sum of polynomial and logarithm functions. The former generates a polynomial exponent signal, which is multiplied by an intensely time-varying function generated from the latter. Its direct estimator based on the weighted integral method provides an exact solution in the noiseless case from a small number of finite (short-time) Fourier coefficients; thus, multiple sinusoids separated in either the time domain or the frequency domain can be estimated independently. Several experimental tests of the basic performances are shown under possible application scenarios including the analog or digital AM/FM wave demodulation, radar/sonar pulse detection and parameterization, and combined uses of the proposed method with pulse compression.