Analysis of discretization errors in if estimation of polynomial phase signals

The peak of the polynomial Wigner-Ville distribution (PWVD) is a method for providing an unbiased estimate of the instantaneous frequency (IF) for polynomial phase signals. The theoretical lower variance bound, assuming a continuous frequency variable, has been studied previously. However, due to the discretization of the PWVD required for computer implementation, there is also another theoretical lower variance bound which is a result of the discretization error. In this paper, we study the relationship between the discretization error bound and the theoretical lower variance bound and determine the minimum number of frequency samples required such that the theoretical lower variance bound can be attained.

[1]  I. Djurovic,et al.  Influence of high noise on the instantaneous frequency estimation using quadratic time-frequency distributions , 2000, IEEE Signal Processing Letters.

[2]  Boualem Boashash,et al.  Polynomial Wigner-Ville distributions and their relationship to time-varying higher order spectra , 1994, IEEE Trans. Signal Process..

[3]  D. C. Reid,et al.  Aircraft flight parameter estimation based on passive acoustic techniques using the polynomial Wigner–Ville distribution , 1997 .

[4]  Braham Barkat,et al.  Instantaneous frequency estimation of polynomial FM signals using the peak of the PWVD: statistical performance in the presence of additive gaussian noise , 1999, IEEE Trans. Signal Process..

[5]  Peter J. Kootsookos,et al.  Threshold behavior of the maximum likelihood estimator of frequency , 1994, IEEE Trans. Signal Process..

[6]  LJubisa Stankovic,et al.  Instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length , 1998, IEEE Trans. Signal Process..

[7]  C.R. Patisaul.  Analog and digital communication systems , 1981, Proceedings of the IEEE.

[8]  F. Taylor,et al.  Estimation of instantaneous frequency using the discrete Wigner distribution , 1990 .

[9]  Srdjan Stankovic,et al.  On the Wigner distribution of discrete-time noisy signals with application to the study of quantization effects , 1994, IEEE Trans. Signal Process..

[10]  Ljubisa Stankovic,et al.  Performance of quadratic time-frequency distributions as instantaneous frequency estimators , 2003, IEEE Trans. Signal Process..

[11]  Martin S. Roden.  analog and digital communication systems, 2nd. ed. , 1985 .

[12]  Braham Barkat,et al.  Design of higher order polynomial Wigner-Ville distributions , 1999, IEEE Trans. Signal Process..

[13]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals , 1992, Proc. IEEE.