NONSTATIONARY SINUSOIDAL MODEL FREQUENCY PARAMETER ESTIMATION VIA FRESNEL INTEGRAL ANALYSIS
Submitted as Stanford University EE 391 Report, Summer 2002

Aaron S. Master

Abstract:

In this report we show, via a Fresnel integral analysis, that linear frequency chirp functions have FFTs with parabolic phase in the FFT region corresponding to the frequencies contained in the signal. We begin with a brief review of Fresnel integrals, and then provide a theoretical discrete-time proof. We state all assumptions and approximations explicitly, and provide rigorous analysis of the error introduced by each assumption. We include examples showing that our model is invertible, and that it obtains estimates of the chirp parameter accurate to within 3% for cases where our assumptions are satisfied. We also mention and provide examples for alternative models for cases where our original assumptions are not satisfied.