Joint detection and high resolution ML estimation of multiple sinusoids in noise

Harmonic analysis, the analysis of signals which consist of a sum of sinusoids (or complex sinusoids) with additive white or colored noise, is a much studied problem, with many important applications. Nevertheless, existing approaches have significant limitations. In many, the model order (number of sinusoids) is assumed known, and in most cases additive white Gaussian noise (AWGN) is assumed. We present a method for jointly determining the model order and estimating the sinusoid parameters in white or colored noise. It uses the notch periodogram in an iterative detection and estimation algorithm. It uses an explicit detection test based on an estimate of the noise power density spectrum (PDS), which is obtained by smoothing the logarithm of the notch periodogram.