AM-FM analysis of a chirp multicomponent signal employing MWL criterion

Abstract

A low complexity algorithm is proposed to decompose a signal into chirp components. The input signal is modeled as a summation of Amplitude Modulated-Frequency Modulated (AM-FM) components, where the number of components is known. The algorithm estimates each component individually while considers a second order innovation model for the phase of each component. Windowed Likelihood Function (WLF) is used as the cost function, as it weights samples differently and can be utilized to suit signal characteristics such as bandwidth. The estimation process is achieved in two steps. First assuming the frequencies are known the amplitudes are estimated by a closed-form solution. In the second step, the frequencies and the frequency change rates are adaptively tracked based on the estimated amplitudes. Lock-in-Range of the algorithm is reported for different windows. Simulations are conducted to study the performance of the algorithm to decompose a signal with known components in different circumstances as well as a voiced segment of speech signal.