Projection-based adaptive AM-FM chirp components signal decomposition

In this paper, the maximum windowed likelihood cost function is utilized to decompose a signal into AM-FM chirp components in presence of the white Gaussian noise. First, the MWL function is deployed in amplitude estimation assuming the frequencies are approximately known. This is equivalent to the projection of the input signal to the signature subspace of the signal. In the frequency and the frequency change rate tracking using this optimum amplitude as a function of the frequency and the frequency change rate, the cost function is optimized. This leads to minimizing the orthogonal projection of the input vector onto the estimated signature subspace of the input signal. A gradient descent adaptive algorithm is deployed to track the frequency and the frequency change rate. Simulations are conducted for both single and two component signals to study the performance of the algorithm. Comparing the results with a similar algorithm, when the estimated amplitude is not considered as a function of the frequency and the frequency change rate in the optimization process of the frequency and the frequency change rate, suggests a faster convergence and a more accurate performance in tracking the crossing frequencies by the proposed algorithm