Peak filter and notch filter for harmonic retrieval using higher-order statistics

In this paper, an algorithm using the well-known notch filter and an algorithm using a peak filter are proposed to estimate the frequencies of sinusoidal signals with a given set of Gaussian noise corrupted measurements y(n) provided that the number of sinusoids is known in advance. The former processes y(n) such that a single fourth-order cumulant of the notch filter output is minimum in absolute value, while the latter processes y(n) such that the same fourth-order cumulant of the peak filter output is maximum in absolute value. Then the unknown frequencies are obtained from the optimum notch filter and the optimum peak filter, respectively. A performance analysis of the two proposed algorithms is then presented followed by some simulation results for a performance comparison of the proposed algorithms and Swami and Mendel´s (1991) SVD low-rank approximation method