Spectrum estimation, notch filters, and MUSIC

A novel extension of the Multiple Signal Classification (MUSIC) algorithm for the frequency estimation problem is proposed in this work. It is shown that the MUSIC algorithm is a data-dependent optimum notch filter design technique. When the input data are passed through this optimum notch filter, the signal-to-noise ratio (SNR) of the output is minimized. The zeros of the optimum notch filter are then used to estimate the frequencies. In the classical MUSIC algorithm, this optimization is carried out over the set of all finite impulse response (FIR) filters having a fixed order. The framework of this paper allows the use of rational notch filters. The fact that the rational filters have sharper spectral characteristics is used to obtain improved estimates, particularly at low SNR. Some interesting properties of the proposed algorithm are derived, and further perspectives on the implementation aspects are provided. The analytical predictions are substantiated using numerical simulation results