Determining Autocorrelation Matrix Size and Sampling Frequency for MUSIC Algorithm
Arunava Naha, Anik Kumar Samanta, Aurobinda Routray, Alok Kanti Deb · IEEE Signal Processing Letters · 2014
Detectability of closely spaced sinusoids in a noisy signal using MUltiple SIgnal Classifier (MUSIC) depends to a great extent on the sampling frequency (Fs) and the size of the autocorrelation matrix (N). Improper choice of any of these may result in increased computational burden and/or unresolved frequency components. This paper presents an analytical approach to determine expressions of lobe width using Fsand N at lobe base (Δfb) and half of the lobe height (Δfh). The required values of Fsand N can be derived from the expression of Δfbfor distortion-less lobe heights of two closely spaced sinusoids. A tighter bound can be found using the expression of only Δfhto resolve two distinct peaks. Probability of resolution using reciprocal of MUSIC peaks is determined for various N and it's limit for full resolvability was verified with the derived analytical expressions.