An efficient Hilbert transform interpolation algorithm for peak position estimation

Abstract

An efficient algorithm for estimating the peak position of a sampled function is presented. The algorithm uses the Hilbert transform of the function for peak detection via interpolation. The accuracy of the proposed method is demonstrated using an example where the frequency of a sinusoid is determined by detecting the peak of the FFT of the signal. It is shown that the algorithm has computational advantage when the positions of many peaks of the sampled function are required to be estimated, e.g. as in the fundamental and harmonic frequency estimation of an audio signal. Spectral characteristics of the Hilbert transform amplitude and phase functions and the rationale for the use of Hilbert transform for interpolation are also discussed in detail.