Joint High-Resolution Fundamental Frequency and Order Estimation

Abstract

In this paper, we present a novel method for joint estimation of the fundamental frequency and order of a set of harmonically related sinusoids based on the MUSIC estimation criterion. The presented method, termed HMUSIC, is shown to have an efficient implementation using FFTs. Furthermore, refined estimates can be obtained using a gradient-based method. Illustrative examples of the application of the algorithm to real-life speech and audio signals are given, and the statistical performance of the estimator is evaluated using synthetic signals, demonstrating its good statistical properties.

An iterative subspace-based multi-pitch estimation algorithm

“…The cost function of (9) is evaluated first using FFT-based method to obtain a coarse estimate of o k . Then, these coarse estimates are used to initialize the gradientbased methods to achieve a refined estimate [5]. Furthermore, our methods are compared with CRLB and non-iterative HMUSIC [10].…”

“…Numerous algorithms have been proposed see, e.g. [1][2][3][4][5][6][7]. In real recorded signals, however, multi-pitch scenarios occur more frequently than single-pitch scenarios.…”

“…The problem is to estimate o k from x(n) with N measured samples. The estimation problem associated with the real case can be cast as (1) by the use of analytic signals, which is valid when there is little or no spectral content of interest near 0 and p. In this paper, we assume that the number of sources K and the model orders L k of the individual sources are known, order estimation can be achieved with multi-dimensional search of the extended cost function [1,5].…”

“…Recently, subspace-based fundamental frequency estimators have shown good estimation performance both for single and multi-pitch cases [5,1,8]. This type of methods is forming a cost function by exploiting the orthogonality properties between the noise and signal subspaces decomposed from a covariance matrix.…”

Default Bayesian Estimation of the Fundamental Frequency

“…Provided that the frequencies of the first and last harmonics are not too close to zero and the Nyquist frequency (relative to N ), respectively, the parameter estimates based on the down-sampled analytic signal are nearly identical to the corresponding parameter estimates based on the real-valued signal [2], [9]. In this paper, the focus is on the complex-valued signal model since it leads to simpler notation and faster algorithms [2], [10]. However, the results for the real-valued signal model are also given.…”