Abstract
Recently, two optimal filter designs for fundamental frequency estimation have been proposed with the first being based on a filterbank and the second on a single filter. The two designs are related in a simple manner and are shown to result in the same residual when used for cancelling out the harmonics of periodic signals. We propose to use this residual for estimating the number of harmonics by combining a noise variance estimate with an order dependent penalty term. This leads to a joint estimator of the fundamental frequency and the order based on the same criterion. Via Monte Carlo simulations, the estimator is demonstrated to have good performance in terms of the percentage of correctly estimated orders.
Highlights
Periodic signals can be characterized by a sum of sinusoids, each parametrized by an amplitude, a phase, and a frequency
We remark that the nonlinear least-squares (NLS), MUSIC and optimal filtering methods under consideration here are comparable in terms of computational efficiency as they all have cubic complexity, involving either inverses of matrices, matrix-matrix products or eigenvalue decompositions of matrices
Since one cannot generally assume that only a single periodic source is present, we will test the methods for a multi-pitch signal containing two sources, namely the signal of interest and an interfering periodic source that is considered to be of no interest to us
Summary
Periodic signals can be characterized by a sum of sinusoids, each parametrized by an amplitude, a phase, and a frequency. The frequency of each of these sinusoids, sometimes referred to as harmonics, is an integer multiple of a fundamental frequency. When observed, such signals are commonly corrupted by observation noise, and the problem of estimating the fundamental frequency from such observed signals is referred to as fundamental frequency, or pitch, estimation. Some signals contain many such periodic signals, in which case the problem is referred to as multi-pitch estimation, this is somewhat of an abuse of terminology, albeit a common one, as the word pitch is a perceptual quality, defined for acoustical signals as “that attribute of auditory sensation in terms of which sounds may be ordered on a musical scale” [1]. The problem under investigation here is that of estimating the fundamental
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