Optimal Filter Designs for Separating and Enhancing Periodic Signals

Abstract

In this paper, we consider the problem of separating and enhancing periodic signals from single-channel noisy mixtures. More specifically, the problem of designing filters for such tasks is treated. We propose a number of novel filter designs that 1) are specifically aimed at periodic signals, 2) are optimal given the observed signal and thus signal adaptive, 3) offer full parametrizations of periodic signals, and 4) reduce to well-known designs in special cases. The found filters can be used for a multitude of applications including processing of speech and audio signals. Some illustrative signal examples demonstrating its superior properties as compared to other related filters are given and the properties of the various designs are analyzed using synthetic signals in Monte Carlo simulations.

Joint Spatio-Temporal Filtering Methods for DOA and Fundamental Frequency Estimation

“…The methods evaluated in these experiments are the optimal, white noise, and approximate filterbank ('bo', 'bw', and 'ba') and single filter ('so', 'sw', and 'sa') methods, the multichannel pitch estimator ('am') in [29], the steered response power method with phase transform ('sp') [30], and the exact and asymptotic nonlinear least squares (NLS) methods ('n' and 'an') in [10]. First, the performance of the proposed methods was evaluated for different 's in scenarios with 1) and an SNR of 30 dB, 2) and an SNR of 20 dB, and 3) and an SNR of 30 dB. The other simulation parameters were:…”

“…At time instance , we can then model the signal observed using the 'th microphone as (1) where is the recording of the desired source, and is the sum of the recorded noise and interference. In this paper, we assume that the desired signal is periodic, which is a reasonable assumption for, e.g., voiced speech and many musical instruments.…”

“…The pitch also often forms the basis of the processing of such signals. Some well-known examples include speech coding, wherein long-term predictors are used to exploit the correlation caused by the quasi-periodicity that causes the pitch, and noise reduction, wherein the pitch can be used to either directly enhance the signal of interest [1] or to estimate the properties of the noise [2]. Filters that extract or attenuate the harmonics of periodic sounds are often referred to as comb filters, due to their characteristic frequency response.…”

“…Later, it was shown that more efficient filters can be obtained via a set of notch or peak filters [4], and a few other examples of such approaches can be found in [5] and the references therein. More recently, it was shown that by generalizing the principle of the Capon spectral estimator, it is possible to design optimal, adaptive FIR comb filters [1], [6]. These filters have a number of properties that make them desirable in several applications.…”

Online Monaural Speech Enhancement Based on Periodicity Analysis and A Priori SNR Estimation

“…Some frameworks have been set up to analysis and separate periodic speech from background noise. One example is the time-domain filtering framework [6,7] which estimates the gain based on correlation calculation similar to that in the Wiener filtering framework. The algorithm described in [7] has shown to outperform two representative statistical-model based algorithms in perceptual evaluation of speech quality (PESQ) score [8] in relative low SNR conditions.…”