Abstract
Abstract In this article, we consider the design of broadband beamformers with low complexity. In fact, the design problem is multi-objective in nature, trading off between speech distortion and noise suppression. Finding a balance between these two objectives is important in order to achieve a desired sound quality. These measures are introduced as the objectives here. The design can then be obtained via a bi-objective integer programming problem, where the coefficients of the filters are expressed as sums of signed powers-of-two terms. We study two different integer spaces and penalty functions for solving the problem. Then, an algorithm based on a discrete filled function is developed for finding the optimal design. In order to illustrate the effectiveness of the algorithm, real data is used and two broadband beamformers are demonstrated.
Highlights
The increased popularity of wireless cellular telephones and their uses in a variety of occasions has motivated the development of handsfree communication devices
Evaluation results [3] have shown that beamformers designed by least-squares technique (LS) have very good distortion controls, while the ones designed by signal-to-noise plus interference ratio (SNIR) have better suppression levels of both noise and interference when compared to LS
For the design of high-pass or low-pass finite impulse response (FIR) filters, the use of signed powers-of-two (SPT) terms via the least squares criterion or the minimax criterion have been widely studied in the literature
Summary
The increased popularity of wireless cellular telephones and their uses in a variety of occasions has motivated the development of handsfree communication devices. For the design of high-pass or low-pass finite impulse response (FIR) filters, the use of SPT terms via the least squares criterion or the minimax criterion have been widely studied in the literature Several optimization methods, such as branch and bound [14], simulated annealing [15], and searching techniques [16,17] have been proposed to tackle this class of problems. A fast and optimal conversion based on a recursive function is introduced and the problem is transformed into an integer programming problem with the number of variables greatly reduced. In order to control the suppression and the distortion simultaneously, the filter design problem is formulated as a nonlinear programming problem given below. Let W = (−1, 1)ML, the when the wordlength is taken as b-bit, the respective infinite precision solutions of Problems 1 and minimal number of SPT terms for wis defined as:. The first step is the selection of an initial point, the second step is a local search, while the third step is a global approach
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