Variable Filter Structure Research Articles

High performance continuous variable bandwidth digital filter design for hearing aid application

A low complexity, low delay reconfigurable digital filter structure for hearing aids is proposed in this paper. The main objective is to match a given human audiogram, with minimum error. The high computational complexity in the conventional uniform and non-uniform filter bank techniques, probes to shift the design paradigm towards variable filter structure. In this paper, Farrow structure based design is used to realize an arbitrary sample rate converter, making use of a differentiator based model, by which the bandwidth can be continuously varied. The proposed design also considers the importance of the power, area, and” delay in such a critical scenario. Exhaustive comparisons are performed with the existing literature on audiogram matching, and our design is very competitive when compared to the designs in the literature, not only with respect to the matching error but also with respect to area, power dissipation, and hardware complexity.

Developments in Constructive Nonstandard Analysis

AbstractWe develop a constructive version of nonstandard analysis, extending Bishop's constructive analysis with infinitesimal methods. A full transfer principle and a strong idealisation principle are obtained by using a sheaf-theoretic construction due to I. Moerdijk. The construction is, in a precise sense, a reduced power with variable filter structure. We avoid the nonconstructive standard part map by the use of nonstandard hulls. This leads to an infinitesimal analysis which includes nonconstructive theorems such as the Heine–Borel theorem, the Cauchy–Peano existence theorem for ordinary differential equations and the exact intermediate-value theorem, while it at the same time provides constructive results for concrete statements. A nonstandard measure theory which is considerably simpler than that of Bishop and Cheng is developed within this context.

Design of 2-D linear phase variable recursive digital filters for parallel form implementation

The magnitude and phase characteristics of digital filters are determined by the transfer function coefficients. These characteristics are often required to vary in real-time in the course of signal processing. This requirement can be achieved by filters with coefficients that are directly computable from the spectral parameters. Such filters are referred to as variable filters. An optimisation technique is proposed for the design of two-dimensional linear phase variable recursive digital filters using the parallel form. The variable coefficients are expressed as computable analytic functions of the spectral parameters defining the desired frequency response. Computer simulations show that the proposed approach can design an entire family of filters using just one variable filter structure. Examples are presented to illustrate the method.