A Function Based on Chebyshev Polynomials as an Alternative to the Sinc Function in FIR Filter Design

TL;DR

This paper proposes a Chebyshev polynomial-based function as an alternative to the sinc function for FIR filter design, reducing passband ripple and offering adjustable parameters for better control over filter characteristics.

Contribution

It introduces a novel Chebyshev polynomial-based function that improves FIR filter design by minimizing passband ripple and providing adjustable transition and stop band features.

Findings

Fourier transform decreases monotonically in the pass band

Intrinsic window function with adjustable parameter

Reduced ripple compared to truncated sinc function

Abstract

The sinc function is often used as the basis for the design of discrete linear-phase FIR filters. However the Fourier transform of the truncated sinc function exhibits ripple in the pass band due to the Gibbs phenomenon. This paper introduces an alternative function based on Chebyshev polynomials whose Fourier transform decreases monotonically in the pass band. Furthermore this function features an intrinsic window function with an adjustable parameter influencing the Fourier transform in the transition and stop bands.