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The sinc function is often used as the basis for the design of discretelinear-phase FIR filters. However the Fourier transform of the truncated sincfunction exhibits ripple in the pass band due to the Gibbs phenomenon. Thispaper introduces an alternative function based on Chebyshev polynomials whoseFourier transform decreases monotonically in the pass band. Furthermore thisfunction features an intrinsic window function with an adjustable parameterinfluencing the Fourier transform in the transition and stop bands.

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