On the design of equal ripple delay filters with Chebyshev stopband attenuation

This paper is concerned with the design of low-pass filters, without all-pass sections, approximating to a constant group-delay in an equal ripple manner which simultaneously exhibit a Chebyshev type of stopband attenuation. A special type of equal ripple delay approximation, referred to as the constrained Chebyshev approximation, is used to derive the polynomial of odd degree in the denominator of the rational transfer functions of these filters. Then, using the procedure, described by Temes and Gyi, the imaginary axis transmission zeros are determined so that the Chebyshev stopband attenuation of the resulting filter is obtained. The steady-state and transient responses of these filters are discussed and shown to be superior when compared with those for the filters using Chebyshev delay approximants with the so-called standarderror function, especially for larger values of the maximum delay deviation. Tables are also presented enabling directdetermination of the odd-ordered approximants for minimum stopband attenuation.