TABLE OF CONTENTS The inverse Chebyshev approximation function, also called the Chebyshev type II function, is a rational approximation with both poles and zeros in its transfer function. This approximation has a smooth, maximally flat response in the passband, just as the Butterworth approximation, but has ripple in the stopband caused by the zeros of the transfer function. The inverse Chebyshev approximation provides better transition characteristics than the Butterworth filter and'better phase response than the standard Chebyshev. Although the inverse Chebyshev has these features to recommend it to the filter designer, it is more involved to design.
The development of the inverse Chebyshev response is derived from the standard Chebyshev response. We will discuss the methods needed to determine the inverse Chebyshev approximation function while leaving the intricate details to the reference works. The name "inverse Chebyshev" is well-deserved in this case since we will see that many of the computations are based on inverse or reciprocal values from the standard computations. Let's begin with the definition of the magnitude frequency response function as shown in (2.34).
The first observation concerning (2.34) is that it indeed has a numerator portion that allows for the finite zeros in the transfer function. Upon closer inspection, we find the use of ? i in place of ?. Equation (2.35) indicates ? i, the inverse of ?, where a pass is replaced with a stop. Because of the differences, we...
