New transformed variables for designing recursive digital filters

In this paper we discuss the use of linear transformations on z+1/z in designing magnitude squared functions . It is shown how the design of lowpass, highpass and nonsymmetric bandpass recursive digital filters with given zeroes is transformed to the problem of designing a magnitude squared function having its passband stretched onto the whole unit circle. This magnitude squared function for equal ripple and maximally flat responses is then obtained analytically using the theory of rational approximations.