Direct Frequency Domain IIR Filter Design Methods ∗

The preceding design methods have been based on designing an analog prototype lter and then converting it to a digital lter. This approach is appropriate for the class of approximations where analytical solutions are possible, but not for many others. In the remaining part of this chapter, methods will be developed that directly design the desired digital lter. Most approaches are extensions of methods used for FIR lters, but they are more complicated for the IIR case where rational approximation is being performed rather than polynomial approximation. In this section a frequency-sampling design method is developed such that the frequency response of the IIR lter will pass through the given samples of a desired response. Since an IIR lter cannot have linear phase, the sampled response must contain both magnitude and phase. The extension of the frequencysampling method to a LS-error approximation is not as simple as for the FIR lter. The method presented in this section uses a criterion based on the equation error rather than the more common error between the actual and desired frequency response[1]. Nevertheless, it is a useful noniterative design method. Finally, a general discussion of iterative design methods for LS-frequency response error is given.