Bilinear Transform IIR Design.
The linear phase FIR filters designed above provide good approximations to the desired transfer functions at a cost in terms of filter order and hence computational load. If the phase response is of less importance it may be possible to realise the magnitude response at considerably lower orders by using IIR filters in the form of recursive rational systems. If the required IIR filter is less than roughly one third of the required FIR order then the IIR filter will be computationally more efficient.
In this section the linear phase constraint will be dropped, and a magnitude only design sought for the low-pass filter using the bilinear transform of Butterworth and Elliptic analog prototypes.
The steps are
(a). Decide on an analog prototype. Elliptic filters provide the sharpest cutoff for a given order while Butterworth provide better pass-band phase response.
(b). Calculate the analog filter band edge frequency parameters by pre-warping the digital parameters.
(c). Estimate the minimum order of the filter that will meet specification.
(d) Determine the poles and zeros and gain for the analogue filter.
(e) Use the bilinear transform to find the pole and zero locations of the equivalent digital filter in the z plane.
(f). Find the numerator and denominator coefficients corresponding to these poles and zeros.