Design of Wideband Sampled-Data Filters

Sampled-data filter representations for continuous filters can be obtained using several different design procedures. 1 A particular design method utilizing the bilinear transformation is developed herein. The method is especially useful in designing wideband* sampled-data filters which exhibit relatively flat frequency-magnitude characteristics in successive pass and stop bands. Filters of this type are widely used in network simulation and data processing problems. 2 The design method possesses two chief advantages over the standard z transform. 3 The first is that the transformation used is purely algebraic in form. This means it can be applied easily to a continuous filter having a rational transfer characteristic expressed in either polynomial or factored form. The second advantage is the elimination of aliasing4 errors inherent in the standard z transform. Thus, the sampled-data filter obtained by this design method exhibits the same frequency response characteristics as the continuous filter except for a nonlinear warping of the frequency scale. Compensation for this warping can be made by a suitable frequency scale modification. Some of the more common filter networks to which the design method can be applied effectively are the Butterworth, Bcssel, Chebyshev, and elliptic filter structures. The essential properties of the bilinear transformation are presented * A s a m p l e d - d a t a filter design will he termed " w i d e b a n d " if t h e frequency range of useful a p p r o x i m a t i o n a p p r o a c h e s half (he sampling f r e q u e n c y .