Design of Wide-Band Sampled-Data Filters

The frequency domain of wide-band linear sampleddata filters is considered. The sampled-data filter is termed ¿wideband¿ when the frequency range of useful approximation to its continuous counterpart approaches half the sampling frequency. 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. The method is especially useful in designing wide-band sampleddata 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 aliasing[4] 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. Compenation 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, Bessel, Chebyshev, and elliptic-filter structures. The design method consists first of obtaining a rational transfer characteristic for a continuous filter that satisfies the design specifications.