Digital Communications with Emphasis on Data Modems

APPENDIX A CLASSICAL FILTERS AND APPLICATIONS

A.1 INTRODUCTION

In this chapter, the application of analog filter designs in the evaluation of systems involving discrete‐time sampled data simulations is described. This approach is straightforward, in that, the use of the impulse‐invariant z‐transform is used in the system simulation where and T_s is the sampling interval. The parameter is the Laplace transform variable. The filter designs are sufficiently band‐limited and the system simulation sampling frequency is sufficiently high so that aliasing is negligible. This is the case in system simulations where the sampling frequency is generally several times the symbol rate to provide for frequency error and receiver timing resolution during acquisition and tracking.

The analog filter designs used in this chapter are classical and appear in a number of references [1–8], so the derivation of the filter design details are not examined. However, the results presented are intended to document the implementation details as embodied in filter and system simulation programs. The filters examined in this appendix are the Butterworth filter with maximally flat amplitude (Section A.2.1), the Bessel filter with maximally flat delay (Section A.2.3), the Chebyshev filter with equal passband ...