Digital Communications with Emphasis on Data Modems

APPENDIX B DIGITAL FILTER DESIGN AND APPLICATIONS

B.1 INTRODUCTION

In this appendix, several methods for the design of digital filters are reviewed. Typical applications involve rate conversion filtering, transmitter waveform filtering for spectral control, demodulator filtering for coherent and noncoherent data detection, image rejection filtering following receiver heterodyning, and a variety of bandpass and lowpass filter applications involved in waveform detection, acquisition, and verification. The two fundamental types of digital filters considered are characterized as infinite impulse response (IIR) and finite impulse response (FIR) filters. The IIR filters involve feedback in which the output is the summation of the input with weighed samples of previous outputs; whereas, the FIR is strictly a feedforward implementation in which the output is the summation of a finite number of weighed input samples. The FIR implementation is also referred to as a transversal filter (TF), tapped delay line (TDL) filter, and sequential filter (SF) in which the input signal samples are sequentially stored in the memory of a TDL.

These filters exhibit a unit sample response h(n) that is linear and shift‐invariant [1] and, for an input x(n), the response y(n) is characterized by the convolution sum

(B.1)

The condition for a linear shift‐invariant filter to be causal requires that ...