Introduction to Digital Signal Processing and Filter Design

CHAPTER 7

Quantized Filter Analysis

7.1 INTRODUCTION

The analysis and design of discrete-time systems, digital filters, and their realizations, computation of DFT-IDFT, and so on discussed in the previous chapters of this book were carried out by using mostly the functions in the Signal Processing Toolbox working in the MATLAB environment, and the computations were carried out with double precision. This means that all the data representing the values of the input signal, coefficients of the filters, or the values of the unit impulse response, and so forth were represented with 64 bits; therefore, these numbers have a range approximately between 10⁻³⁰⁸ and 10³⁰⁸ and a precision of ∼2⁻⁵² = 2.22 × 10⁻⁶. Obviously this range is so large and the precision with which the numbers are expressed is so small that the numbers can be assumed to have almost “infinite precision.” Once these digital filters and DFT-IDFT have been obtained by the procedures described so far, they can be further analyzed by mainframe computers, workstations, and PCs under “infinite precision.” But when the algorithms describing the digital filters and FFT computations have to be implemented as hardware in the form of special-purpose microprocessors or application-specific integrated circuits (ASICs) or the digital signal processor (DSP) chip, many practical considerations and constraints come into play. The registers used in these hardware systems, to store the numbers have finite length, and the memory capacity ...