Page 74 - DSP Integrated Circuits

DIGITAL SIGNAL

PROCESSING

3.1 INTRODUCTION

In Chapters 3 and 4 we will present terminology and, in brief, synthesis and anal-
ysis methods used in the design of some common digital signal processing func-
tions. In practice, the DSP system design process comprises a mixture of empirical
and ad hoc methods aimed at coping with large system complexity and minimizing
the total cost [8]. Typically, the resulting DSP system is composed of blocks repre-
senting well-known "standard" functions—for example, frequency selective niters,
adaptive filters, correlation, spectral estimation, discrete Fourier and cosine trans-
forms, and sample rate converters. The design of such basic DSP functions is
therefore a topic of interest.
It is useful to apply different design methodologies to some well-known DSP
subsystems in order to better understand the advantages and disadvantages of a
given approach. Such design studies may provide not only a better understanding
of the strengths and weaknesses of the design methodology, but also a better
insight into the computational properties of DSP algorithms. Further, they may
provide points of reference and a basis for the design of more complex DSP sys-
tems. We will therefore carry out the first design iteration for three fixed-function
subsystems that will demonstrate different implementation trade-offs.
The objective of the first design iteration is to investigate the feasibility of
the selected implementation approach and estimate major system parameters,
such as power consumption and chip area. Two of these functions involve dis-
crete transforms used in many DSP applications—for example, for data compres-
sion, spectrum analysis, and filtering in the frequency domain. One of the best-
known discrete transforms is the DFT (discrete fourier transform). The signal
processing properties of the DFT are similar to the discrete-time Fourier trans-
form [4, 9, 17, 39, 401. The practical usefulness of a transform is governed not
only by its signal processing properties, but also by its computational complexity.
The number of arithmetic operations required to directly compute the DFT is
very large for long sequences. It was therefore a major breakthrough when a fast