DISCRETE-SIGNAL ANALYSIS AND DESIGN- P5 pdf

6 DISCRETE-SIGNAL ANALYSIS AND DESIGN
capabilities of Mathcad are used. MATLAB users will have no trouble trans-
lating everything in this book directly to their system. Keep printouts and
notes for future reference. Mathcad also has an excellent relationship with
an EXCEL program that has been conÞgured for complex algebra. EXCEL
is an excellent partner to Mathcad for many purposes.
An excellent, high-quality linear and nonlinear analog and digital cir-
cuit simulator such as Multisim (Electronics Work Bench, a division of
world-famous National Instruments Co., www.ni.com), which uses accu-
rate models for a wide range of electronic components, linear and nonlin-
ear, is another long-term investment for the serious electronics engineer
and experimenter. And similar to Mathcad, your circuit diagram, with
component values and many kinds of virtual test instruments, appears
on the screen. A sophisticated embedded graphing capability is included.
Less expensive (or even free) but fairly elementary alternatives are avail-
able from many other sources. For example, the beginner may want to
start with the various forms of SPICE. However, Multisim, although the
up-front cost is signiÞcant, is a valuable long-term investment that should
be considered. Multisim offers various learning editions at reduced cost. I
recommend this software, especially the complete versions, very highly as
a long-term tool for linear and nonlinear analysis and simulation. An added
RF Design package is available for more sophisticated RF modelling.
Mathcad is also interactive with LabVIEW, another product of National
Instruments Co., which is widely used for laboratory data gathering and
analysis. See for more informa-
tion on this interesting topic.
Another approach that is much less expensive, but also much less pow-
erful, involves structured programming languages such as BASIC, Fortran,
C
++
, Pascal, EXCEL, and others with which many readers have previous

experience. However, my suggestion is to get involved early with a more
sophisticated and long-enduring approach, especially with an excellent
program such as Mathcad.
For the website-friendly personal computer, the online search engines
put us in touch very quickly with a vast world of speciÞc technical refer-
ence and cross-referenced material that would often be laborious to Þnd
using traditional library retrieval methods.
INTRODUCTION 7
MathType, an Equation Editor for the word processor (http://www.
dessci.com/en/), is another valuable tool that is ideal for document and
report preparation. This book was written using that program.
And of course these programs are all available for many other uses
for many years to come. The time devoted to learning these programs,
even at the introductory level, is well spent. These materials are not free,
but in my opinion, a personal at-home modest long-term investment in
productivity software should be a part of every electronics engineer’s
and experimenter’s career (just like his education), as a supplement to
that which is at a school or company location (which, as we know, can
change occasionally).
Keep in mind that although the computer is a valuable tool, it does
not relieve the operator of the responsibility for understanding the core
technology and math that are being utilized. Nevertheless, some pleasant
and unexpected insights will occur very often.
Remember also that the introductory treatment in this book is not meant
to compete with the more scholarly literature that provides much more
advanced coverage, but hopefully, it will be a good and quite useful initial
contact with the more advanced topics.
REFERENCES
Oppenheim, A. V., and R. W., Schafer, 1999, Discrete-Time Signal Processing,
2nd ed., Prentice Hall, Upper Saddle River, NJ.

Simon, B., Various Mathcad reviews, Department of Mathematics, California
Institute of Technology.

1
First Principles
This Þrst chapter presents an overview of some basic ideas. Later chapters
will expand on these ideas and clarify the subtleties that are frequently
encountered. Practical examples will be emphasized. The data to be pro-
cessed is presented in a sampled-time or sampled-frequency format, using
a number of samples that is usually not more than 2
11
=2048. The fol-
lowing “shopping list” of operations is summarized as follows:
1. The user inputs, from a tabulated or calculated sequence, a set of
numerical values, or possibly two sets, each with N =2
M
(M =3, 4,
5, ,11) values. The sets can be real or complex in the “time”
or “frequency” domains, which are related by the Discrete Fourier
Transform (DFT) and its companion, the Inverse Discrete Fourier
Transform (IDFT). This book will emphasize time and frequency
domains as used in electronic engineering, especially communica-
tions. The reader will become more comfortable and proÞcient in
both domains and learn to think simultaneously in both.
2. The sequences selected are assumed to span one period of an eternal
steady-state repetitive sequence and to be highly separated from
Discrete-Signal Analysis and Design, By William E. Sabin
Copyright 2008 John Wiley & Sons, Inc.
9


10 DISCRETE-SIGNAL ANALYSIS AND DESIGN
adjacent sequences. The DFT (discrete Fourier transform), and DFS
(discrete Fourier series) are interchangeable in these situations.
3. The following topics are emphasized:
a. Forward transformation and inverse transformation to convert
between “frequency” and “time”.
b. Spectral leakage and aliasing.
c. Smoothing and windowing operations in time and frequency.
d. Time and frequency scaling operations.
e. Power spectrum and cross-spectrum.
f. Multiplication and convolution using the DFT and IDFT.
g. Relationship between convolution and multiplication.
h. Autocorrelation and cross-correlation.
i. Relations between correlation and power spectrum using the
Wiener-Khintchine theorem.
j. Filtering or other signal-processing operations in the time domain
or frequency domain.
k. Hilbert transform and its applications in communications.
l. Gaussian (normal) random noise.
m. The discrete differential (difference) equation.
The sequences to be analyzed can be created by internal algorithms
or imported from data Þles that are generated by the user. A library of
such Þles, and also their computed results, can be named and stored in a
special hard disk folder.
The DFT and IDFT, and especially the FFT and IFFT, are not only very
fast but also very easy to learn and use. Discrete Signal Processing using
the computer, especially the personal computer, is advancing steadily into
the mainstream of modern electrical engineering, and that is the main
focus of this book.
SEQUENCE STRUCTURE IN THE TIME

AND FREQUENCY DOMAINS
A time-domain sequence x (n)ofinÞnite duration −∞ ≤ n ≤+∞that
repeats at multiples of N is shown in Fig. 1-1a, where each x(n) is uniquely