Page 200 - Mechanical Engineers' Handbook (Volume 2)

Mechanical Engineers’ Handbook: Instrumentation, Systems, Controls, and MEMS, Volume 2, Third Edition.

Edited by Myer Kutz

Copyright  2006 by John Wiley & Sons, Inc.

CHAPTER 6
SIGNAL PROCESSING
John Turnbull
Case Western Reserve University
Cleveland, Ohio
1 FREQUENCY-DOMAIN 3.1 z-Transforms 198
ANALYSIS OF LINEAR 3.2 Design of FIR Filters 198
SYSTEMS 189 3.3 Design of IIR Filters 201
3.4 Design of Various Filters from
2 BASIC ANALOG FILTERS 191 Low-Pass Prototypes 203
2.1 Butterworth 193 3.5 Frequency-Domain Filtering 205
2.2 Tchebyshev 194
2.3 Inverse Tchebyshev 195 4 STABILITY AND PHASE
2.4 Elliptical 195 ANALYSIS 206
2.5 Arbitrary Frequency Response 4.1 Stability Analysis 206
Curve Fitting by Method of 4.2 Phase Analysis 206
Least Squares 196 4.3 Comparison of FIR and IIR
2.6 Circuit Prototypes for Pole Filters 208
and Zero Placement for
Realization of Filters Designed 5 EXTRACTING SIGNAL FROM
from Rational Functions 197 NOISE 208
3 BASIC DIGITAL FILTER 197 REFERENCES 208

1 FREQUENCY-DOMAIN ANALYSIS OF LINEAR SYSTEMS
Signals are any carriers of information. Our objective in signal processing involves the en-
coding of information for the purpose of transmission of information or decoding the infor-
mation at the receiving end of the transmission. Unfortunately, the signal is often corrupted
by noise during our transmission, and hence it is our objective to extract the information
from the noise. The standard method most commonly used for this involves filters that exploit
some separation of the signal and noise in the frequency domain. To this end, it is useful to
use frequency-domain tools such as the Fourier transform and the Laplace transform in
designing and analyzing various filters. The Fourier transform of a function of a time is
1
2
F{ƒ(t)} F( ) ƒ(t)e j t dt j 1 (1)
2
For continuous systems, the transfer characteristics of a filter system is a function that gives
information of the gain versus frequency. The Laplace transform for a given time-domain
function is

L{ƒ(t)} F(s) ƒ(t)e st dt (2)
0
The steady-state Laplace transform (i.e., neglecting transients) for the derivative and integral
of a given function is

189