X ( z ) x(k ) z k
We restrict the Z-transform in two important and practical ways
We focus our attention primarily on time signals that are of finite duration
, x(0), x(1)," , x( N 1)
We evaluate X ( z ) at the finite num
I A digital lter is a discrete-time system that is designed to reshape the
spectrum of the input signaI in order to produce desired spectral characteristics
in the output signal.
I We focus on the FIR lter in this chapter.
mth order FIR fil
8.5 Bilinear-transformation Method
I Now that we have a collection of analog prototype lters to select from, the
next problem is to transform an analog lter into an equivalent digital lter.
Analog Analog Digital
Fundamentals of Digital Signal Processing
Robert J. Schilling
Sandra L. Harris
Digital signal processing(DSP) is a modern discipline built
around engineering techniques that enjoy widesprea
I In this chapter, we investigate the design of digital innite impulse response
x(k) yUt) _ b0 +512" +-+bmz"
X(z) n3) H(Z)_ l+a]z"+-+anz'"
I A digital lter is a frequency-selective lter that modies the magnitude
spectrum and th
xa (t )
ya (t )
ya (t ) a1 ya
( n 1)
(t ) " an ya (t )
(t ) b1 xa
( m 1)
y (k )
y (k ) a1 y (k 1) " an y ( k
We use the term filter to describe a LTI system used to perform
spectral shaping or frequency-selective filtering.
Filtering is used in DSP in a variety of ways.
removal of undesirable noise from desired signals
spectral shaping such as e
For the LTI discrete-time system of H ( z ) with the input x(k ), the
zero-state response y (k ) is the convolution
y (k )
h(i) x(k i)
To measure the degree to which the pattern of an L-point signal
h(k ) is similar to the patte
84 Classical Analog Filters
I An effective way to decrease the width of the transition band is to allow
ripples or oscillations in the passband or the stopband.
I Chebyshev-I lter of order n is designed to allow an ripples with in