Digital Signal Processing Reference
In-Depth Information
Finite Impulse Response Filters
•
Introduction to the
z
-transform
•
Design and implementation of finite impulse response (FIR) filters
•
Programming examples using C and TMS320C6x code
The
z
-transform is introduced in conjunction with discrete-time signals. Mapping
from the
s
-plane, associated with the Laplace transform, to the
z
-plane, associated
with the
z
-transform, is illustrated. FIR filters are designed with the Fourier series
method and implemented by programming a discrete convolution equation. Effects
of window functions on the characteristics of FIR filters are covered.
4.1 INTRODUCTION TO THE
z
-TRANSFORM
The
z
-transform is utilized for the analysis of discrete-time signals, similar to the
Laplace transform for continuous-time signals. We can use the Laplace transform
to solve a differential equation that represents an analog filter or the
z
-transform
to solve a difference equation that represents a digital filter. Consider an analog
signal
x
(
t
) ideally sampled
•
Â
0
()
=
()
(
)
xt
xt t kT
d
-
(4.1)
s
k
=
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