Copyright
©Andreas Spanias
1
DSP EEE 407/591
by
Andreas Spanias, Ph.D.
Chapter 2
[email protected]
http://www.eas.asu.edu/~spanias
Copyright
©Andreas Spanias
2
Discrete-time Linear Systems – Digital Filters
x(n)
h(n)
y(n)
The output is produced by convolving the input with the impulse response
)
(
*
)
(
)
(
)
(
)
(
m
x
m
h
m
n
x
m
h
n
y
m
=
−
=
∑
∞
−∞
=
This operation can also involve a finite-length impulse response(FIR)
sequence
∑
=
−
=
L
m
m
n
x
m
h
n
y
0
)
(
)
(
)
(
An FIR filter is programmed using a multiply-accumulate instruction

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Some Definitions
•A digital filter is linear if it has the property of
generalized superposition.
•A digital filter is causal if it non anticipatory,
i.e., the present output does not depend on future
inputs.
•All real-time systems are causal.
• Non-causalities arise in image processing where
the signal indexes are spatial instead of temporal.
• Unless otherwise stated all systems in this
course will be assumed causal
Copyright
©Andreas Spanias
4
Some More
Definitions
L
b
.
∑
1
−
z
T
or
;unit delay
x(n)
x(n-1)
x(n)
b
L
x(n)
x(n)
x(n-1)
x(n)+x(n-1)
;signal scaling by a
filter coefficient
;signal addition
x(n)
x(n-1)