Digital Signal Processing Reference
In-Depth Information
1
1
0
0
−1
−1
−4
−2
0
2
4
−4
−2
0
2
4
(a) n (Seq1)
(b) n (Seq2)
1
1
0
0
−1
−1
−4
−2
0
2
4
−4
−2
0
2
4
(c) n
(d) n
1
1
0
0
−1
−1
−4
−2
0
2
4
−4
−2
0
2
4
(e) n
(f) n
Figure 2.24:
(a) First Sequence; (b) Second Sequence; (c) Second sequence time reversed (TR) and
oriented to compute the first value of the convolution sequence (arrow shows direction the second sequence
will slide, sample-by-sample, to perform convolution); (d) TR second sequence oriented to compute the
second value of the convolution sequence; (e) TR second sequence oriented to compute the third value of
the convolution sequence; (f ) TR second sequence oriented to compute the fourth value of the convolution
sequence.
Since the nonzero portion of the sequence begins at
n
= -1,
h
[
n
]
is not causal.
2.5.6 LTI SYSTEM AS A FILTER
An LTI system that has been designed to achieve a particular purpose or perform a given function, such
as frequency selection or attenuation, is called a
Filter
. There are two basic types of digital filter, the FIR
filter and the IIR filter, each having certain advantages and disadvantages that determine suitability for a
given use.
The FIR
The Finite Impulse Response (FIR), or Transversal Filter, comprises structures or algorithms that produce
output samples that are computed using only the current and previous input samples. The response of
such a system to a unit impulse sequence is finite, and hence such a system is called a Finite Impulse
