Digital Signal Processing Reference
In-Depth Information
MACs can be arranged in a line, as shown in Figure 3.16. To alter this lter for
more taps, simply add more MACs to the right of it. From this gure, it is easy to
verify that this matches the general FIR lter form|just rearrange it to have the
adders along the top and the delay units down the left side.
a
a
a
0
1
2
x[n]
D
D
D
0
Figure 3.16: Multiply accumulate cells as a lter.
Similar to MACs are Processing Elements (PEs), which are less standardized.
PEs are modular like MACs, though their operations are not xed.
3.5
Frequency Response of Filters
FIR lters can implement several dierent functions just by changing the lter
coecients. The functions of a lter depend upon how it treats an input signal in
the frequency-domain. That is, an input signal will have dierent frequencies, and
the lter will leave some frequencies alone while getting rid of others. Thus, a lter
can be described as lowpass, highpass, bandpass, bandstop, or notch, depending on
which frequencies pass through the lter relatively unchanged. Some people prefer
the term \bandreject" to \bandstop," since these lters reject a band of frequencies.
Also, the word \notch" is often used as just another name for a bandstop lter,
though notch lters usually reject a very narrow frequency range. There are other
types of lters, such as dierentiators, allpass, and adaptive lters, but they are
outside the scope of this chapter. Also, a system is a superset of a lter. In other
words, a lter is a type of system, but a system is not necessarily a lter.
The terms lowpass and highpass are fairly self-explanatory. A good example
of a lowpass lter's frequency magnitude response appears in Figure 3.17, while
the frequency magnitude response for an example highpass lter can be seen in
Figure 3.18. Along the x-axis we have a percentage of the frequencies from 0 to
1, though the actual frequencies will depend upon the sampling rate f
s
and range
from 0 Hz to f
s
=2 Hz, which is explained in Chapters 4 and 5, \Sinusoids" and
\Sampling."
