Biomedical Engineering Reference
In-Depth Information
Practically, most filters can be subdivided into three broad classes, according to how they
modify the frequency spectrum of the desired signal. These broad classes include
,
low-pass
filters. Low-pass filters work by removing high frequencies from a
signal while selectively keeping the low frequencies (Figure 11.17a). This allows the low
frequencies of the signal to pass through the filter uninterrupted, hence the name low-pass.
In some instances, low frequencies could be accentuated further by magnifying them while
selectively removing the high frequencies. High-pass filters perform exactly the opposite
function of a low-pass filter (Figure 11.17b). They selectively pass the high frequencies
but remove the low frequencies of the signal. The treble control in an audio system is a form
of high-pass filter that accentuates the high frequencies, thus producing crisp and rich
sound. In contrast, the bass control is a form of low-pass filter that selectively enhances
low frequencies or the “bass,” creating a “warmer” sound quality. Band-pass filters fall
somewhere in between the low-pass and high-pass filter. Rather than simply removing
the low or high frequencies, band-pass filters remove both high and low frequencies but
selectively keep a small “band” of frequencies (Figure 11.17c), hence the name. The function
of a band-pass filter could be achieved by simply combining a low-pass and high-pass fil-
ter, as we will see subsequently.
Since filters are linear systems, the output of a filter is expressed by the convolution
between the input and the filter's impulse response (Eq. (11.32)). Conversely, if the output
is determined in the frequency domain, the output corresponds to the product of the filter
, and
high-pass
band-pass
H (
ω)
Passband
1
Stopband
Stopband
0
w c
w c
ω
(a)
H ( ω)
Passband
Passband
1
Stopband
0
w c
w c
(b)
ω
H ( ω)
Passband
Passband
1
Stopband
Stopband
Stopband
0
w 2
w 1
w 1
w 2
ω
(c)
FIGURE 11.17
, of the ideal (a) low-pass filter, (b) high-
pass filter, and (c) band-pass filter. Signals in the shaded region, the passband, are preserved at the output, whereas
signals in the stopband are selectively removed from the output.
Frequency domain magnitude response plot,
j
H
(oÞ
j
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