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A highpass filter
can be constructed by shifting a lowpass filter by an amount
equal to half the sampling rate.
This is equivalent to a modulation by
in the time
domain. Hence,
Summarizing:
- To design a high-pass filter, first design a finite length,
causal lowpass filter
- Use a lowpass cut-off frequency equal to
(highpass cut-off)
- Design the lowpass filter as in the previous section
- Modulate the impulse reponse by
to exchange dc and
Alternatively, if the passband of the prototype lowpass filter
is very flat or equal-ripple about unity gain, a highpass filter
can be designed by simply subtracting from
:
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