Elementary Zero-Phase Filter Examples
A practical zero-phase filter was illustrated in Figures 10.1 and 10.2. Some simple general cases are as follows:
- The trivial (non-)filter
has frequency response
, which is zero phase for all
.
- Every second-order zero-phase FIR filter has an impulse
response of the form
are assumed real. The transfer function of the general, second-order, real, zero-phase filter is
.
- Extending the previous example, every order
zero-phase real FIR filter has an impulse response of the form
and frequency response
are real.
- There is no first-order (length 2) zero-phase filter, because,
to be even, its impulse response would have to be proportional to
. Since the bandlimited digital impulse signal
is ideally interpolated using bandlimited interpolation [91,84], giving samples of sinc
--the unit-amplitude sinc function having zero-crossings on the integers, we see that sampling
on the integers yields an IIR filter:
sinc
sinc
- Similarly, there are no odd-order (even-length) zero-phase filters.
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Simple Linear-Phase Filter Examples
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Example Zero-Phase Filter Design