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Given a desired delay
samples, an order allpass filter
can be designed having maximally flat group delay equal to
at DC using the formula
where
denotes the th binomial coefficient.
- without further scaling
- For sufficiently large , stability is guaranteed
rule of thumb:
- It can be shown that the mean group delay of any stable
th-order allpass filter is samples
[426].I.3
- Only known closed-form case for allpass interpolators of arbitrary order
- Effective for delay-line interpolation needed for tuning since
pitch perception is most acute at low frequencies.
- Since Thiran allpass filters have maximally flat group-delay at
dc, like Lagrange FIR interpolation filters, they can be considered
the recursive extension of Lagrange interpolation.
Subsections
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