Allpassphase - Repack

[ H(z) = \fraca_2 + a_1 z^-1 + z^-21 + a_1 z^-1 + a_2 z^-2, \quad |a_2| < 1 ]

For a second-order all-pass filter:

The key property: poles and zeros are . If a pole is at ( z = p ), a zero is at ( z = 1/p^* ). This reciprocal relationship ensures unity magnitude response for all frequencies. 3. Phase Response Characteristics First-Order All-Pass The phase response ( \phi(\omega) ) for a first-order all-pass is: allpassphase

where ( \omega ) is normalized frequency (0 to ( \pi )). [ H(z) = \fraca_2 + a_1 z^-1 +

More commonly, for a first-order all-pass filter: \quad |a_2| &lt