Allpassphase

For a first-order all-pass:

| Frequency (Hz) | Phase (degrees) | Group Delay (samples) | |----------------|----------------|----------------------| | 0 | 0 | ≈0.28 | | 500 | -22 | 0.31 | | 2000 | -95 | 0.55 | | 5000 | -162 | 0.21 | | 10000 | -176 | 0.06 | allpassphase

[ \phi(\omega) = -\omega - 2 \arctan\left( \fraca \sin \omega1 + a \cos \omega \right) ] For a first-order all-pass: | Frequency (Hz) |

The name says it all: they pass all frequencies with unity gain (0 dB magnitude response). Their entire purpose lies in their . 2. Mathematical Definition An all-pass filter’s transfer function ( H(z) ) (in the discrete-time domain) has the general form: allpassphase

For a second-order all-pass filter: