Allpassphase 2021 -

The pole-zero placement (complex conjugate pair) allows tuning of both the center frequency and bandwidth of the phase transition. While phase shift matters, the group delay ( \tau_g(\omega) = -\fracd\phi(\omega)d\omega ) often matters more in practical systems.

The phase is given by:

More commonly, for a first-order all-pass filter: allpassphase

For a second-order all-pass filter:

| 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

where ( \omega ) is normalized frequency (0 to ( \pi )). allpassphase