Allpassphase !!install!! 〈95% TRUSTED〉

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.

For a second-order all-pass filter:

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 first-order all-pass:

More commonly, for a first-order all-pass filter: Their entire purpose lies in their

[ H(z) = \fraca + z^-11 + a z^-1, \quad |a| < 1 ] \quad |a| &lt

| 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 |