Allpassphase Guide

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:

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

[ H(z) = \fracz^-N - a_1 z^-(N-1) - \dots - a_N1 + a_1 z^-1 + \dots + a_N z^-N ] The name says it all: they pass all

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

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.