Allpassphase May 2026

The coefficient a is related to cutoff frequency fc and sample rate fs by:

Where ( a ) is the coefficient determining the cutoff frequency. The magnitude ( |H(z)| = 1 ) for all ( z ), but the phase ( \angle H(z) ) shifts from 0 to -180 degrees (or 0 to -360 degrees for second-order filters). To understand allpassphase, you must understand group delay —the derivative of phase with respect to frequency. Group delay measures the time delay each frequency component experiences as it passes through a system. allpassphase

Whether you are designing a reverb algorithm, correcting a loudspeaker’s time alignment, or simply trying to understand why your snare drum sounds "soft," the key lies in the phase. By learning to measure, design, and listen for allpassphase effects, you move from being a passive user of filters to an active sculptor of time itself. The coefficient a is related to cutoff frequency

[ H(z) = \fraca_2 + a_1 z^-1 + z^-21 + a_1 z^-1 + a_2 z^-2 ] Group delay measures the time delay each frequency