Allpassphase -

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.

While the amplitude remains untouched, the filter introduces a frequency-dependent delay. Low frequencies might pass through almost instantly, while high frequencies are delayed (or vice versa, depending on the filter topology). This alteration of the signal’s internal timing structure is the "allpassphase." allpassphase

Introduction: The Phase You Never Hear, But Always Feel In the world of digital signal processing (DSP), most discussions revolve around amplitude—how loud a sound is, how steep a filter cuts, or how much gain an amplifier provides. Yet, lurking beneath the surface is an equally powerful, often misunderstood phenomenon: phase . Specifically, when engineers discuss the peculiar behavior of phase without altering magnitude, they are venturing into the domain of the allpass filter and its associated allpassphase . Where ( a ) is the coefficient determining