Allpassphase

Imagine a snare drum hit. Its raw transient has a sharp, coherent edge. Now, pass it through an allpass filter. The level meter doesn't budge; the bass still booms, the highs still sizzle. But listen closely. The phase has been smeared. The attack feels slightly rounded, the tail oddly dispersed, as if the sound passed through a crystal made of staggered mirrors.

Mathematically, the transfer function of a first-order allpass filter is:

Output: [ y[n] = a x[n] + x[n-1] - a y[n-1] ]

In mathematical terms, the frequency response of an ideal all-pass filter has a constant magnitude of unity (1 or 0 dB) across the entire spectrum: allpassphase

An all-pass filter has the following characteristics:

: It is frequently cited as a free, lightweight alternative to commercial plugins like Kilohearts Disperser Technical Details AllPassPhase - enummusic - Gumroad

For a 2nd-order all-pass: Phase goes 0° → -360°, with steeper transition near resonance. Imagine a snare drum hit

One of the most creative applications of all-pass filters is the effect, widely used in music production and guitar pedals. A phaser consists of a series chain of first-order all-pass filters (typically 4 to 12 stages) with a time-varying parameter controlling the pole and zero location, plus a feedforward path that mixes the original signal with the all-pass output.

What are you using (Matlab, Python, C++)?

It is important not to confuse Allpass filters with Linear Phase EQs. The level meter doesn't budge; the bass still

: These shift the phase by a total of 180 degrees. They offer a smooth, gradual timing change across the frequency spectrum but do not allow you to adjust how sharp the shift is.

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