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An all-pass filter is an electronic filter that passes all frequencies equally, but changes the phase relationship between various frequencies. It does this by varying its propagation delay with frequency. Generally, the filter is described by the frequency at which the phase shift crosses 90°.
They are generally used to compensate for other undesired phase shifts that arise in the system, or for mixing with an unshifted version of the original to implement a notch comb filter.
They may also be used to convert a mixed phase filter into a minimum phase filter with an equivalent magnitude response or an unstable filter into a stable filter with an equivalent magnitude response.
Analog Implementation
The following operational amplifier circuit implements an all-pass filter with one pole and one zero. At high frequencies the capacitor is a short circuit, thereby creating a unity-gain voltage buffer. At low frequencies and DC, the capacitor is an open circuit and the circuit is an inverting amplifier with unity gain. Where ωCR=1, the circuit introduces a 90 degree shift.
The resistor has often been replaced with a FET to implement a voltage controlled phase shifter: the voltage on the gate adjusts the phase shift. In electronic music, a phaser consists of typically four or six of these phase-shifting sections connected in tandem and summed with the original. A low-frequency oscillator LFO ramps the control voltage to produce the characteristic swooshing sound.
Digital Implementation
A Z-transform implementation of an all-pass filter is
This filter can be cascaded with an unstable or mixed phase filter to create a stable or minimum phase filter, without changing the magnitude response of the system. By proper choice of z0, a pole or zero that is outside of the unit circle can be canceled and reflected inside the unit circle.
