The allpass filter is an important building block for digital audio signal processing systems. It is called ``allpass'' because all frequencies are ``passed'' in the same sense as in ``lowpass'', ``highpass'', and ``bandpass'' filters. In other words, the amplitude response of an allpass filter is 1 at each frequency, while the phase response (which determines the delay versus frequency) can be arbitrary.
We have high-pass and low pass filters, and it turns out that we can create both filter effects using a single piece of hardware called a tunable filter. Tunable filters rely on a device called an allpass filter to create other types of filter outputs.
An all-pass filter is a signal processing filter that passes all frequencies equally, but changes the phase relationship between various frequencies. It does this by varying its propagation delay with frequency
The operational amplifier circuit shown in Figure 1 implements an active all-pass filter with the transfer function
which has one pole at -1/RC and one zero at 1/RC (i.e., they are reflections of each other across the imaginary axis of the complex plane). The magnitude and phase of H(iω) for some angular frequency ω are
As expected, the filter has unity-gain magnitude for all ω. The filter introduces a different delay at each frequency and reaches input-to-output quadrature at ω=1/RC (i.e., phase shift is 90 degrees).
This implementation uses a high-pass filter at the non-inverting input to generate the phase shift and negative feedback to compensate for the filter's attenuation.
- At high frequencies, the capacitor is a short circuit, thereby creating a unity-gain voltage buffer (i.e., no phase shift).
- At low frequencies and DC, the capacitor is an open circuit and the circuit is an inverting amplifier (i.e., 180 degree phase shift) with unity gain.
- At the corner frequency ω=1/RC of the high-pass filter (i.e., when input frequency is 1/(2πRC)), the circuit introduces a 90 degree shift (i.e., output is in quadrature with input; it is delayed by a quarter wavelength).
In fact, the phase shift of the all-pass filter is double the phase shift of the high-pass filter at its non-inverting input.
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