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What on Earth is an all-pass filter?

-December 15, 2013

You already know about high-pass, low-pass, and band-pass filters – but don't forget the all-pass. No, I'm not kidding. It's not April 1st yet.

The all-pass filter sounds a touch oxymoronic, like invisible ink or write-only memory (or here).

But no, this one's real. OK, here's the catch. An all-pass filter (APF) does, as its name implies, pass all frequencies, but it alters the phase of a signal depending on the frequency.

One and two-pole APFs. The two-pole filter is a Wien type design (my CAD system was in the garage).

Take the single-pole APF above – it's easy to understand intuitively. Assume the inverting gain is one. At low frequencies, C1 is open, so the circuit inverts, or has a 180 degree phase shift. At high frequencies, C1 is a short. The circuit becomes a follower – zero degrees phase shift. It doesn't have a gain of two, as it would if R1 were grounded, but one, because there's no voltage across R1. By exchanging C1 and R3, we get the opposite behavior – low frequencies following, high frequencies inverting.

Where on Earth might an APF be of use? Sometimes, they are used to equalize the phase response of a channel, or of another filter. In the audio world, they are (or used to be) an integral part of artificial reverberation units.

Closer to home, the surround-sound processor I designed some years ago required full audio-band 90° phase shifters. The only reasonable way to accomplish this was to design two multi-stage APFs, each possessing a widely varying phase response over the band, but always maintaining a 90° difference between the two of them. After going through this parallel pair of APFs, one output became the new reference phase, and the other the quadrature phase. The original input was not used in subsequent processing stages.

The SSP-1 surround-sound processor, ca. 1999.

So there you have it. The all-pass filter. Not so strange after all, is it?

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