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Microphone Month 5

Linear-Phase

Filtering is inseparable from digital audio. Analog or digital filters, and sometimes both, are required in ADCs, DACs, in the data channels of digital recorders, and in sampling rate converters and equalizers.

Linear-phase describes the response of a filter. When a signal goes through a filter, it experiences a time delay or phase shift. In a “perfect” filter, all frequencies should experience the same time delay (known as pure time delay), which preserves the wave shape as much as possible. All filters have phase shift. However, it is possible to design a filter so that the phase shift is linear with respect to frequency, and thus translates into a pure time delay. The phase shift doesn’t “color” the sound. A time delayed signal sounds just like the original, just later. A system that accurately preserves such relationships is said to be phase linear. A properly designed FIR filter is an example of a linear phase filter.

If some groups of frequencies experience a different delay from others (called group-delay error), it will color the sound or cause audible artifacts. A filter that experiences group-delay errors cannot be phase linear. Clearly, for most accurate sound reproduction, nothing in the audio chain must distort the phase relationship between frequencies. Most filters have some amount of group delay, and are not linear phase. We have become accustomed to the phase problems created by non linear phase filters over the years, to the extent that their sound is embedded in our perception of what EQ and other filtering devices should sound like.

True linear phase filters are only possible in the digital domain. Here, a math trick is employed to negate the phase shift that would normally occur in a filter. By running the data through the filter one direction and then turning it around and running it through the other way the amplitude of the frequencies are affected by double, but the phase shift, happening forwards and backwards, ends up negated. If a filter shifts, say, 5 kHz 90 degrees to the right, then running the data through the filter both forwards and backwards shifts it 90 degrees to the right and then back to the left, resulting in no phase shift at 5 kHz and double the effect of the filter with respect to frequency amplitude.

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