linear vs. minimum phase

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mflorio
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linear vs. minimum phase

Post by mflorio »

I'm curious as to what is the recommended setting for use on a whole mix vs. individial tracks ? I really don't fully understand linear phase vs. minimum phase... I seem to like the minimum phase setting in HB better on most everything.

Can someone point me to a good reference that explains what they are and the differences ?

Thanks,

Mike
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Post by HarBal »

Hi Mike,

Not sure of a good reference discussing the difference between minimum phase and linear phase but I'll give you an explanation.

For causal linear systems (which all analog gear is) you only get an output response when you have an input, not before. If it has a non flat frequency response then you will have a non-linear (as in not a straight line as opposed to distortion) phase versus frequency response. This type of phase response in communications systems is generally not good because it ends up distorting the shape of pulse signals in digital comms. This makes it harder to decode in the presence of noise. Prior to digital filtering this issue was corrected for using phase equalisation networks (basically all pass networks with a phase response to compliment that of the filter). With digital filtering you can use a linear phase FIR which, by virtue of the phase response, does not distort the shape of pulse signals except to the degree caused by eliminating various harmonics.

To obtain a linear phase response requires a filter in which the impulse response is symetrical around its middle. This response is a non-causal response (meaning you get an output before you get an input) which is clearly not realisable. However, if you have a finite length impulse response and introduce a delay of half the filter length you can realize a linear phase filter. The delay is what gets us around the causality issue.

So for communications systems linear phase is generally better than minimum phase (unless you can't live with the latency of a linear phase filter). In audio however, when don't really hear in the time domain, we hear in the frequency domain. Because of this factor linear phase is really not important to how we hear. In fact, linear phase can and does sound unatural owing to the "pre echo" brought about by having a symetrical impulse response. A minimum phase filter is causal and does not have this behaviour so you wont hear any pre-echo.

Going a little further, there is also a thing called maximum phase as well. The "minimum" in minimum phase refers to the fact that for a given magnitude frequency response, the minimum phase realisation has the smallest phase delay. You can also realize a filter with the same magnitude response which has the largest phase delay and this is called maximum phase. Minimum phase is generally the optimum (for analog systems) because it yields the fastest response.

So, if you find you like the sound of minimum phase best then I'd suggest using it all the time. I'd agree, I find minimum phase more natural and that is why it is the HarBal default.

Cheers,


Paavo.
mflorio
Posts: 43
Joined: Sun Dec 05, 2004 5:32 pm
Location: New York
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Post by mflorio »

Thanks for the explanation Paavo. I had to read it a few times to get my head around it - but I somewhat understand it now - at least enough to see why I like the min phase filter better.

Mike
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