A Word Of Compliment To Audacity

One of the open-source applications which can be used as a Sound-Editor, is named ‘Audacity’. And in an earlier posting, I had written that this application may apply certain effects, which first involve performing a Fourier Transform of some sort on sampling-windows, which then manipulate the frequency-coefficients, and which then invert the Fourier Transform, to result in time-domain sound samples again.

On closer inspection of Audacity, I’ve recently come to realize that its programmers have avoided going that route, as often as possible. They may have designed effects which sound more natural as a result, but which follow how traditional analog methods used to process sound.

In some places, this has actually led to criticism of Audacity, let’s say because the users have discovered, that a low-pass or a high-pass filter would not maintain phase-constancy. But in traditional audio work, low-pass or high-pass filters always used to introduce phase-shifts. Audacity simply brings this into the digital realm.

I just seem to be remembering certain other sound editors, that used the Fourier Transforms extensively.

Dirk

 

About +90⁰ Phase-Shifting

I have run into people, who believe that a signal cannot be phase-advanced in real-time, only phase-delayed. And as far as I can tell, this idea stems from the misconception, that in order for a signal to be given a phase-advance, some form of prediction would be needed. The fact that this is not true can best be visualized, when we take an analog signal, and derive another signal from it, which would be the short-term derivative of the first signal. ( :1 ) Because the derivative would be most-positive at points in its waveform where the input had the most-positive slope, and zero where the input was at its peak, we would already have derived a sine-wave for example, that will be phase-advanced 90⁰ with respect to an input sine-wave.

90-deg-phase-y

But the main reason this is not done, is the fact that a short-term derivative also acts as a high-pass filter, which progressively doubles in output amplitude, for every octave of frequencies.

What can be done in the analog domain however, is that a signal can be phase-delayed 90⁰, and the frequency-response kept uniform, and then simply inverted. The phase-diagram of each of the signal’s frequency-components will then show, the entire signal has been phase-advanced 90⁰.

90-deg-phase

(Updated 11/29/2017 : )

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