de-click via differentiation then limiting then integration

[Paul L]

You may be losing less signal than you think. If you subtract the original from the modified signal, there may be phase shifts in retained frequencies, giving the false impression that you are subtracting some of the real sound. If original is a sine wave and modified is shifted half a cycle, for instance, the difference is even louder than either.

Or in other words the power spectrum of the difference is not the difference of power spectra.

Is there a better way to calculate the perceptual difference of sounds?

If you use Nyquist's slope and then integrate the result, the sound is not unchanged, but it loses the last signal and is offset to begin with a zero sample. This is not phase shifted, but perhaps the other steps introduced shifts.

[Paul L]

Also the slope function seems always to assign a zero start time, contrary to the documentation, which might matter in other programs, but not in the sound returned to Audacity, which ignores the sound's start anyway and only uses the sample sequence.

[Trebor]

You may be losing less signal than you think. If you subtract the original from the modified signal, there may be phase shifts in retained frequencies, giving the false impression that you are subtracting some of the real sound. If original is a sine wave and modified is shifted half a cycle, for instance, the difference is even louder than either.

The destructive interference was just to get an approximate idea of the frequency content of what was being removed.

... Is there a better way to calculate the perceptual difference of sounds?.

Superimposing the spectrograms ? ...

looks like frequencies over a wide range (at least half the frequency range of the sample) are being removed

before-after spectrograms showing the spectral content of noise removed.gif (339.6 KiB) Viewed 688 times

[Paul L]

Are those spectrograms really different?

Tell me how to make such pictures in case I need to demonstrate befores and afters too.

I was wondering if there is a way to present the difference of spectra aurally, better than just subtracting one signal from another.

[Trebor]

Are those spectrograms really different?

I can see vertical spikes in the "before" spectrogram which aren't in the "after", their timing corresponds with the noises isolated by the destructive-interference method.

Tell me how to make such pictures in case I need to demonstrate befores and afters too.

I used free photoshop-type software called GIMP to created a simple gif animation : (the fiddly bit was getting the two spectrograms perfectly aligned).

I was wondering if there is a way to present the difference of spectra aurally, better than just subtracting one signal from another.

The difference can be detected by having the "before" and the "after" tracks playing simultaneously (and in-sync) and toggling between the recordings.

[Paul L]

Of course there is that method, but is there any way to listen to something that approximates the difference of power spectra without that bit of murmur of the original that could only be phase shift?

Audacity's noise removal for instance has an isolate radio button. I could not get rid of the murmur and naively thought at first that I was losing some signal with the noise. But maybe not.