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I have two audio signals that look incredibly similar when plotted. However, when I play them, they sound quite different. The only difference I can even see in their plots is that one signal looks darker than the other. Why would this be happening?enter image description here

FYI: The signal on the top is one that has been reconstructed from a reconstruction algorithm and the one in the bottom is the original one.

Here's some further data about how the signal has been produced. The original signal is a sample audio data I downloaded off the internet. The purpose of my experiment is to produce a close enough signal from only the amplitude spectrum and without the phase information. For similar, but slower algorithms, one can look at the Griffin and Lim algorithm and also the single pass spectrogram inversion paper.

In my case, I'm getting a waveform very close to the original signal, but there's a significant "noise" when listening to the output waveform.

So in short, the question is: waveforms looking so close to each other sound very different which is not very intuitive. Also, when signals look so similar, it is difficult to discern that there's any kind of noise involved. So what kind of hidden noise is this?

One last piece of information: the correlation function gives 0.69 as the output when comparing these two signals. Not sure if that's useful

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  • $\begingroup$ What is the energy of their difference? $\endgroup$
    – MBaz
    Commented Apr 2, 2019 at 18:34
  • $\begingroup$ Doing a simple summation of square of all elements of the signal give me the following- For original signal, energy is 130.32, For reconstructed signal, energy is 130.32, For difference of the signals, energy is 80.313. I've also updated the plot for more clarity $\endgroup$
    – Paddy
    Commented Apr 3, 2019 at 0:40
  • $\begingroup$ There you have it, then: the signals look similar when plotted, but they're actually quite different. If you plot only a few samples at a time you may be able to actually see the differences. $\endgroup$
    – MBaz
    Commented Apr 3, 2019 at 1:45
  • $\begingroup$ I was expecting the signals to have some phase shift, so I thought that the difference in the signal is expected. However, isn't it counter intuitive for a signal that looks so very similar to have that much of a difference, especially while listening to it? If one can characterize this difference in perception as some kind of noise, what could this noise be called? It's obviously not detectable by just viewing the signals unlike white noise $\endgroup$
    – Paddy
    Commented Apr 3, 2019 at 1:49
  • $\begingroup$ (1) One problem is that the plots compress hundreds of thousands of samples into a few pixels. The signals indeed have some general similarities, but closer inspection is needed. (2) Regarding the type of noise, impossible to say without knowing more about the signals. It's obviously not just a phase shift since then they would sound the same. $\endgroup$
    – MBaz
    Commented Apr 3, 2019 at 1:56

2 Answers 2

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First, the original $x$ and reconstructed $\hat{x}$ signals have a peak amplitude around $0.35$. Their difference peaks above $0.40$. That happens between two time-shifted like-alike signals.

Second, the difference seems to relate to the amplitude. Processing maybe be non-linear, and it could be interesting to look at relative differences like $2(x -\hat{x})/(x +\hat{x})$ as well.

To enhance understanding, what would 3D plots $(x[n],x[m],x[n]-x[m])$ and $(x[n],x[m],2\frac{x[n]-x[m]}{x[n]+x[m]})$ like like?

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Phase (and phase noise) plays an important role in audio quality, that's why many state-of-the-art algorithms work with complex-valued representations (one paper example from ICLR 2019).

Perhaps you should examine closer such local differences as MBaz suggested.

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