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When comparing spectrum images between two different audio sources in order to determine which has better quality, I sometimes come to an impasse. For example, consider the following images from two 320kbps mp3 files:

spek plot from yahel avalanche n1

spek plot from yahel avalanche n2

Optical difference of RGB values:

Difference image of spectra plots (here is the difference between waveform-synced versions of the above examples, but it's quite the same)

The second version has a cutoff at 20 KHz, while the first contains some audio information above that frequency, albeit very low in intensity, and probably inaudible.

On the other hand, this extra audio portion at the top of the plot appears to be noise, since it's composed by an almost continuous "blurry" zone. In addition, looking carefully at the two images, some subtle differences can be observed at the lower frequencies.

I'm inclined to think that the second version is better quality, theoretically, since the lower cutoff limit may allow for the encoder to make better use of the available bandwidth, so that it can more acuratelly represent the lower frequencies. That aside, I really don't know how to interpreted those subtle differences between the two images in order to make an objective decision.

So, when comparing spectrum images, what specific details can help determine which encoder did a better job?

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    $\begingroup$ indeed, that violet-blueish bar at around 20kHz might well be aliases of the audio at low frequencies $\endgroup$ – Marcus Müller Jul 20 '17 at 8:23
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    $\begingroup$ But to be 100% fair, I, myself, can't claim to hear differences between different MPEG encoders at extremely high bitrates like 320kb/s (I remember one could easily tell really badly configured MPEG2 audio Layer 3 codecs from others, which were at least very barely tolerable, at 64 kb/s – but that memory is from 1997) – my gut feeling is that if you (for example, by virtue of professionally producing audio) need to care about that, you simply shouldn't be using MP3, but maybe a) a more modern MPEG or Ogg audio codec or b) something lossless like FLAC. $\endgroup$ – Marcus Müller Jul 20 '17 at 8:25
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    $\begingroup$ So, that leads us to the question I kind of always ask myself after reading a question: For what purpose? What's the reason you're comparing implementations of a 24 year old audio compression standard at bit rates it was never really designed for? $\endgroup$ – Marcus Müller Jul 20 '17 at 8:29
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    $\begingroup$ @LaurentDuval excellent idea, look at my question edit $\endgroup$ – Marcus Müller Jul 20 '17 at 8:54
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    $\begingroup$ FLAC should be lossless, shouldn't it? $\endgroup$ – Laurent Duval Jul 20 '17 at 11:27
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At those relatively high rates, the possibility (for a human) to hear a difference depends a lot on the device it is played on. My first suggestion would be to rely on a panel of testers (possibly bats, for the high frequencies), use the best audio system you can, and compute a Mean Opinion Score.

I do agree that the frequency limitation around 20 kHz might seem in disadvantage of the second image, but as you said, low-freq bits can then be better allocated (possibly some).

Similarly as @Marcus Müller, I suspect the high-freq band in the first to be spurious. Especially since it really looks symmetric in the time-frequency plane (modulo the contamination with the real audio), and the aliasing hypothesis sounds nice here.

As said in a comment, you can subtract one decompressed sound from the other. Hopefully, by a careful listening, you could check whether the difference is meaningful, or not.

So, I'll, too, go for the second for the best.

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