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I have been doing some research on objective sound metrics used to classify the quality of a sound signal. According to my research, the most usually used are loudness and sharpness ( definitions can be found here )

I have encountered a fair amount of literature on the matter, and i am familiar with the way these metrics are calculated ( loudness is strictly defined by national and international standards, and sharpness according to DIN 45692 ).

This analysis though takes place in the frequency domain, and all of the plots i see use as the x-axis the so called critical band rates ( info on critical bands here )

My question: I also encounter some plots though that show the evolving of the phenomena with respect to time. My guess is that researchers break the original time signal to parts, and do analysis on these parts to create these kind of plots. As the definition of these metrics does not explicitly depend on time, i cannot be sure of how they derive that. Am i missing something here? Is there another way to deal with this on the time domain?

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It looks like you are referring to the Fourier transform between time and frequency domains. In math, the Fourier transform is usually done on the entire space. An example of this could be a Fourier spectrum of a photo image. In music this is not very useful, because it corresponds to a Fourier transform of the entire composition. The musical equivalent of such a transform would be a list of all musical notes used in the composition without their sequential order. To make this practically useful we must preserve the time sequence of the notes, such as bars. This is practically done exactly as you are suggesting. The time sequence is broken into short periods, which are analyzed by a Fourier transform of each period separately and then the results are put back in a time sequence. This is equivalent to a Fourier transform of a movie by transforming every frame separately and then putting the results back in a time sequence frame after frame. The difference in this example from music or audio is that a movie is already broken into frames while the audio sequence is not, and so breaking it into time periods is arbitrary and is a part of the conversion process.

An example of this is a spectrum of a song commonly used in audio processing. The spectrum is plotted along the horizontal time axis. this seems a contradiction of terms, as spectrum in in the frequency domain rather than time domain. However, all this means is a time sequence of the spectra of small time periods joined together. The attached image shows a stereo spectrum of the same song uncompressed on the right and MP3 compressed on the left where you can see the high frequency information removed (black areas) to reduce the storage space needed.

enter image description heres

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