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I am very much a beginner in this field - but find it really interesting. However I am a little confused on a certain area of knowledge.

If I have understood correctly: At any point in an audiosignal, for instance when someone is strumming a D-Major on a guitar, i can reproduce that exact sound in that moment by looking at the frequency spectrum for that time, do a Fourier Transform, and recieve a periodic signal in the time domain presented as a fourier series. If I play that signal, I will hear the sound that was in that exact moment of a song, just as a never ending note. In this scenario the frequency spectrum tells me what pitches were played- and the frequency domain will change for point in time.

However, If a look at a three-minute-song in the time domain, I dont quite understand what the fourier-transform will tell me. If I have this audiofile, and I view it in the timedomain, what will it tell me? (view picture) And if I transform it to the freq. domain, what will it tell me?

As far as my logic goes, I wont ge able to tell any of musical features just of an amplitude value in the time domain.

(And the confusion continues when we sample an audiosignal, and all we get is an amplitude value for a given time. How can any musical information be there?)

Example of audiofile

Thanks for answers.

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    $\begingroup$ any moment in time doesn't have a frequency. It can't – how would you assign a frequency to a single audio sample in isolation. $\endgroup$ – Marcus Müller Nov 5 '17 at 14:43
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As far as my logic goes, I wont ge able to tell any of musical features just of an amplitude value in the time domain.

That's wrong. The amplitude-over-time actually is the way the song is played by your sound card (we call that PCM). So, this is your song.

What you really need to understand that your analog audio (i.e. the variations in air pressure over time) is being sampled and stored digitally, and reconstruction happens based on these samples.

Aside from that, you're absolutely right, the Fourier Transform and the time domain signal are equivalent representations of the same signal.

Regarding the question what a graphical representation will tell you: That's quite impossible to answer, as it depends on you ;) Now, there's a few basic things that one can note: For example, if you look at a plot of the time domain signal, and you see high amplitudes in a certain range of time, you can assume that it's loud during that time. Same goes for the absolute of the Fourier Transform: If the amplitude spectrum is large for a range of frequencies, then you can assume that a loud tone of that frequency range is audible.

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  • $\begingroup$ Aaah! I it is the combination of samplevalues that makes up a signal?!. One signal amplitude value in it self doesnt possess any information, but when we have several, we can reconstruct the signal. Does that also mean, that if we adjust the sample value down, we will also modify how the signal sounds, since we might "lose" information? Another question then - is the amplitude value for the signal a way of saying how "loud" it is in that point of time? $\endgroup$ – Zimenez Nov 6 '17 at 10:36

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