Explain Fourier Transform

[zenith folio]

I’m studying Signal Processing in college, and we’ve started learning about Fourier Analysis. I understand how the Fourier Transform converts a signal from the time domain (t) into the frequency domain (omega) but what exactly does the result (the transformed function) represent or tell us?

[wicked sandal]

It just allows us to check out the discrete frequencies of the signal that we transformed

It makes things look neatier

Even helps us alter the frequencies easier as well and then we perform inverse fourier transform to the modified signal

[zenith folio]

hmm

so for example

if i recorded a chord on a piano

and i get the signal function from that chord

what does the fourier transform does

and what is the result of the transform?

[wicked sandal]

discrete frequencie graphs

[zenith folio]

is it a number or another function or something?

[wicked sandal]

Basically another function

Like I said it helps us to visualise and modify the frequencies of a signal

to get the desired result

there is also the fourier series which is basically getting a sum of cosine and sine waves from a periodic signal

[zenith folio]

ahh i see

thanks

[south pond]

Maybe this may help you visualise it https://www.desmos.com/calculator/cm8v2lfaab

a,b,c are the frequencies of the notes (262hz for middle C, 330hz for E, 392hz for G but all scaled down for a clearer visual)
Aa,Ab,Ac are the amplitudes

The bars are frequency domain, wave is time domain

Notice how much easier it is to alter the chord in frequency domain than time domain

In reality, there would probably be more unwanted signals (called noise) from whatever other sounds a microphone may pick up

Filtering noise in time domain is damn near impossible, whereas in freq domain it should clearly be a much easier task

[zenith folio]

thats really cool!

[zenith folio]

may i use that for my assignments lol

[south pond]

Do as you wish

[zenith folio]

alr thanks