The Fourier Transform Applied to Sound

The Fourier Transform Applied to Sound
Nathan Ruffatto, Carroll College
The Fourier Transform is one of mathematics' most useful tools. In particular, it is very useful for studying and manipulating sound, as it turns a periodic function into one that represents that function's frequencies. Focuses of this project include analyzing the frequencies of sound waves over time and fitting trigonometric functions to periodic data. In particular, we take a look at data generated by the human voice.

[@gator1984atcomcast]

One of the best presentations of FT on KZbin. Practical application.

[@thierrypauwels]

If you fit something separately on each subinterval of the sample, at the connections between the intervals, the amplitudes and phases will not match, and that will cause discontinuities in your modeled sound, and this will produce the clicking sounds.

[@martinsanchez-hw4fi]

Awesome introduction

[@paulensor9984]

I enjoyed your teaching style, thank you

[@PaulDriessenFX]

missing here: overlap of segments, windowing, peaking, retrieving frequency from phase progression or parabola interpolation and a few other things..

[@sirousmohseni4]

Thanks for the video.

[@ralvarezb78]

on 11:05 I would take into account the phase for least squares fitting

[@muznamalik4798]

your voice is quite low while talking.

[@petercoleman7617]

Great expose

[@teebaalhmdani2864]

May I know the source of any book?

[@riittap9121]

There are people who see colors, when they listen to music. I still don't understand how on earth, but now I understand why!

[@ogrenciadasukaradag3412]

hey. thanks for the video first of all. Do you know an app that I can use to turn the raw piano sound that ım gonna record into a position over time function?

[@yektacifteler]

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[@yektacifteler]

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[@yektacifteler]

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[@ANJA-mj1to]

I come back to Your study because of I wanted to see again how we can apply sound in researching with yours clearly voice animated sound that we have had imagine! Also because I notice worth including here which can be useful later when considering computing Fourier transform. If you look better it is easy to separate the real and imaginary parts of complex function and divide into their symmetric and antisymmetric parts the combine complex Fourier transform to see realisam of Yours model. Yours Channel I remeber and have been writen as intesresting because of sustainable building on lend and in the water as well as noise of urbanistic area that can be describe with implying yours topic in Fourier transform. Like in the science will say : step by step will bring own benefit of research knowledge.

[@psteffensen]

Hi, thanks for the video. I have a similar problem with the repeated clicking sounds. I fft 4096 samples and find the amplitudes (not the phase) for fixed frequencies from 20-14000Hz. Then I generate sinusoids with the same amplitudes and play the sound. I don't understand why the sound is periodic and clicking.

[@mcmundn5100]

Look into windowing. If your sample is discontinuous if you stitch it together you end up with clicking.

[@psteffensen]

@@mcmundn5100 it turned out that the clicking came from equidistant frequencies

[@rajeshb6851]

Sorry not understanding. We are in computer application. Is it of any use in computer application ?

[@OlivierBCO]

In 5', the integrand should be f(x) exp(-iwx).... not f(x) exp(iwx)😉. Indeed, you need to multiply f(x) by the conjugate of exp(iwx) which is exp(-iwx). This is how you calculate the inner product in the space L2[R,C] and e(w) a basis of that space.

[@OlivierBCO]

At 6'26, the inverse Fourier Transform is correct as f^(w) plays the role of the coefficient for each frequency w in order to reconstruct f(x).😉

[@audiononsense1611]

Speak with more enthusiasm, please!

[@16876]

just don't fake it ;)