Can someone explain Fast Fourier transform in laymans terms to me please

[bigsocks]

Hi guys,
Been looking into Fast Fourier transform briefly as there appear to be some unique indie coded plugins available for sound design. I've tried reading the wiki on FFT but it is extremely confusing to wrap your head around.

I know it's a method of splitting the sound into a frequency spectrum based on time that is viewable in graphs, but how does this involve sound design tools?

Any help is appreciated

[Clueless]

Originally Posted by bigsocks

Hi guys,
Been looking into Fast Fourier transform briefly as there appear to be some unique indie coded plugins available for sound design. I've tried reading the wiki on FFT but it is extremely confusing to wrap your head around.

I know it's a method of splitting the sound into a frequency spectrum based on time that is viewable in graphs, but how does this involve sound design tools?

Any help is appreciated

This is not really a high-end question, but one possible answer to you question is this: typical sound files are amplitude vs time, making it fairly easy to make broad-band changes to amplitude (by transforming the Y axis). Transformations to the X axis (time) affect all frequencies uniformly, but also change tempo/duration as well. You gotta sing slowly if you want to do a chipmunks record. If you do selective transformations in the Y axis (e.g., as a function of X), you get volume fades up and down.

After the Fourier transform (fast or otherwise), you have frequency in the X axis and amount of that frequency in the Y axis (time disappears into a term in frequency and overall amplitude scatters into the sum of all individual frequency amplitudes). If you now do transformations in the X axis, you affect frequencies without changing tempo or duration. If you do a broadband transformation in the Y axis you get louder or softer, but if you do selected transformations in the Y axis (e.g., as a function of X) you get a parametric EQ or a filter function.

The bottom line is that if you want to play with amplitudes over time (which is basically the function that a loudspeaker implements), you play with your BWAV (or AIFF) file. If you want to play with frequencies (and you can do that over time, too), the FFT gets to there and the inverse FFT gets you back to something your loudspeaker can then play.

(Note that the inverse FFT is no more special than the inverse square, which is just a square root, or the inverse of multiplication, which is reciprocal.)

[wrenc]

It's probably helpful to think of it like this: say you're talking about an EQ. A digital filter is made up of a formula and a system of delays - when you want to cut a frequency on an EQ, the way that change in spectrum is implemented is by delaying that signal by a tiny bit and adding it back to the original signal. The phase cancellation that occurs is how that specific amount of that frequency is cut.

The theory behind FFT is somewhat analogous to the theory behind additive synthesis: that is, all sounds can be seen as a collection of sine waves added together. With additive synthesis, you can theoretically replicate any complex waveform by taking precise measurements of all the frequencies in that waveform and put together the appropriate collection of sine waves at the appropriate amplitude(s) and with the appropriate envelope(s), and voila! Same sound. In theory.

Rather than synthesizing a complex waveform from scratch, FFT is a process that takes an existing complex waveform and breaks it down into many, many different frequency components. You can then manipulate those frequency components separately (in amplitude, speed, &etc.) before they get put back together and become a complex waveform again.

That whole explanation is pretty oversimplified, but that's the basics of how it works.

[Branmong]

The above is actually a very good explanation. Its actually quite a profound moment when you realise that all sounds can be considered as sine waves of different frequencies summed together.

In terms of "how does this involve sound design tools", a good example is spectral morphing, which you hear a lot in Amon Tobin's latest album.

Process:

1) use FFT to get the sine waves which make up sound a)
2) Repeat step 1 for sound b)

Once you have the spectra for both sounds, you can then interpolate between them to create a sound which is a kind of average of both sounds. This is a brief and probablu somewhat confusing explanation, but I'd say if you look up spectral morphing, it should give you an idea of why the FFT is so useful in sound design.

As far as I know, the FFT has actually been abandoned, in general, in favour of more efficient algorithims, but these algorithims rely on the same fundemental principles.

[Dean Roddey]

At the most fundamental level, the way to think of it (actually already said above but just not so directly I guess):

- There are two ways to look at music. One is the 'time domain' and the other is the 'frequency domain'.

- The time domain is what you are dealing with with a WAV file. It's a regular sampling of the sound wave in time. So you end up a sequence of samples in a row at regularly spaced intervals. This is a very useful view, but it tells you nothing about the frequency content of the sound. You might get some rough ideas by looking at it I guess, but basically it's just telling you where the sound level was at a given point in time.

In theory, time domain based views can be infinitely accurate, i.e. you can divide time into ever smaller sub-divisions.

- The frequency domain shows you what frequency components are in the signal within a given slice of time. It doesn't say anything about the amplitude of the signal at a specific point in time, just the frequency content and amplitude within a selected slice of time (where the slices have to be considerably larger than the sample period.)

And, because frequency is a reflection of change over time, it cannot be infinitely accurate. It has to work over some length of time. The shorter the length of time, the less accurate it is, because frequency content isn't infinitely divisible. E.g. if you pick any short snippet of a WAV file, some frequency content will be moving into the window you choose and some will be moving out of it. So you can't get a completely accurate view since there are discontinuities on either edge of the window. Usually you have to overlap some of each of the ongoing slices of the time based view in some way to try to blend them together (and you always have to work with slices since you are wanting to process sound as it's happening, not at the end of the song.)

And it means that you can't be sure exactly what's happening when, because it's not time based. You only know that the window you have selected and analyzed has certain frequency components somewhere inside it. And the more accurate you want to be about the frequency content (larger slices) the less accurate your understanding of where in time those frequencies are occuring.

- So that makes time based views more useful or accurate for some thing sand frequency based views more useful or accurate for other things.

- FFT and reverse FFT allow you to move between those two views of the signal.


Anyhoo, that's my capsule high level understanding of it. Someone correct me if I'm wrong.

[The Real MC]

Hardware analog processing is achieved in the time domain which is a two axis representation of the signal in terms of level and time.

In order to accomplish the same tricks in digital it has to be done in the frequency domain which is a two axis representation of the signal in terms of level and frequency. A FFT converts the digitized time domain signal into frequency domain, the computer performs the processing, and another FFT converts back to time domain when reproduced to your speakers.

Performing FFT on digitized signals at a 44.1Khz sampling rate puts a major load on your computer processor and is often the achilles heel of digital recording.

There are several Fast Fourier Transform algorithms with varying degrees of processing time and accuracy. You could have real accurate results at the expense on time or really fast results at the expense of accuracy but not both. Faster processing times equates to higher sample rates, shorter latency, or more horsepower to perform complex nonlinear processing such as reverb, tube emulation, or compression.

[ezrecords]

Try to explain the FFT in no more than 50 words and in an easy way, understable for children, could be maybe as difficult as launch a man in the moon.

In any case I think that a good approach that matchs fine with the real issue is that the FFT are the algorithms developed for computers and DSP enviroment to solve the DFT (Discrete Fourier Transform), using the properties of the DFT. The FFT provides a faster and less computation charge reducing the resources consumption. By numerical methods and using the properties of the DFT to reduce the complex of the numerical calculations a computer could solve a discrete fourier transform yielding very good results, very close to a real DFT solution.

[electronaut]

Originally Posted by ezrecords

Try to explain the FFT in no more than 50 words and in an easy way, understable for children, could be maybe as difficult as launch a man in the moon.

It's all about bins. Say you work at a factory, and your job is to pull widgets off a conveyor belt and sort them into bins according to color. After a while, you can easily see how many of each color you have, since they're sorted into bins. Before that, it was just a long stream of randomness that was harder to understand.

An FFT does the same thing -- it takes the long stream of randomness (audio waveform) and sorts frequencies into bins so you can see how much you have of each frequency.


Bah! 96 words.

[The Real MC]

Originally Posted by ezrecords

Try to explain the FFT in no more than 50 words and in an easy way, understable for children, could be maybe as difficult as launch a man in the moon.

Oh so sorry I'll try that again

Hardwaraanalogprocessingisachievedinthetimedomainwhichisatwoaxisrepresentationofthesignalintermsoflevelandtime.

Inordertoaccomplishthesametricksindigitalithastobedoneinthefrequencydomainwhichisatwoaxisrepresentationofthesignalintermsoflevelandfrequency. AFFTconvertsthedigitizedtimedomainsignalintofrequencydomainthecomputerperformstheprocessingandanotherFFTconvertsbacktotimedomainwhenreproducedtoyourspeakers.

PerformingFFTondigitizedsignalsata44.1Khzsamplingrateputsamajorloadonyourcomputerprocessorandisoftentheachillesheelofdigitalrecording.

ThereareseveralFastFourierTransformalgorithmswithvaryingdegreesofprocessingtimeandaccuracy. Youcouldhaverealaccurateresultsattheexpenseontimeorreallyfastresultsattheexpenseofaccuracybutnotboth. Fasterprocessingtimesequatestohighersampleratesshorterlatencyormorehorsepowertoperformcomplexnonlinearprocessingsuchasreverbtubeemulationorcompression.

There, that's seven words innit?