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Asked: 2026-05-20T02:33:48+00:00

I was asked an interview question where I needed to use it but I

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I was asked an interview question where I needed to use it but I have no idea what it is.
So in plain english what is the Fast Fourier Transform and how can I use it to find the derivative of a function given its (x, y) values as input?

How would you implement it?

EDIT:
I am asking this because given a sequence of (x, y) values I needed to calculate how the function looks like, derive it and find the number of times it is constantly changing (that is, (0, 1), (1, 2) is counted as one) or does not change at all (0, 5), (1, 5) is also counted as one change).

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  1. Editorial Team

    As for the first part of the question, a former Physics professor, Bartosz Milewski, has a very nice explanation, what FFT is and how it works.

    Also, Mastering The Fourier Transform in One Day is worth reading as well.

    In English (?)

    Say you have a sound coming from the speaker.

    You then set up, let’s get a nice round number here, 1024 harmonic oscillators that resonate to specific frequency ranges.

    Play the sound for, say, a second.

    Oscillators begin to resonate to the sound coming from the speaker. After the said second you read how much every oscillator is resonating. As a result you get a discrete fourier transform, meaning you get a chart of how much each of the frequency ranges contributed to the sound coming from the speaker.

    Instead of visualising the sound as amount of air pressure caused by the waveform, changing in time slots, you visualized it as a series of intensities of the frequency ranges.

    Of course in explaining the DFT, the speakers part is not really appropriate since you have to work on sampled input. So in this case the 1024 digital “oscillators” should actually be measured after 1/44th of a second, given the audio is sampled at the rate of 44kHz.

    Fast Fourier Transform is an algorithm to perform a Discrete Fourier Transform that’s pretty easy for computers to run on an incoming signal. It imposes some constraints you have to work with in your implementation (e.g. the number of samples has to be a power of 2), because it uses some clever tricks to drastically reduce the amount of calculation performed on the sample buffer.

    There is really no need to go deeper, since the two links I gave provide a pretty clear explanation. And note that it’s impossible to go from theory to implementation without knowing the math behind it.

    I hope this introduction makes some sense!

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