# Questions tagged [fast-fourier-transform]

Use this tag for questions related to the fast Fourier transform, an algorithm that samples a signal over a period of time (or space) and divides it into its frequency components.

148 questions
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### Translation of the work of Gauss where the fast Fourier transform algorithm first appeared

As far as I know, the fast Fourier transform algorithm first appeared in 1805 in "Theoria interpolationis methodo nova tractata", by Carl Friedrich Gauss. This work is available in Latin, which, to ...
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### Does the fast Fourier transform have equivalents in other transforms?

I've seen the Mellin transform described as the "multiplicative" analogue to the Laplace transform, as well as the Fourier transform when $x\to\log y$. Would a discrete Mellin transform be able to ...
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### How to decompose a 2d shape into sin and cosin modes?

Assume that you have a circle with radius $r_0$, then you keep adding cosine modes as below: $r=r_0+a_1\cos(1\theta)+a_2\cos(2\theta)+a_3\cos(3\theta)+a_4\cos(4\theta)+~...$ if you plot this as ...
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### DFT is not a sampling of FT?

From wikipedia: The discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time ...
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### Any Efficient Multiplication with a Primitive Root over Prime Field?

Description: to multiply the "complex unit" $w^{N/4}$ over a prime field, i.e., $w^N \equiv 1 \bmod (\,p)$ (suppose $p, N$ do provide such primitive root). I am implementing the radix-4 Number ...
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### Increasing frequency resolution of FFT on a windowed sample of a signal

Okay, this gets a bit technical, let me explain the background. In doing loudspeaker measurements for its direct sound in normal rooms that have reflections, what we do is measure the whole impulse ...
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### Discrete versions of the Fourier Slice-Projection Theorem

I understand the continuous version of the Fourier Slice-Projection theorem, which says that given a (nice enough) function $f:\mathbb{R}^3\to\mathbb{C}$ the following operations give the same result: ...
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### Unable to solve nonlinear equation using scipy.optimize.fsolve

I am using scipy.optimize.fsolve to solve a nonlinear equation in Fourier pseudospectral space but it does not work. It gives the same output as the input u0, which is a trivial solution. The equation ...
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### Solving differential equation using FFT: dealing with zero frequencies

To get started using spectral methods to solve differential equations I am currently using Matlab and its FFT library. I have successfully approximated a first derivative of a function using the ...
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### understanding Fourier transform results for probability distribution

I think I do not understand Fourier transform results properly. I am trying to improve my understanding. It would be very kind if someone can help by commenting/answering. This is the following ...
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### FFT convolution for log-domain calculations?

I'm dealing with convolution among some large functions. Say f1 and f2. The values f1(i) ...
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### DFT implementation: relationship between number of samples and resolution of frequency

I come from an engineer background and I am sorry that this got so long. If $f(t)$ is a continuous signal, let $f[k]$ be the discretized signal for a timerange $T$ between two samples with for ...
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### How do spherical harmonic degrees compare to the Fourier domain

I have a filter in the spherical harmonic domain (say a simple cosine taper between degrees 80 and 550) and need to apply that same filter in the Fourier domain (after applying the fft to the data). ...