Questions on the computational aspects of Fourier analysis, including the various applications of the fast Fourier transform (FFT).
Questions tagged [fourier-analysis]
122 questions
71
votes
5 answers
How do I take the FFT of unevenly spaced data?
The Fast Fourier Transform algorithm computes a Fourier decomposition under the assumption that its input points are equally spaced in the time domain, $t_k = kT$. What if they're not? Is there another algorithm I could use, or some way I could…
David Z
- 3,383
- 2
- 27
- 34
8
votes
2 answers
Quick and simple discrete 2D Helmholtz-Hodge Decomposition using FFTs?
For a silly screen saver I'm trying to develop, I'd like to randomly generate a divergence-free 2D array of 2D vectors, and then use it to generate a line integral convolution plot. I've heard$^1$ that one way to do this is to generate random noise,…
DumpsterDoofus
- 287
- 1
- 8
5
votes
1 answer
Complete (an incomplete) explanation of the phenomenon of "aliasing", when using Fourier series to approximate functions?
Consider the approximation of a function by a truncated (finite) Fourier series, using complex notation:
\begin{equation}
f(x) \approx F_M(x) = \sum_{\alpha = -M}^{M} \hat{f}_{\alpha}e^{-i\alpha x} \quad (1)
\end{equation}
Where $\hat{f}_{\alpha}$…
bzm3r
- 669
- 5
- 21
3
votes
0 answers
Is the given equation for Fractional Fourier Transform wrong?
In order to compute $$ \hat{f}_k = \sum_{m = 0}^{M - 1} e^{-2\pi i k m \theta} f_m, \ \ k = 0, ..., M - 1$$
for any $\theta$, my book states that this can be done using fractional Fourier transform as follows.
So, as you can see, they define the…
eAOoe
- 31
- 1
2
votes
0 answers
differences between all the FFTs?
Wikipedia lists a lot of FFT algorithms:
Cooley–Tukey FFT algorithm, Prime-factor FFT algorithm, Bruun's FFT algorithm, Rader's FFT algorithm, and Bluestein's FFT algorithm
What are the pros and cons of each algorithms?
And which one do you prefer?
user8005
- 55
- 2
2
votes
1 answer
Convolution of two real functions using discrete Fourier transform (FFT): zero-padding and normalization
I want to obtain the convolution of two discretized real functions $f$ and $g$,
$$
c(t) = \int_{-\infty}^{+\infty} \mathrm{d}{x} \, f(x) \, g(t-x)
\tag{1}
$$
via discrete Fourier transform (DFT).
As a concrete example, let $x \in [-6, 6]$ be the…
AlQuemist
- 187
- 7
1
vote
1 answer
What to look for in a discrete fourier transform
I was attempting to do a discrete Fourier transform through a computer program on a list of numbers. Before doing that I decided to test it by running through a list of 1000 numbers which I created by summing 20 sine waves which were created by the…
Patrick
1
vote
0 answers
Sine series using exponential based FFT
I have such a problem - I would need to expand a discrete function in a sine fourier series but I would like to use exponential based library for FFT (I will use CUDA to compute it).
What have I to do with the signal I'm sending to the procedure so…
azbri
- 73
- 5
1
vote
0 answers
Can convolution be generalized to 2D from several 1D convolutions?
I have a function $\mu(x)$ that I need to convolve with several functions $\nu_n(x)$. I'm currently taking the DFT of $\mu$ and multiplying it individually with the N DFTs of the functions $\nu_n$ and then taking the inverse DFT to obtain the…
SgrA
- 111
- 1
0
votes
0 answers
Efficiently compute the Fourier series coefficients of a piecewise trigonometric function
I am searching for the most efficient algorithm to compute the Fourier series coefficients of a number of given functions $f(\theta)$
$$a_k = \int_0^{2\pi} f(\theta)\cos(k\theta) \\
b_k = \int_0^{2\pi} f(\theta)\sin(k\theta)$$
for $k \in {1,...,N}$.…
Hosein Javanmardi
- 193
- 4
0
votes
2 answers
Amplitude of discrete Fourier transform of Gaussian is incorrect
I am trying to understand why the amplitude of the FFT (computed with numpy) of a Gaussian differs from its analytic solution.
The $\mathcal{F}\{e^{-\pi t^2}\} = e^{-\pi f^2}$. However if I calculate it with
the FFT function in numpy the resulting…
trienko
- 3
- 2