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.
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iFFT a Known Transformed Function to Get the Unknown Complex-valued Initial Function
Background:
In my case, I need to get the solution of a series of 2D equations. The analytical expression of this solution ($f$) is not available but the transformed one is. Therefore, I need to ...
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Given Green's function, can I find the corresponding operator?
Green's function is the solution to the equation $L G(x;x') = \delta(x-x')$, where $L$ is a linear differential operator. Usually, we want to find the Green's function of a given $L$. Instead, if we ...
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Is the product of exponentiated elliptic curve basis elements invariant under FFT of scalars?
I am working with an elliptic curve defined over a finite field $\mathbb{F}_p$ and have a basis set of points ${g_0, g_1, \ldots, g_n}$. When I perform the FFT on these points, I obtain a new basis ${...
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How to prove that discrete sine and cosine waves have zero sum in one period? [closed]
I am trying to prove that ifft of all possible fft of a vector is same vector itself and vice versa, to do that I must prove bellow;
So, how can we rigorously prove that:
$\sum_{k=0}^{N-1} e^{i2\pi\...
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Fast Fourier transformation in a lattice $H_{\vec{R}}(m,n,l)$ to $H_{\vec{k}}(a,b,c)$
I have a Hamiltonian defined on a lattice grid $H_{\vec{R}}(m,n,l)$ with $m,n,l \in \mathbb{N}$ and ranging in [-M,M], [-N,N], [-L,L]. Based on the $H_{\vec{R}}(a,b,c)$, a discrete Fourier ...
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How to accelerate calculation of a nested integral
Setup
Let $A(t)$ and $B(t)$ be positive functions defined on $t \in [t_1, t_2]$. They are sampled uniformly within this interval, with a timestep of $\Delta t$.
Question
I want to calculate the ...
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The Fourier transform of product of derivatives
I have the task to compute the Fourier transform of the product in matlab:
$$ \left( \frac{\partial u(t, x)}{\partial x} \right)^2 \left( \frac{\partial^2 u(t, x)}{\partial x^2 } \right)$$
I was ...
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How to correctly calculate Poisson's equation for electric potential using FFT with zero-padding?
I'm working on a program that simulates the electrostatic field in 3D using FFT to solve Poisson's equations based on the following formulas:
$$
\phi_{(k)} = \frac{\rho_{(k)}}{\epsilon_0 \times K^2}
$$...
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Inversion formula for discrete sine and cosine transforms
$\newcommand{\wh}[1]{{\widehat{#1}}}$
$\newcommand{\R}{{\mathbb{R}}}$
I am looking for a proof of the inversion formulas for the discrete sine and cosine transforms, i.e. a proof of the fact that ...
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What function can model a decay, whose linear slope smoothly changes around a certain x value.
am a biology student trying to find a fitting function to model the $1/f$ decay or 'aperiodic component' of a neural power spectrum.
In an (over)simplified way it can often be describes with the ...
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Help with understanding Inverse Discrete Fourier transform
I am trying to program a simple implementation of Inverse discrete Fourier transform. I thought I understood, but something in my understanding is obviously lacking since my results are wrong.
For a ...
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Discrete Fourier transform for time series with small time-shift measurements
I have a time series that can only take positive integer values in the range [0, 100]. This time series shows periodically recurring patterns which can be uncovered by using the discrete Fourier ...
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Why is the FFT output divided by the data length?
I am working with FFT using NumPy in Python, and I noticed that it's common to divide the output of the np.fft.fft function by the length of the data array. Here's a simplified example of my code:
<...
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convolution-like computation of bivariate distribution
I would like to optimize code to compute a bivariate distribution like this (for example the bivariate poisson distribution):
$f_{n,m} = \sum_{i=0}^{n-1} a_i \times b_{n-i} \times c_{m-i}$
It really ...
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Interpretation of the impact of n on the fourier transform of exp(np(w)) or way to simplify expression
My goal is to find
$$IFT\{exp(np(\omega)\} = \int_{-\infty}^{\infty} exp(np(\omega) + 2i\pi \omega f) d\omega $$
that is the Fourier transform of $exp(np(\omega))$
Here $n>0 \in {\rm I\!R}$
$p(\...
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