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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How do i get fourier series of signals given below [on hold]
how can i calculate and plot $Ae^{-at}$ amplitude and phase spectrum?
how can i determine the trigonometric fourier series of the signal given below ?
Your help is appreciated !! Thanks
2
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1answer
40 views
FFT from scilab is different than wolfram alpha [closed]
I am getting completely different values of FFT([1,2]) in scilab and Wolfram. I wondering what is going on and who is right.
...
0
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0answers
10 views
Analytical expression for PSD
Is it possible to obtain an analytical expression for the PSD?
The PSD is defined as follows,
$S(\omega) = lim_{T \rightarrow \infty} \frac{1}{T} |Y(\omega)|^2 $
Assuming there is $Y(\omega)$ ...
0
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0answers
10 views
Unexpected results for Fourier synthesis using IFFT in 2D
I am trying to recover a 2D function using inverse DFT, to my understanding the IDFT outputs the coefficients of the fourier series of the original function up to the Nyquist frequency.
So for ...
2
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0answers
43 views
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 ...
0
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1answer
28 views
even/odd signals and their FFT
I want to use the following property of the Fourier transform:
Even functions have even transforms; odd functions have odd transforms.
in mathematical terms:
if $f(t)$ is a function that has an ...
0
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1answer
25 views
How does matrix vector multiplication scale a norm of vector?
Given a square Vandermonde matrix
$\mathbf{V} =$\begin{pmatrix}
1 & x_0 & x_0^2 & \ldots x_0^{n-1}\\
1 & x_1 & x_1^2 & \ldots x_1^{n-1}\\
\vdots\\
1 & x_{n-1} & x_{n-1}...
0
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0answers
35 views
Circulant matrix-vector product procedure
A circulant matrix $C$ can be represented as
$$C = F^{-1} \mbox{diag}(Fc) \, F$$
When $C$ is multiplied by vector $b$
$$C b = F^{-1} \mbox{diag}(Fc) \, (F b)$$
My question only about procedure. ...
0
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1answer
33 views
Applying Fourier transform to represent equation with integral as a sum of variables
According to a paper the equation with integral
$\int_{-\infty}^{\infty}dx \rho_0(\lambda)e^{-b\lambda}=1/N$ (#1) where
$\rho_0(\lambda)$ is a distribution function, $N$ is a natural number, can be ...
1
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0answers
17 views
Is it possible to use FFT to derive a Fourier series fitting to data?
I want to do something like what is done in this question about fitting , ie find a Fourier series that approximates a continuous but complicated function. However I want to know whether it is ...
1
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1answer
28 views
Question about the FFT version of the gradient of a function.
We know that for a sufficiently smooth function $f:\mathbb{R}^{3}\to\mathbb{R}$, its Fourier Transform $\hat{f}(\mathbf{k}) \colon= \mathcal{F}\{f\}$ should satisfy (using integration by parts):
$$\...
0
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1answer
22 views
order of accuracy for numerically evaluating $u''(x) +u'(x) +u(x) = e^{-x^2}$ with regard to grid resolution
I was asked (an homework assignment) to apply FFT in order to approximate a solution for the ODE $u''(x) + u'(x) + u(x) = e^{-x^2}$ such that $u(x)$ satisfies the conditions: $u(\pi) = u(-\pi) , u'(\...
0
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0answers
9 views
How to convert X,Y Cartesian data to 3D spectrum (frequency, direction, spectral density)?
My question is as follows. I have x,y motion. normally I would ignore directionality and just look at the spectral density of each by performing a FFT on it. For my current problem directionality is ...
0
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0answers
12 views
Multiplying Many-Variable Polynomials Using Fast Fourier Transforms
I'm having some trouble figuring out how to use Fast Fourier Transforms to multiply multivariate polynomials. I'm writing a program that intended to expand a large polynomial made of lots of small ...
0
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1answer
32 views
Comparability of Analytic Signal with (Discrete) Fourier Analysis
I am working with a finite signal response from an experiment. Basically, I feed in a uniform amplitude sine wave which ramps from 20Hz to 20kHz over the course of 50 seconds, and I read the output, ...
0
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1answer
20 views
Confused With using Fast Fourier Transformation for solving equations
As far as I know, the 3 steps of FFT while solving $F_nc = y$ :
Split c into c', c'' such that c' contains elements with even indexes from c and c'' contains the odd ones.
Now we have $F_mc' = y'$ ...
1
vote
1answer
209 views
FFT: Multiplying multiple poynomials in O(KSlogS) time
I have a problem where I have to use the Fast Fourier Transform (FFT) algorithm $K$ polynomials $P_1,...,P_K$ where $\mbox{deg}(P_1) + · · · + \mbox{deg}(P_K) = S$.
I have to show that I can find the ...
0
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2answers
33 views
Fast Fourier Transform with Negative Integer Exponent
Given $f(x)=ax+b+\frac{c}{x}$ and $N$, I'd like to ask how to calculate $\sum_{i=1}^{N}f(x)^i$ efficiently using fast Fourier transform?
0
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0answers
24 views
Convert Real and Imaginary part from FFT to bands
how can I convert real and imaginary part from FFT to octave bands? I know how to do it for Absolute value, but dont know for Re, Im parts.
Thanks
1
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1answer
66 views
Question about roots of unity in the Fast Fourier Transform
I am learning about the Fast Fourier Transform, which converts a polynomial from its coefficient representation into its point-wise form using divide-and-conquer. The Fast Fourier Transform evaluates ...
1
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0answers
57 views
How to implement boundary value in Python using spectral methods
I want to solve the heat equation $$u_t=au_{xx},\quad 0\leq t, \ 0\leq x\leq\pi$$ in Python using spectral methods. I set $u(0,x)=\sin(x)$ as initial value for the time and choose $a=2$. My Code:
<...
0
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0answers
20 views
How does scaling in frequency domain affect real space?
I have a 3 dimensional array of real data corresponding to measurements in physical 3D space, and its corresponding data in spectral space.
I want to scale certain specific frequencies in the ...
0
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0answers
110 views
Fast Fourier transform of the Gaussian function
As I know, the Fourier transform of the Gaussian function is also Gaussian.
The simple verification for that is shown below.
http://mathworld.wolfram.com/FourierTransformGaussian.html
But fast ...
1
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1answer
23 views
Can FFT be used to cluster sound waves based on their similarity?
I am new to this so apologies if the question appears trivial.
Say we have n sound files and we want to cluster them to identify which ones are more similar. I ...
1
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0answers
48 views
circulant matrix inversion using fast fourier transform
I am Huda. May I know, if I have a circulant matrix, can I calculate its inversion using fast fourier transform? If yes, I really need an explanation.
Thank you.
1
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0answers
7 views
2D FFT with unit stride data access?
I am trying to design a large 1D FFT by splitting N into two smaller FFTs of sizes N1 and N2. This is common approach stemming from the Cooley Tukey Algorithm. My FFT is taking time sampled data in ...
0
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0answers
14 views
How to re-scale and do correctly the discrete Fourier transform.
I'm stuck with the re-scaling and the proper choice of parameters in doing the discrete Fourier transform. I explain: Suppose you want to calculate the Fourier transform
$$
F(p) = \frac{1}{2\pi}\int ...
0
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0answers
20 views
Average of product of Fourier transform of two signals
I have two signals which depend on x and z, $a(x,z)$ and $b(x,z)$. Their Fourier transform along both directions is denoted as $A(k_x,k_z)$ and $B(k_x,k_z)$, respectively. I would like to compute the ...
0
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0answers
28 views
Matrix factorisation of the Fourier matrix
I am currently reading a paper Low Communication FMM-Accelerated FFT on GPUs
In that I am not able to understand the definition of the twiddle factor matrix $T_{P, M}$.
The Fourier matrix $F_N$ is ...
0
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0answers
12 views
DFT of a series of RC exponentials
Context: I'm trying use matlab to apply a single-pole filter to a time-domain ramp waveform that is generated by a sequence of time-shifted "RC steps" that are added together.
The time domain voltage ...
0
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1answer
23 views
Calculate $Av^{\rightarrow}$ using FFT
Given a vector $v^{\rightarrow} = (v_0,v_1, ... v_{n-1})$
And given the matrix A =
$(a_0, a_1 ... a_{n-1})$
$(a_{n-1}, a_0,...., a_{n-2})$
$(a_{n-2}, a_{n-1}, a_0,...., a_{n-3})$
.....
$(a_1, ......
0
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0answers
46 views
Fourier tranform of the derivative
I have been recently studing Fourier transform and there is a proposition that says: If $\lim \limits_{x \to\infty}xf(x)=\lim\limits_{{x}\to -\infty}xf(x)=0$ then $$\hat{f'}(z)=-iz\hat{f}(z)$$
and ...
2
votes
1answer
26 views
Could families of “Airys” and “Bairys” of integer “frequencies” be useful?
A very famous family of functions are the complex exponentials and in the case of real valued functions, the sin and cos functions. They are related by the famous Euler formulas:
$$\exp(i\phi) = \cos(...
0
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3answers
45 views
Fast Fourier Transform algoritm - simple explanation(step by step)
I can't find step by step explanation of the FFT algorithm. Why it is faster than common DFT?
As I understand, we calculate DFT for $X$, and for $Y$, then merge them and got the final DFT.
2
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0answers
44 views
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 ...
0
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0answers
17 views
Fourier odd and even extension of descending steps function
Can anybody help me find even and odd extension of the descending steps function if $f(x)$ be:
\begin{cases}
f(x)= 1 & x\in[0,1]\\
f(x)= (0.5) & x\in[1,2]
\end{cases}
0
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0answers
11 views
Should DFT of cosine function be infinite at its frequency?
The Fourier transform of the cosine function is an infinite spike (Dirac delta function) at the frequency of the cosine wave. But it seems most DFT programs give a finite spike corresponding to the ...
0
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0answers
42 views
Discrete Fourier transform of sampled sin function nothing like continuous?
So I'm a little confused about what is going on with the discrete Fourier transform.
I tested out discrete Fourier transform with a little python script on a sin function
...
1
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1answer
40 views
Coordinates of a vector FFT
I was reading a paper about DFT, at the end he got the relations $Y=\frac{1}{\sqrt N}W_n \cdot y$ and $y=\frac{1}{\sqrt N}W_n \cdot Y$, where $y$ is a vector and $Y$ is the coordinates of that vector ...
1
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1answer
14 views
Why is the dot product of two columns $j$ and $k$ in FFT equal to $1+w^{j-k} + \dots + w^{(n-1)(j-k)}$?
The matrix is of the following form:
$\begin{pmatrix}
1 & 1 & \cdots & 1 & 1 \\
1 & w & \cdots & w ^{n-2} & w^{n-1} \\
\vdots & \vdots & \ddots & \vdots &...
2
votes
1answer
67 views
How to minimize sum of matrix-convolutions?
Given $A$, what should be B so that
$\lVert I \circledast A - I \circledast B \rVert _2$
is minimal for any $I$?
$I \in \mathbb{R}^{20x20}, A \in \mathbb{R}^{5x5}, B \in \mathbb{R}^{3x3}. $ Note ...
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0answers
22 views
Fourier transform of delta(dirac) function-multiplication with exp function
I am trying to find an integral of multiplication exponential function with a delta function.
I know a property of delta function that if I would like to take the integral of the multiplication delta ...
0
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0answers
39 views
Informations about Fourier Transform for a Python project (sound manipulation)
I have a project in Python with a friend where we want to manipulate music sound, and we'll need Fourier Transforms, so I made research online and wanted to know if I understand correctly the concepts....
0
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0answers
8 views
Most efficient method to find peak frequency of an FFT
I'm using a real to complex fft to get the peak frequency of a signal. What I want to know is the most efficient way to find the index of that peak. I currently use im^2 + re^2 and compare to the ...
0
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1answer
42 views
Efficient way to do a Fourrier Transform like operation
Suppose we have two functions $f,g:[0,\infty) \rightarrow [0,\infty)$. Then one can use Fast Fourrier Transforms to quickly compute $\int_0^t f(t-s) g(s) \, ds$ for $t$ in some range of values $[0,T]$ ...
0
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2answers
152 views
How to calculate 8-point FFT of data by hand
Given the following data:
Two period sine; samples = [0, 1, 0, -1, 0, 1, 0, -1];
I am asked to calculate the FFT of the sampled data to find the complex coefficients.
I don't necessarily want the ...
0
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0answers
11 views
fft algorithm - twidle multiplication
im trying to understand how fft(fast fourier transform) algorithm work and after watching several videos i couldn't understand why there is multiplication with Wn in this specific places and why the ...
0
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0answers
20 views
Not getting expected results with FFT
So I made this virtual car that moves at a velocity that is the sum of three different sine waves (whose individual frequencies I know). I constructed this velocity time graph
Then I perform a FFT on ...
0
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0answers
11 views
Discrete Hartley Transform when N=8
Hi I am currently studying FHT Algorithm but have a hard time to grasp it.
I want to calculate FHT when N=8.
http://mathworld.wolfram.com/HartleyTransform.html
thanks to (19) of the upper link, the ...
1
vote
1answer
16 views
Discrete Hartley Transform Diagram
Hi I am looking for DHT diagram(or pseudo code) for N=8
but cannot gain any result.
since I am not major in math, cannot grasp whole article.
So is there anyone who can draw DHT diagram in N=8 for ...
