Questions tagged [fast-fourier-transform]

Question 1

I was reading stuff about discrete Fourier transform (DFT) and its inverse when I produced the following proof which seems to lead to a contradiction for me. I don't know where the error is. Could ...

Question 2

I'm trying to compare my numerical vs exact solution to the anti-derivative of the piecewise function $$u(x)=\begin{cases}1,&x<\frac{\pi}{2}\\2,&\frac{\pi}{2}\leq x<\frac{3\pi}{2}\\1,&...

Question 3

I have a hundred time series, all sampled at the same time interval. I did an FFT of all of these time series and arranged them row by row in a matrix ($\mathbf{X}$). I have a target variable ($\...

Question 4

Background: Last year, I wrote a Master's thesis on WSS vectors. I derived various WSS process results (such as the Wiener-Khinchin theorem) using vanilla matrix algebra. My intention was, first, to ...

Question 5

I need to evaluate: $u(x_j) = \sum_{j=0}^N \hat{u}_j \phi_j(x_j) $ where the coefficients $\hat{u}_j$ are known and the interpolation polynomial is: $\phi_j(x)=T_k(x)+a_kT_{k+1}(x)+b_kT_{k+2}(x)$ ...

Question 6

Let $\mathbf{m}(\mathbf{r})$ be a vector field defined at every point in three-dimensional Euclidean space, subject to the pointwise constraint $|\mathbf{m}(\mathbf{r})|^2 = 1$. I wish to compute ...

Question 7

I have a sum of the form $$ c(x) = \sum_{0\leq k\leq n} c_k \cos^kx $$ for some collection of real numbers $c_k$ that I'd like to evaluate at an evenly spaced collection of $m$ points between $0$ and $...

Question 8

Suppose we have the following equation: $$A^T A x = A^T G$$ Where $A$ is a square matrix composed of shifted versions of a known vector $v$, represented as: $$A=\begin{pmatrix} v_0 & 0 &...

Question 9

I am following the discussion on Using FFT to calculate derivatives and the answer from ConVexHUll. I extended N=2048 and L=64*pi, and fact=1/32. As the plots show, the difference has oscillation ...

Question 10

If I have a rank r matrix $A\in \mathbb{R}^{n\times n}$, $r<n$. If we do a discrete fourier transform on $A$, we get $\hat{A}$. my question is that the rank of $\hat{A}$ is still r or not. I did ...

Question 11

I have been studying digital control theory from the Digital Control of Dynamic Systems. Here in section 12.2 regarding identification of a nonparametric model of a dynamic systems I have found ...

Question 12

Let's say I have an $n$x$m$ grid of points in 3D space. The grid has some random displacement along its normal, so it's not just a flat plane. If I take a 2D Fourier transform of the x, y, and z ...

Question 13

I was studying ways to obtain functions in Taylor Series format from differential equations that describe them, and at one point I came across a special case of linear convolution. I'll use an example ...

Question 14

Assuming the exponential and trigonometric forms of the Fourier series for a $2 \pi$-periodic function are defined as $$f(x)=\sum\limits_{n=-\infty}^\infty c_n\, e^{i n x}\tag{1}$$ and $$f(x)=\frac{1}{...

Question 15

Let's say I have an digital audio signal that is very short (only a few seconds). This signal is kind of simple (can't come up with a good example, but something like mobile phone notification, or ...

Stack Exchange Network

Questions tagged [fast-fourier-transform]

Inverse discrete Fourier transform and Fourier series : contradiction ? What's wrong in my proof?

Numerical vs exact antiderivative using Fourier spectral method

Plotting the betas of multiple linear regression on an FFT

Extending finite results about wide-sense stationary (WSS) processes to the infinite case [closed]

Chebyshev interpolation using DCT with multiple terms interpolation polynomial

How to compute Fourier-space derivatives while preserving a unit-norm constraint?

How to efficiently evaluate a cosine power series

Simplifying the solution to $A^T A x = A^T G$ for a lower triangular Toeplitz matrix $A$

The difference between calculated derivative from FFT and original derivative has oscillation

The rank of the matrix of Fourier coefficients

How to determine phase frequency response from measured response to a chirp input signal?

Intersection between 2D Fourier Transform and linear function.

Special case of "half of linear convolution" - How to resolve in $O(N\log N)$?

Can Parseval's theorem be extended to the "nested" Fourier series representation of $f(x)$?

FFT audio and get back original audio with IFFT

Hot Network Questions