1
vote
1answer
28 views

Relative error when computing derivatives via FFT

I want to compute a discrete derivative via the FFT. This amounts to multiplication by the wave number in Fourier space, as detailed in the stack exchange answer here. When I increase the ...
2
votes
1answer
41 views

Fourier series of oscillation in form $\cos(2 \pi \frac{k}{T}+\phi)$

I would like to calculate the fourier coefficients of $\cos(2 \pi \frac{k}{T}+\phi)$ where $T \in \mathbb{N}$ is the period and is arbitrary but fixed, $k \in [1, N-1]$ is the number of oscillations ...
1
vote
1answer
36 views

How can we represent an image using basis images?

I have read that using Fourier transformation we can decompose any arbitrary image into orthogonal basis images and reconstruct it back. But i don't understand terms like "orthogonal " and "basis ...
1
vote
2answers
32 views

trigonometric interpolation of a sampled signal

Given N sampled points, using the FFT we can get the Fourier transform of those N points $X_k$. With N/2 the Nyquist frequency and $X_0$ the DC value. Using the inverse we can then get back the ...
1
vote
3answers
80 views

Calculating own dft via matlab?

We are asked to code our own dft function from the formula : If everything is done correctly it should give the same result with matlab's own dft function, in the end I'm comparing them but they ...
0
votes
1answer
43 views

Discrete fourier transform problem

We have taken $1000$ observations from signal $s(t),t \in\Bbb{R}$ $$h(k)=s(k\Delta t+t_0),k=0,1,\dots,999,$$ where $\Delta t=1/200 $ and $t_0=-2$ (in seconds). When we calculate discrete fourier ...
2
votes
2answers
1k views

Understanding Fourier transform example in Matlab

I'm studying about Fourier series and transform and I get confused with the following Matlab example of Fourier transformation: ...
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votes
1answer
45 views

spectral structure of sinusoidal model

let us consider following code ...
1
vote
0answers
126 views

Matlab FFT conj Ifft

i have 2 questions 1) How can i get something to work 2) Why does it do what it does. 1) In matlab i have an image. On the image i apply the function (-1)^(x+y) in order to center the DFT (fft). In ...
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votes
2answers
390 views

Programming discrete fourier coefficients in matlab

Alright so I am having the following issue: I want to figure out how to find the fourier coefficients of the following function: $$D(X)=\frac {a'(x)} {1+a'(x)^2}$$ Where $a(x)$ is an arbitrary ...
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votes
1answer
135 views

Changing Frequency of a Fourier Transformed signal

How can I change the frequency of a signal after taking its fourier transform? I am taking voice input from user in MATLAB and than I take its fourier transform to convert the signal in frequency ...
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votes
1answer
3k views

Rebuilding original signal from frequencies, amplitude, and phase obtained after doing an fft

Rebuilding original signal from frequencies, amplitude, and phase obtained after doing an fft. Greetings I'm trying to rebuild a signal from the frequency, amplitude, and phase obtained after I do ...
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votes
1answer
271 views

Substituting Periodic Fourier series expansion equation with standing wave equation

Substituting Periodic Fourier series expansion equation with standing wave equation Greetings All I can re-create a periodic signal using Fourier series expansion using sin and cos waves. But how ...
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vote
1answer
592 views

How can I increase/decrease (frequency/pitch) and phase using fft/ifft

How can I increase/decrease (frequency/pitch) and phase using fft/ifft I think I have the basic code but I’m not sure what to do next PS: It's done in Octave/matlab code Example I have a signal that ...
2
votes
1answer
188 views

FFT and changing frequency and vectorizing FOR loop

I can increase and decrease the frequency of a signal using the combination of fft and a Fourier series expansion FOR loop in the code below but if the signal/array is to large it becomes extremely ...