The fourier-series tag has no wiki summary.
2
votes
1answer
113 views
Benefit to know Fourier series for image processing? [closed]
I know there's a benefit of knowing the Fourier Transform for image processing, but is there a benefit to know Fourier series, or could you just skip them? Would you recommend skipping Fourier series ...
0
votes
2answers
67 views
Fourier series - time and frequency domain confusion
I am computing the fourier series of the following function between $[-0.5, 0.5]$
$$\displaystyle f(t) = \frac{1}{2} - |t|$$
According to the definition of Fourier Series the coefficients are given by
...
1
vote
0answers
52 views
A Laymans Fourier transform and harmonics explanation?
Please bear with me, I know some of you will scoff but I have looked on Wiki and in various literature (see below) and can't quite get a handle on a few things.
I am a general business programmer, ...
4
votes
1answer
107 views
Gibbs phenomenon in Hamming's digital filters
In 'Digital Filters' by Hamming there is a cryptic section where he describes how the Gibbs phenomenon can be viewed as the displacement between the centers of two functions as they are convolved ...
2
votes
1answer
370 views
FFT has unexpected DC component
I have a mixture of Gaussians and I want to look at their power power spectrum. The spatial distribution looks like this:
It's already been convolved with a Gaussian window function. I subtract ...
6
votes
1answer
165 views
Intuition behind the scaling property of Fourier Transforms
The Fourier transform of $f(ax)$ is $\frac{1}{|a|}F(\frac{u}{|a|})$. So the frequencies are scaled horizontally but the magnitudes are also scaled when the graph of $f$ is scaled horizontally.
On the ...
3
votes
2answers
196 views
Given the Graph of a Fourier Series $\sum c_k e^{2\pi ikx}$ Find the Graphs of $\sum c_{3k} e^{2\pi ikx}$ and $\sum (c_k)^2 e^{2\pi ikx}$
Define a 1-periodic function on $\mathbb{R}$ by:
$f(x) :=$
$\left\{\begin{matrix}
1 & if & 0<x<\frac{1}{10}\\
0 & if & \frac{1}{10}<x<1
\end{matrix}\right.$
with ...
3
votes
2answers
2k views
The Fourier Series Of This Triangle Wave
I am using matlab to study digital signalling and have come across a problem which i was wondering if anyone with more experience could help me with.
I need to work derive the Fourier series of a ...
9
votes
2answers
728 views
A good mathematical explanation of Gibbs phenomenon
I was explaining to someone how Fourier series work in context of constructing signals that are not everywhere differentiable, e.g. square waves, sawtooth waves, etc. When I mentioned the Gibbs ...
