0
votes
0answers
27 views

stroboscope effect

I have a disc with a line drawn on one of his radius that is turning with frequency $f$, and I want to sample the place of the line to find the frequency of the disc. So we know from the ...
0
votes
1answer
16 views

How do the Fourier Transform of sampling and the Frequency-domain convolution match?

The Fourier Transform(FT) is $X(\upsilon) = \int_{-\infty}^{\infty}x(t)e^{-2{\pi}i{\upsilon}t}dt$. The impulse train is $\delta_1(x)=\sum\limits_{k=-\infty}^{\infty}\delta(x-k)$, and its FT is ...
1
vote
0answers
213 views

Shannon vs dirichlet kernel interpolation method for signal reconstruction

I am currently studying fourier transform, and especially the way that the signal could be reconstructed from its spectrum. In many lectures, I have seen the shannon interpolation method to ...
3
votes
0answers
155 views

Relationship between DFT and FFT/DTFT

Question 1: Assume we already know $x(t):[0,2\pi]\to\mathbb{R}$'s Fourier series $x[n]_{n=-\infty}^\infty$. Perform DFT on $x[n]_{n=0}^N$. How is the result connected to $x(t)$? WHY? Question 2: ...
1
vote
1answer
65 views

sampling functions and effect on DFT

I'm looking for help on pointing me to the right literature.... My question is as follows... Let's assume I have a discrete function (sinusoidal in nature) sampled at N equi-spaced points. However ...
3
votes
2answers
183 views

Determining sparse frequency distribution via discrete Fourier transform

Consider the function $$f(t) = 2 \sin(t)+\sin(2t)+25 \sin(400t)$$ (for example). In this case, how many samples of this function would I have to take, and at what sampling frequency, to determine the ...