Linked Questions
11 questions linked to/from Absolute convergence of periodic sinc interpolation
11
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5
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21k
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How to get Fourier coefficients to draw any shape using DFT?
I'm teaching myself about Fourier Series and the DFT and trying to draw a stylised $\pi$ symbol by fourier epicycles as detailed by Mathologer on youtube (from 18:39 onwards), and the excellent ...
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11
votes
4
answers
4k
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Whittaker-Shannon ($\mathrm{sinc}$) interpolation for a finite number of samples
Given an infinite number of samples $(N)$, a higher (or lower) number of samples $(cN)$ can be derived using sinc interpolation followed by sampling. How can this be applied to finite length signals?
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- 457
20
votes
3
answers
7k
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Frequency-domain zero padding - special treatment of X[N/2]
Suppose we wish to interpolate a periodic signal with an even number of samples (e.g. N=8) by zero-padding in the frequency domain.
Let the DFT X=[A,B,C,D,E,F,G,H]
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- 391
3
votes
3
answers
2k
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Resampling and removing high frequency noise?
I am currently working on a simple sampler that will allow me to load in a wav file and use my MIDI keyboard to play the loaded wav sample at the frequency according to the note played.
Now I need ...
- 51
7
votes
2
answers
846
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Why Zero Padding in the Center of the DFT Interpolates / Upsamples the Signal (Sinc Interpolation / DFT Interpolation / Periodic Interpolation)
I'm experimenting with the Inverse Discrete Fourier Transform. Starting from the two-cycles continuous $x(t)$ signal below:
I have the discrete signal $x(n) = \{ 1, 0, -1, 0, 1, 0, -1, 0 \}$ leading ...
- 315
4
votes
3
answers
335
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Inverse DFT: Is there a valid / intuitive interpretation of results for non-integral timestamps?
I implemented the plain DTF / inverse DFT algorithm in C++ in order to help me understand the method. As a sample input I considered
f(x) = sin( x * PI / 5 )
and ...
- 43
2
votes
1
answer
3k
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Frequency Domain Interpolation: Convolution with Sinc Function
I am reading the paper, Design of an energy-efficient accelerator for training of convolutional neural networks using frequency-domain computation, and I came across the following definition of sinc ...
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0
votes
1
answer
2k
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Using fourier coefficients to reconstruct data in matlab
When doing a discrete fourier transform on some data using matlab's fft function, its output is a set of fourier coefficients but I was wondering how do I go about converting these into an and bn so I ...
- 1
1
vote
2
answers
906
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Sinc interpolation of pure sine wave sampled just at Nyquist frequency
Following this question: Shannon-Nyquist theorem reconstruct 1Hz sine wave from 2 samples
could you explain the algorithm to apply for sinc interpolation to avoid the "sawtooth" effect due to linear ...
- 683
1
vote
1
answer
512
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One sided frequency spectrum (Matlab vs. Origin)
There are a lot of queries on fft frequency all over the web. I guess the following point not discussed anywhere explicitly. Hope someone can provide an insight here.
If we have and even number of ...
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1
vote
3
answers
177
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How to distinguish between FFT power leak or close frequencies
This week I was having an interview with a Professor for Grad School. He asked a bunch of questions related to signal processing that lead up to some questions about power leak on the FFT spectrum. So ...
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