21k views

### 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 ...
4k views

### 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? ...
7k views

### 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] ...
2k views

### 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 ...
846 views

### 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 ...
335 views

### 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 ...
3k views

### 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 ...
2k views

### 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 vote
906 views

### 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 ...
1 vote