New answers tagged

2 votes

Why do DFT frequency buckets need to be divided by sample period?

I might be late to this question but the problem with frequency bins isn't about normalization. After your FFT, each frequency bin is calculated as $$ f_k = \frac{k}{N} \cdot f_\mathrm{s} $$ where $f_\...
BoltzBooz's user avatar
  • 159
1 vote

Reconstructing the original signal from its DFT

I need to reconstruct $x(t)$ from its DFT $X(k)$. I don't want to sound flip here but the way to do this would be to use the inverse DFT, i.e. $$x[n] = \frac{1}{N} \sum_{k=0}^{N-1} X[k]e^{j2\pi\frac{...
Hilmar's user avatar
  • 42.5k
0 votes

Scaling Property in DFT

But 1/ab is scaling the magnitude. Here limits are for the indices.
user70160's user avatar
0 votes

Finding Discrete Fourier Transform (DFT) for different DFT size

This exercise is aimed at showing that zero-padding in the time domain interpolates the frequency domain. Since this is homework, I'll give you the beginning of the solution. Just like you did, start ...
Jdip's user avatar
  • 5,212
0 votes

Real discrete Fourier transform

This is a very well presented question. I always had problems with DFT stuff, but what I learned using it is that complex numbers decrease your work by more than half: you do not deal with $a$ and ...
messelim's user avatar
0 votes
Accepted

What's the distribution of the DFT of a real-valued, zero-mean, normally distributed random vector?

As the DFT of real $X$ is conjugate symmetric, $\hat{X}$ is not N-dimensional jointly Gaussian and neither your two distributions is correct. Representing the N-dimensional DFT by a $2N$ dimensional ...
AlexTP's user avatar
  • 6,080
0 votes

FFT: Sinewave frequency displacement when zero-padding

The Fourier transformation (FFT is a faster method with the same result) attempts to replace an infinitely long signal with a combination of a finite number of sin and cos functions. The frequencies ...
9herbert9's user avatar
6 votes
Accepted

FFT: Sinewave frequency displacement when zero-padding

(I show only positive frequencies): which is part of the problem here :-) You would get the expected behavior if you used a complex sine, i.e. $x[n] = e^{j2\pi\frac{n}{N}}$ but a sine wave actually ...
Hilmar's user avatar
  • 42.5k

Top 50 recent answers are included