Linked Questions

12 votes
5 answers
22k 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 ...
Chris's user avatar
  • 123
7 votes
4 answers
2k views

Is Fourier series a sampled version of Fourier transform?

I recently learned about dtft and how dft/dfs is the sampled version of dtft. I was wondering if Fourier series is also obtainable by sampling Fourier transform? I am a noob in the subject so sorry if ...
Kartik Hegde's user avatar
3 votes
3 answers
2k views

Finding the time domain equation corresponding to a given DFT

I'm stuck with the following exercise while self-studying the Discrete Fourier Transform: Consider sampling exactly three cycles of a continuous $x(t)$ sinusoid resulting in an 8-point $x(n)$ time ...
Sylvain Leroux's user avatar
1 vote
2 answers
7k views

Understanding the phase in DFT

Although using regularly the FFT algorithm to compute DFTs, I don't really understand how the phase part works. e.g. in Matlab: ...
SheppLogan's user avatar
5 votes
3 answers
887 views

Absolute convergence of periodic sinc interpolation

An $N$-periodic complex discrete-time sequence $[x_0, \dots, x_{N-1}]$ can be resampled to an $M$-periodic sequence $[y_0, \dots, y_{M-1}]$ with $M>N$, using sinc interpolation: $$\begin{align}y_m ...
Olli Niemitalo's user avatar
2 votes
2 answers
957 views

Where is the Nyquist frequency in an FFT spectrum?

I've been working with even length audio for a while, so I've had no problem finding the Nyquist frequency in the FFT spectrum, as it's shape is: $$(\text{dc_component}, f_1, f_2, ..., f_{N/2-1}, f_\...
Tobi Akinyemi's user avatar
1 vote
2 answers
402 views

What is the effect of wiping the right half of Fourier Transform bins?

I'm trying to change the pitch of a signal using a Fourier Transform (FFT) followed by an Inverse Fourier Transform (IFFT). I've found many examples, some of which zero out the right half of the real ...
MysteryPancake's user avatar
1 vote
1 answer
575 views

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 ...
AChem's user avatar
  • 569
0 votes
1 answer
100 views

Practical question about DFT in Matlab

Please consider this piece of code: ...
SheppLogan's user avatar
0 votes
1 answer
65 views

What does imaginary Component of a bin's phase in the Fourier Transform mean?

I have been recently working with the FFT and realized that each frequency within a bin corresponds to a phase. This concept I have no problem with because if you wanted to construct the summation of ...
Cabbage Champion's user avatar