Discrete Fourier Transform Calculator and Plotter
CIIEC-BUAP
May 11th, 2024
Source Code
Introduction
This Web App calculates and plots the Discrete Fourier Transform (DFT). You can type a function and a value for a sampling rate or you can paste your own data.
If the data size is a power of 2, this app uses the Fast Fourier Transform algorithm , otherwise it uses the direct formula for the DFT .
Enter a Function of Time and a Sampling Rate
Function x(t):
Frequency f1(t) in Hz:
Frequency f2(t) in Hz:
Time (s):
Sampling Rate (Hz):
Paste your Own Data Here
Title:
Column X:
Column Y:
Separator:
Sampling Interval:
Unit:
Select if Column X has Epoch Timestamps
Discrete Fourier Transform
Window: None
Window: Cosine
Window: Hanning
Window: Hamming
Window: Blackman
Display DFT Values
Fourier Analysis
Definition of the DFT
$$\huge \definecolor{energy}{RGB}{0,0,0} \definecolor{freq}{RGB}{0,0,0} \definecolor{spin}{RGB}{0,0,0} \definecolor{signal}{RGB}{0,0,0} \definecolor{circle}{RGB}{0,0,0} \definecolor{average}{RGB}{0,0,0} \color{energy} X_{\color{freq} k} \color{black} = \color{average} \sum_{n=0}^{N-1} \color{signal}x_n \color{spin} e^{-\mathrm{i} \color{circle} 2\pi \color{freq}k \color{average} n/N} $$
$$\huge \definecolor{energy}{RGB}{0,0,0} \definecolor{freq}{RGB}{0,0,0} \definecolor{spin}{RGB}{0,0,0} \definecolor{signal}{RGB}{0,0,0} \definecolor{circle}{RGB}{0,0,0} \definecolor{average}{RGB}{0,0,0} \color{energy} X_{\color{freq} k} \color{black} = \sum_{n=0}^{N-1} \color{signal}x_n \color{spin} cos( \color{circle} 2\pi \color{freq}k \color{average} n/N) - \mathrm{i}\sum_{n=0}^{N-1} \color{signal}x_n \color{spin} sin( \color{circle} 2\pi \color{freq}k \color{average} n/N)$$
for
$$\huge 0\le k \le N-1 $$
DFT Calculation for Index k =