Discrete Fourier Transform Example

or

The Transform of a Sine Wave and its Frequency Spectrum
Showing how Kaiser-Bessel Windowing Reduces Ringing
from the Jump Caused by the Periodic Continuation of the
Endpoints

Sine wave with known frequency.

Number of points in the DFT.

Sampling frequency.

Mapping from index to frequency.

Maximal frequency at index = n/2.

Frequency of sine wave in Hz.

Sine wave points from 0 to n-1.

Import values from a file and readjust the length and sampling frequency.

Plot the discretized sine wave.

Kaiser-Bessel Window.

Fourier Transform.

Compute a Fourier transform and plot its power spectrum.

Windowed Fourier Transform.

Window the time domain first.

Now compute the power spectrum.  Note it is much cleaner.