This calculator is available free of cost and is an online sandbox for playing with Discrete Fourier Transform (DFT). It uses real time DFT, which is the version of Discrete Fourier Transform that uses real numbers in order to represent the input and output signals. 

DFT is a part of Fourier analysis, which in turn is a set of mathematical techniques based on decomposing signals into sinusoids. While numerous books have listed graphs trying to illustrate DFT, it is always wondered how these sinusoids actually look like, or how they will be changed if we change the input signal a little-bit.

Now, this sandbox can answer such common questions. By default, it is filled with 32 samples altogether, with mostly all zeros except the second one which is set to 5. 

Now for this set of samples, the calculator displays graphs for real values, imaginary values, magnitude values and phase values (basically all sorts of possible values). It also draws up graphs with all sinusoids and also with summed signals. You can, although, change samples as you wish and then the graphs will be updated accordingly.

There are four types of Fourier Transform that one must know of namely: 

  1. The Fourier Transform (for aperiodic continuous signal) 
  2. The Fourier series (for periodic continuous signal) 
  3. The Discrete Time Fourier Transform (for aperiodic discrete signal) 
  4. The Discrete Fourier Transform (for periodic discrete signal)