DFTJEW

Discrete Fourier Transform

The Fourier Transform is a powerful tool to convert a continuous function from the time domain into the frequency domain. The Fourier transform, however, is an integral transform; it is done by integration. This cannot be done with a discrete function. The Discrete Fourier Transform (DFT) allows us to transform a discrete function from the time domain into the frequency domain.

Let $x(n)$ be a discretized function in time.

Then the DFT of $x(n)$ would be:

$\text{DFT}[x(n)]\equiv X(m)\equiv \sum _{n=0}^{N-1}x(n)e^{-j\frac{2\pi nm}{N}}$

Principle author: Jeffrey Wonoprabowo