The Fourier Transform

The Discrete Fourier Transform (DFT) is the most widely used method for determining the frequency spectra of digital signals. This is due to the development of an efficient algorithm for computing DFTs known as the Fast Fourier Transform (FFT).

The discrete Fourier transform, v(m), of an N-element, one-dimensional function, u(k), is defined as:

The inverse transform is defined as:

IDL implements the Fast Fourier Transform in the FFT function. You can find details on using IDL's FFT function in the following sections and in "FFT" (IDL Reference Guide).