The Discrete Fourier Transform

The Discrete Fourier Transform (DFT) is a mathematical process that transforms a sequence of data points, like a digital sound or image, from the time or space domain into the frequency domain. It breaks down complex signals into simpler sine and cosine waves, revealing their underlying frequencies and strengths. This helps analyze, filter, or compress signals—like identifying musical notes in a sound or removing noise—by understanding which frequencies are present and how they contribute to the original data. Essentially, the DFT uncovers the hidden pattern of frequencies within a digital signal.