In addition to spectral analysis of signals, discrete transforms play important role in data compression, signal detection, digital filtering and correlation analysis. The discrete cosine transform (DCT) is the most widely used transform coding compression algorithm in digital media, followed by the discrete wavelet transform (DWT).
Transforms between a discrete domain and a continuous domain are not discrete transforms. For example, the discrete-time Fourier transform and the Z-transform, from discrete time to continuous frequency, and the Fourier series, from continuous time to discrete frequency, are outside the class of discrete transforms.
Classical signal processing deals with one-dimensional discrete transforms. Other application areas, such as image processing, computer vision, high definition television, visual telephony, etc. make use of two-dimensional and in general, multidimensional discrete transforms.