Discrete transform

In signal processing, discrete transforms are mathematical transforms, often linear transforms, of signals between discrete domains, such as between discrete time and discrete frequency.^[1]

Many common integral transforms used in signal processing have their discrete counterparts. For example, for the Fourier transform the counterpart is the discrete Fourier transform.

In addition to spectral analysis of signals, discrete transforms play important role in data compression, signal detection, digital filtering and correlation analysis.^[2]

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.

See also

• List of transforms#Discrete transforms

References

1. ^ Jerry C. Whitaker (2001). Television receivers. McGraw-Hill Professional. p. 147. ISBN 9780071380423. http://books.google.com/books?id=n3hxYt1u8vwC&pg=PA147&dq=%22discrete+transforms+are%22&hl=en#v=onepage&q=%22discrete%20transforms%20are%22&f=false. 
2. ^ Graham Wade (1994). Signal coding and processing (2nd ed.). Cambridge University Press. p. 332. ISBN 9780521423366. http://books.google.com/books?id=CJswCy7_W8YC&pg=PA332&dq=%22discrete+transforms+are%22&hl=en#v=onepage&q=%22discrete%20transforms%20are%22&f=false.