10. Linear Transforms

  1. Donald G. Bailey

Published Online: 2 JUN 2011

DOI: 10.1002/9780470828519.ch10

Design for Embedded Image Processing on FPGAs

Design for Embedded Image Processing on FPGAs

How to Cite

Bailey, D. G. (2011) Linear Transforms, in Design for Embedded Image Processing on FPGAs, John Wiley & Sons (Asia) Pte Ltd, Singapore. doi: 10.1002/9780470828519.ch10

Author Information

  1. Massey University, New Zealand

Publication History

  1. Published Online: 2 JUN 2011
  2. Published Print: 1 JUN 2011

ISBN Information

Print ISBN: 9780470828496

Online ISBN: 9780470828519



  • discrete cosine transform (DCT);
  • Fourier transform;
  • image compression;
  • image processing;
  • linear transformations;
  • video coding;
  • wavelet transform


Linear transformations are often used to rearrange the data into a particular form. In particular they can be used to separate different components of an image, for example separating signal from interference or noise. The Fourier transform is one of the most commonly used linear transforms in image and signal processing. Closely related to the Fourier transform is the discrete cosine transform (DCT). Whereas the Fourier transform has both sine and cosine components, the DCT is made purely from cosine terms. The application of the DCT to image and video coding is discussed in more detail in. As with the Fourier transform,wavelets have a wide range of applications within image processing and some of the main applications are introduced in this chapter. One of the most significant applications of the wavelet transform is in image compression.

Controlled Vocabulary Terms

data compression; discrete cosine transforms; Fourier transforms; image processing; video coding