Advertisement

Transforms and Subband Decomposition

  • Mrinal Kr. Mandal
Chapter
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 716)

Abstract

The properties of the audio and video signals, and the digitization process have been discussed in the previous Chapters. When a signal is digitized, further processing of these signals may be needed for various applications, such as compression, and enhancement. The processing of multimedia signal can be done effectively when the limitation of our hearing or visual systems is taken into account. For example, it was shown in Chapter 3 that the human ear is not very sensitive to audio signals with frequencies above 10–12 KHz. Similarly, the eyes also do not respond well above 20 cycles/degree. This dependency of our sensory systems on the frequency spectrum of the audio or visual signals has led to the development of transform and subband-based signal processing techniques. In these techniques, the signals are decomposed into various frequency or scale components. Various components are then suitably modified depending on the application at hand. In this Chapter, we will discuss mainly two types of signal decomposition techniques: transform-based decomposition and subband decomposition.

Keywords

Wavelet Coefficient Finite Impulse Response Digital Filter Finite Impulse Response Filter Lena Image 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. K. Jain, Fundamentals of Digital Image Processing, Prentice Hall, 1989.Google Scholar
  2. 2.
    E. O. Brigham, The Fast Fourier Transform, Prentice Hall, 1974.Google Scholar
  3. 3.
    K. R. Rao and R. C. Yip, The Transform and Data Compression Handbook, CRC Press, New York, 2000.CrossRefGoogle Scholar
  4. 4.
    P. P. Vaidyanathan, Multirate Systems and Filterbanks, Prentice Hall, 1992.Google Scholar
  5. 5.
    C. S. Burrus, R. A. Gopinath, and H. Guo, Introduction to Wavelets and Wavelet Transforms, Prentice Hall, 1998.Google Scholar
  6. 6.
    S. G. Mallat, “A theory for multiresolution signal representation: the wavelet decomposition,” IEEE Trans, on Pattern Analysis and Machine Intelligence, Vol. 11, pp. 674–693, July 1989.zbMATHCrossRefGoogle Scholar
  7. 7.
    M. K. Mandai, Wavelet Theory and Implementation, Chapter 3 of M.A.Sc Thesis, Wavelets for Image Compression, University of Ottawa, 1995 (Included in the CD).Google Scholar
  8. 8.
    R. C. Gonzalez and Richard E. Woods, Digital Image Processing, Addison Wesley, 1993.Google Scholar
  9. 9.
    B. P. Lathi, Signal Processing and Linear Systems, Berkeley Cambridge Press, 1998.Google Scholar
  10. 10.
    A. N. Akansu and R. A. Haddad, Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets, 2nd Edition, Academic Press, San Diego, 2001.Google Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Mrinal Kr. Mandal
    • 1
  1. 1.University of AlbertaCanada

Personalised recommendations