skip to main content
article

Linear filtering in DCT IV/DST IV and MDCT/MDST domain

Published: 01 June 2009 Publication History

Abstract

In this paper, expressions for convolution multiplication properties of DCT IV and DST IV are derived starting from equivalent DFT representations. Using these expressions methods for implementing linear filtering through block convolution in the DCT IV and DST IV domain are proposed. Techniques developed for DCT IV and DST IV are further extended to MDCT and MDST where the filter implementation is near exact for symmetric filters and approximate for non-symmetric filters. No additional overlapping is required for implementing the symmetric filtering in the MDCT domain and hence the proposed algorithm is computationally competitive with DFT based systems. Moreover, inherent 50% overlap between the adjacent frames used for MDCT/MDST domain reduces the blocking artifacts due to block processing or quantization. The techniques are computationally efficient for symmetric filters and provides a new alternative to DFT based convolution.

References

[1]
Strang, G., The discrete cosine transform. SIAM Review. v41 i1. 135-147.
[2]
Rao, K.R. and Yip, P., Discrete Cosine Transforms: Algorithms, Advantages, Applications. 1990. Academic Press, San Diego, CA.
[3]
Chitprasert, B. and Rao, K.R., Discrete cosine transform filtering. Signal Processing. v19. 233-245.
[4]
Martucci, S.A., Symmetric convolution and the discrete sine and cosine transforms. IEEE Transactions on Signal Processing. v42 i5. 1038-1051.
[5]
Reju, V.G., Koh, S.N. and Soon, I.Y., Convolution using discrete sine and cosine transforms. IEEE Signal Processing Letters. v14 i7. 445-448.
[6]
Kresch, R. and Merhav, N., Fast DCT domain filtering using the DCT and the DST. IEEE Transactions on Image Processing. v8 i6. 821-833.
[7]
Bongiovanni, G., Corsini, P. and Frosini, G., One-dimensional and two-dimensional generalized discrete Fourier transforms. IEEE Transactions on Acoustics Speech and Signal Processing. vASSP-24. 97-99.
[8]
Oppenheim, A.V., Schafer, R.W. and Buck, J.R., Discrete Time Signal Processing 2/e. 1999. Pearson Education Inc.
[9]
Johnson, A.W. and Bradley, A.B., Adaptive transform coding incorporating time domain aliasing cancellation. Speech Communication. v6. 299-308.
[10]
H.S. Malvar, Signal Processing with Lapped Transforms, Artech House, Norwood MA, 1992.
[11]
Princen, J. and Bradley, A., Analysis/synthesis filter bank design based on time domain aliasing cancellation. IEEE Transactions on Acoustics Speech and Signal Processing. vASSP-34 i5. 1153-1161.
[12]
Princen, J., Johnson, A. and Bradley, A., Subband/transform coding using filter bank designs based on time domain aliasing cancellation. In: Proceedings of the ICASSP 1987, pp. 2161-2164.
[13]
Sorensen, H.V., Jones, D.L., Heideman, M.T. and Burrus, C.S., Real-valued fast Fourier transform algorithms. IEEE Transactions on Acoustics Speech and Signal Processing. vASSP-35. 849-863.

Cited By

View all

Recommendations

Comments

Information & Contributors

Information

Published In

cover image Signal Processing
Signal Processing  Volume 89, Issue 6
June, 2009
302 pages

Publisher

Elsevier North-Holland, Inc.

United States

Publication History

Published: 01 June 2009

Author Tags

  1. Convolution
  2. Discrete cosine transforms
  3. Discrete sine transforms
  4. Modified discrete cosine transform
  5. Modified discrete sine transform
  6. Transform domain filtering

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 0
    Total Downloads
  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 09 Jan 2025

Other Metrics

Citations

Cited By

View all

View Options

View options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media