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Discrete cosine transforms (DCTs) are widely used in speech
coding and image compression. They resemble Karhunen-
Loeve transform for first-order Markov stationary random
data and are classified into four groups. Finding fast
computational algorithms for DCTs has been a rather active
subject. These methods all tried to reduce
the amount of multiplications. It is very important
to low-power implementations of DCTs on mobile devices
that no floating multiplications or less multiplications are
needed. At the same time, the parallel hardware methods
also have been developed for designing fast DCT processors. Among them the systolic array
methods have been given more attentions due to their
easy VLSI implementation.
By using a modular mapping and truncating, DCTs are approximated by linear sums of discrete
moments computed fast only through additions. This enables us to use computational
techniques developed for computing moments to compute DCTs efficiently.
We demonstrate this by applying our earlier systolic solution to this problem. The method can
also be applied to multidimensional DCTs as well as their inverses.
J. G. Liu, Y. Z. Liu, G. Y.Wang, "Fast DCT-I, DCT-III, and DCT-IV via Moments", 2005.
Index Terms: DCT, discrete cosine transform, moments, moment, fast transform, systolic array, Matlab source code.
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Figure 1. DCT coefficients |
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A simple and effective source code for Discrete Cosine Transforms based on Moments. |
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Demo code (protected
P-files) available for performance evaluation. Matlab Image Processing Toolbox is required. |
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Release |
Date |
Major features |
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1.0 |
2007.02.07 |
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We recommend to check the secure connection to PayPal, in order to avoid any fraud. This donation has to be considered an encouragement to improve the code itself. |
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Fast DCT Via Moments 1.0 - Click here for
your donation. In order to obtain the source code you
have to pay a little sum of money: 50 EUROS (less
than 70 U.S. Dollars). |
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Once you have done this, please email us luigi.rosa@tiscali.it As soon as possible (in a few days) you will receive our new release of Fast DCT Via Moments. Alternatively, you can bestow using our banking coordinates:
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The authors have no relationship or partnership
with The Mathworks. All the code provided is written in Matlab
language (M-files and/or M-functions), with no dll or other
protected parts of code (P-files or executables). The code was
developed with Matlab 14 SP1. Matlab Image Processing Toolbox is required.
The code provided has to be considered "as is" and it is without any kind of warranty. The
authors deny any kind of warranty concerning the code as well
as any kind of responsibility for problems and damages which may
be caused by the use of the code itself including all parts of
the source code.
