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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.
Figure 1. DCT coefficients
A simple and effective source code for Discrete Cosine Transforms based on Moments.
Demo code (protected P-files) available for performance evaluation. Matlab Image Processing Toolbox is required.
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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.
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