Abstract
The discrete Karhunen-Loève transform (KLT) requires knowledge of the covariance function of the source and a solution for the eigenvectors of the covariance matrix. In general, especially for large N, the solution and the transform are computationally burdensome procedures with no fast algorithms for their execution. Instead, one almost always uses a source-independent transform with a fast execution algorithm. We present several useful sub-optimal transforms and calculate coding gains of two of them.
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Notes
- 1.
The matrices \(\textbf{H}_{2N}\) are called Hadamard matrices and when the rows are re-ordered accorded to sequency (analogous to frequency but with \(\pm 1\) as the basis) are called Hadamard-Walsh or Walsh-Hadamard matrices.
- 2.
Theoretically, L can be an integer multiple of N other than 2, but the literature does not report any instance of such use.
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Pearlman, W.A. (2023). Suboptimal Transforms. In: Mathematical Transformations and Wavelet Filters for Source Coding and Signal Processing Systems. Synthesis Lectures on Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-031-34684-2_3
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DOI: https://doi.org/10.1007/978-3-031-34684-2_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-031-34683-5
Online ISBN: 978-3-031-34684-2
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