Abstract
This chapter discusses the detailed relationship between the discrete cosine transform (DCT) and the statistically optimal KLT. The transform that exactly diagonalizes the correlation matrix of any signal is the Karhunen-Loéve transform (KLT). The KLT is a series representation of a given random signal, whose orthogonal basis functions are obtained as eigenvectors of the corresponding autocorrelation matrix. This chapter examines the interpretation of KLT and provides a discussion on how this transform minimizes the mean square error (MSE) of a truncated representation of the actual signal. The accuracy of reconstructing the signal depends on how the signal is transmitted. If it is sampled and each sampled value of the signal is sent over the medium, then Shannon's sampling theorem determines how many samples per second would be required for the exact duplication of the signal at the receiving end, and this rate of transmission is dependent on the frequency contents of the signal. The KLT also serves well as a benchmark against which other discrete transforms may be judged.
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