THE USE OF DISCRETE KARHUNEN-LOEVE TRANSFORM TO CHARACTERIZE THE SIGNAL AND NOISE PORTIONS IN MODERN STATISTICAL SIGNAL PROCESSING

Document Type : Original Article

Author

Associate Professor, Elec. Eng. Dept., Military Technical College, Cairo, Egypt.

Abstract

Frequently in communication and radar signal processing problems it is useful to expand a function as a linear combination of orthogonal basis functions. The orthogonality of the basis functions makes the representation efficient and mathematically convenient. In signal processing applications it also guarantees that the components of the signals with respect to the basis functions do not interfere with each other. For example, in communication problems the use of orthogonal functions permits several different signals to share the same transmission medium, such as a cable or fiber optic link. This paper shows that the use of orthogonal basis functions, in reconstructing an original signal from a received noisy observation, increases the signal-to-noise ratio and is counterpart for the nonstationary noise case to eliminating the out-of-band noise. The proposed signal representation is based on the discrete Karhunen-Loeve transform. The proposed filtering method reconstructs the original signal from a received noisy observation based on real data and does not depend on any prior statistical knowledge. Numerical results show that the proposed filtering method is very efficient.

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