Summary: The Statistics of Normalized Data in Electrical
P. Hashemzadeh, 2
A. Adler and 1
Department of Natural Science, Middlesex University, NW4 4BT, London, UK. 2
Department of Systems and Computer Engineering, Carleton University.
Abstract. This study focuses on the noise statistics of the normalized data, in
time-difference imaging. The commonly practiced normalization procedure, represents
the normalized data as the ratio of two random variables. We provide closed form
expressions for computing estimates of the first, second order moments, and the
covariance matrix of normalized data. The expressions are derived using Taylor series
expansion method for the function of random variables (propagation of uncertainty,
delta method), and accurate provided that the signal to noise ratio of the reference
measurement is larger than 16 dB. The analysis presented here, provides an explanation
as well as insight, into the potential cause and presence of spikes in normalized data.
Furthermore, we demonstrate that the statistics of normalized data, is significantly