Page 65 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

Chapter 2

PROBABILITY AND RANDOM PROCESS
Algorithm Collections

1. INDEPENDENT COMPONENT ANALYSIS

Consider ‘m’ mixed signals y 1(t), y 2(t)…y m(t) obtained from the linear
combination of ‘n’ independent signals x 1(t) , x 2(t) … x n(t) , where n>=m is
given below.

y 1(t) = a 11 x 1(t) + a 12 x 2(t) + a 13 x 3(t) + …a 1nx n(t)
y 2(t) = a 21 x 1(t) + a 22 x 2(t) + a 23 x 3(t) + …a 2nx n (t)
y 3(t) = a 31 x 1(t) + a 32 x 2(t) + a 33 x 3(t) + …a 3nx n(t)
y 4(t) = a 41 x 1(t) + a 42 x 2(t) + a 43 x 3(t) + …a 4nx n(t)
…
y m(t) = a m1 x 1(t) + a m2 x 2(t) + a m3 x 3(t) + …a mnx n(t)

Independent signals are obtained from the mixed signals using
Independent Component Analysis (ICA) algorithm as described below

1.1 ICA for Two Mixed Signals

The samples of the signals x 1(t) and x 2(t) are represented in the vector
form as x 1=[x 11 x 12 x 13 …x 1n] and x 2=[x 21 x 22 x 23 … x 2n] respectively. The
signals y 1(t)=a 11*x 1(t)+a 12*x 2(t) and y 2(t)=a 21*x 1(t)+a 22*x 2(t) are represented
in the vector form as y 1=[y 11 y 12 y 13 …y 1n] and y 2=[y 21 y 22 y 23 … y 2n]

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