Page 74 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

62 Chapter 2

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b 11(t+1) = E[(b 11 (t)z 1i+b 21(t) z 2i ) z 1i ]-3*b 11 (t)
3
b 21(t+1) = E[(b 11 (t)z 1i+b 21(t) z 2i ) z 2i ]-3*b 21 (t)

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b 12(t+1) = E[(b 12 (t)z 1i+b 22(t) z 2i ) z 1i ]-3*b 12 (t)
3
b 22(t+1) = E[(b 12 (t)z 1i+b 22(t) z 2i ) z 2i ]-3*b 22 (t)

Recall that the columns of the matrix B are made orthonormal to each
other. This can be explicitly performed in every iteration, after updating the
values using the equation given above.

1.1.1 ICA algorithm

Step 1: Given mixed signals y1(t) and y2(t) are converted into z1(t) and
z2(t) using Hotellilng transformation such that the covariance matrix
computed using the converted signals z1(t) and z2(t) is the identity
matrix.[Use Hotelling Transformation]

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Step 2: Initialize the values for the matrix B such that B B=[I]
Step 3: Update the elements of the matrix B using the Iteration formula
displayed above.

Step 4: Columns of the matrix B is made orthonormal to each other as
mentioned below.

B = B * real(inv(B' *B)^(1/2));

Step 5: Repeat step 3 and step 4 for ‘N’ Iteration.

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Step 6: Independent signals are obtained by multiplying B with the Z
matrix