Page 68 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

56 Chapter 2

Estimating the best values for the matrix [B] such that kurtosis measured
T
T
for the column vectors of the matrix [X] = [[B][Y]] as defined above is
maximum
We require another constraint about the matrix [B] to obtain the values of
the matrix [B] which is described below
The covariance matrix (COV(Y)) computed for the group of vectors
T
collected row-by-row of the matrix Y is computed using the formula as
displayed below

Let M = (y 11 + y 12 +y 13+…y 1n) / n

(y 21 + y 22 +y 23+…y 2n) / n

COV(Y) =

T
y 11 y 11 y 21 + y 12 y 12 y 22 + … y 1n y 1n y 2 n /n - MM
y 21 y 22 y 2n

T
T
(i.e) COV(Y) = E[YY ] - MM

The matrix computed is of size 2x2. The value at the position (1,1)
conveys the information about how the first elements of the collected vectors
are correlated with itself (variance). The value at the position (1,2) conveys
the information about how the first elements are correlated with second
elements of the collected vectors.
For example the covariance matrix computed for 2D vectors collected
from the particular independent signals and the corresponding mixed signals
are given below.
0.2641 x 10 -006 -0.1086 x 10 -006
COV independent =
-0.1086 x 10 -006 0.5908 x 10 -006

COV mixed = 0.1086 0.0613

0.0613 0.0512