Page 104 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

92 Chapter 3

Also, any vector in the generated vector space is represented as the linear
combination of E1 and E2. The co-efficients are obtained as the inner product
of vector and the corresponding Eigen vector.

For instance, the vector V 1=[20 16] is represented as

C 1E 1+C 2E 2

C 1 is obtained as the inner product of E 1 and V 1
C 2 is obtained as the inner product of E 2 and V 2

C 1 = -20.4269
C 2 = -15.4513

Thus V 1 = C 1E 1+C 2E 2
= -20.4269 *[-0.2459 -0.9693]+ -15.4513 *[-0.9693 0.2459].

Eigen vectors corresponding to the insignificant Eigen values are
contributing less to the vector representation. In such situation number of
orthornormal Eigen basis to represent the particular vector is reduced.
Note that the vectors mentioned in the figure 3-3 is obtained by applying
KLT transformation to the vector space mentioned in the Fig 3-2. The Eigen
vectors for this space are E 1=[1 0] and E 2=[0 1]

Figure 3-3. Vector space after KLT and the corresponding eigen vectors