Example (Energy compaction and decorrelation ):

Consider zero mean vector that is unitarily transformed to,

where and represents the correlation between and . It is required to find the energy of the transformed coefficients.

Given

We have

From the matrix

Total average energy of 2 is distributed equally between and .

But from we note , and .

The total average energy is 2, but average energy in is greater than that in .

If , then of total average energy is packed in first sample.

Correlation between and is

Now

It follows that: ρ

that is, is less in absolute value than for .

For we find

correlation between transform coefficients has reduced.