# Energy Compaction and Variances od Transform Coefficients

If $\mu_u$ e $R_u$ denote the mean and covariance of a vetor $u$ and $v$ is a transformed vetor of $u$, using a unitary transform i.e $v=Au$. Then due to the fact that $\sum_{k=0}^N|\mu_v(k)|^2=\sum_{n=0}^N|\mu_u(n)|^2$ e $\sum_{k=0}^N\sigma_v(k)^2=\sum_{n=0}^N\sigma_u(n)^2$ $\Rightarrow$ $\sum_{k=0}^N|E[v(k)]^2|=\sum_{n=0}^N|E[u(n)]^2|$.

My question are: Why this?. What is a role of the covariance result?. Whats is a relation of this result with Energy Compaction?

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