Re: [WM]: DCT energy compression

[Teddy Furon <teddy.furon@ieee.org>]

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> 
> I've read in everal papers that the Discrete Cosine Transform has an 
> energy ( defined as the variance, as in Principle Components Analysis)

> compaction
> 
> property, and as such is a good approximation of PCA decomposition. 
> Though I have never seen this asumption been denied while 
> experimenting on audio signals, I'd like to know if there is a 
> theoretical proof of this,

Robert Gray "Toeplitz and Circulant Matrices: A review" document
available at www-isl.stanford.edu/~gray/toeplitz.pdf might give several
clues for a theoretical proof. It gives an understandable explanation of
Szego works for "engineers lacking the background to attack mathematical
literature on the subject" like me.

As far as I remember:
Weakly stationary time series have toeplitz covariance matrices,
diagonal via KLT. These are asymptotically equivalent (in a certain
sense) to circulant matrices, diagonal via Fourier transform.

Hope this helps.
Teddy 




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