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I have a question regarding an ACTUAL Differential Pulse Code Modulation system setup. The prediction algorithm is predicated upon the assumption that an input to it is a correlated signal, and the objective therefore is to reduce redundant information when it is sampled at rates higher than the Nyquist rate.

Now, the prediction error when a linear prediction filter of order P is used, is given by

[tex]e_{n} = x[n] - \sum_{i=1}^{P}p_{k}x[n-k][/tex]

But for an uncorrelated input, the discrete time Weiner Hopf equations degenerate to

[tex]R_{X,0}Ip = 0[/tex]

where [itex]R_{X,0} = E[x[n]^2][/itex], [itex]I = diag(1, 1, \ldots, 1)[/itex] and [itex]p = (p_{1}, p_{2}, \ldots, p_{P})^{T}[/itex].

For a nontrivial signal then, this just reduces to [itex]p = 0[/itex], which simply implies that the predictor coefficients are all zero. If this is the case, the prediction error is [itex]e_{n} = x[n][/itex].

My question is: What happensphysicallyif such a situation arises?

TIA.

(PS--This isn't homework.)

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# Uncorrelated input to a DPCM system?

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