# Uncorrelated input to a DPCM system?

1. Nov 15, 2008

### maverick280857

Hi

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

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

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

$$R_{X,0}Ip = 0$$

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

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

My question is: What happens physically if such a situation arises?

TIA.

(PS--This isn't homework.)