- #1
maverick280857
- 1,774
- 5
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
[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 happens physically if such a situation arises?
TIA.
(PS--This isn't homework.)
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 happens physically if such a situation arises?
TIA.
(PS--This isn't homework.)