24-04-2014, 04:58 PM
Adaptive Signal Processing
Adaptive Signal .ppt (Size: 377.5 KB / Downloads: 90)
Problem: Equalise through a FIR filter the distorting effect of a communication channel that may be changing with time.
If the channel were fixed then a possible solution could be based on the Wiener filter approach
We need to know in such case the correlation matrix of the transmitted signal and the cross correlation vector between the input and desired response.
When the the filter is operating in an unknown environment these required quantities need to be found from the accumulated data.
Basic principles:
1) Form an objective function (performance criterion)
2) Find gradient of objective function with respect to FIR filter weights
3) There are several different approaches that can be used at this point
3) Form a differential/difference equation from the gradient.
Kalman Filters
The problem is normally stated as:
Given a sequence of noisy observations to estimate the sequence of state vectors of a linear system driven by noise.
Standard formulation
Cholesky Factorisation
In situations where storage and to some extend computational demand is at a premium one can use the Cholesky factorisation tecchnique for a positive definite matrix
Express , where is lower triangular
There are many techniques for determining the factorisation