30-06-2012, 12:09 PM
Adaptive Filter Implementation
adaptive filter is implemented.ppt (Size: 137 KB / Downloads: 409)
Generalities of Adaptive Filters
The coefficients of Adaptive filters are variable with time in order to optimize a given criterion.
The most commonly used algorithm to adapt the coefficients is the LMS (Least Mean Square) algorithm.
Most adaptive filters are implemented as FIR filters, because they are inherently stable.
They are widely used in digital communications:
Echo cancellation, equalizers ...
Stochastic Gradient Algorithm: LMS
The mean values E(e(n)x(n-i)) are not known.
In the stochastic gradient algorithm, they are replaced by e(n)x(n-i).
The algorithm converges if the adaptation step is small enough.
Algorithm named: LMS (Least Mean Square) or Widrow algorithm:
Fixed Point Implementation
When LMS adaptive filter is implemented on a fixed point DSP:
The precision of calculation is important:
If rnd(ei*xn-i) is smaller than the used precision, no adaptation is performed.
The precision of convergence depends on:
Adaptation step : the largest , the fastest convergence but the worst precision.
The number of coefficients N: the residual error is proportional to N.
When N is too large, it may be worth considering using block adaptive filtering.