01-12-2012, 04:13 PM
Adaptive Signal Processing
Adaptive Signal Processing.ppt (Size: 10.62 MB / Downloads: 156)
Definition of filtering
A term filter or estimator is commonly used to refer to a system that is designed to extract information about a prescribed quantity of interest from noisy data.
Applications
Communications; radar, sonar,
Control Systems; navigation,
Speech/Image Processing; echo and noise cancellation, biomedical engineering
Others; seismology, financial engineering, etc.
Linear Optimum Filter
In statistical approach to the solution of the linear filter, we assume the availability of statistical parameters (i.e. mean and correlation functions ) of the useful signal and unwanted additive noise
A requirement is to design a linear filter with noisy data as input and minimize effect of noise at the output according to the statistical criterion.
Useful approaches
Nonlinear:
Maximum Likelihood (ML) sense (very difficult to implement)
Linear:
Minimum Mean Square Error (MMSE) sense
Wiener filters, (Stationary environment)
Kalman filters, (Non-stationary environment)
Adaptive Filters
Wiener Filter requires
Priori information of about the statistics of data to be processed.
Filter is optimum only when the statistical parameter of input data matches with the priori information on which filter is designed.
Adaptive filtering can overcome these disadvantages!
Recursive algorithm
No complete a priori information required
Algorithm develops this information with increasing number of iterations.
If the environment is stationary → converges to the Wiener soln.
non-stationary → tracks the changes.