Fixed and adaptive - optimal filtering, Electrical Engineering

Optimal Filtering

1389_Fixed and Adaptive.png

A system identi?cation structure is shown in Figure 1. The discrete-time signal [ ] forms the input to an unknown system represented by a moving average, FIR, ?lter with parameters, {ω01 ωn} . The output of the unknown system is given by

466_Fixed and Adaptive1.png

This can be represented more concisely in vector notation as

1891_Fixed and Adaptive2.png

where ω and x[k] are Nw + 1 element column vectors, underlines are used to denote vector quantities and the superscript (·)T represents a vector transpose.

A noise signal n[k] is added at the output of the system to yield a realistic measured output signal z[k]. An optimum ?lter is to be designed which operates on the input signal x[k] and measured output signal z[k] to yield the closest match to the unknown system. The optimum ?lter is assumed to be a moving average ?lter with the same number of parameters as the unknown system, i.e. opt.

This problem arises in many applications, for example control of some machinery plant, or of acoustic and electrical echoes in telecommunications. The Wiener solution is found by minimising the mean-square error between z[k] and y[k], where y[k] is the output of the optimum ?lter driven by x[k]. The circum?ex is used to denote that the output of the optimum ?lter is an estimate of the output of the unknown system.

If x[k]and n[k] are assumed to be uncorrelated stationary random discrete signals then the mean square error is de?ned as

2274_Fixed and Adaptive3.png

where {·} is the statistical expectation operation, which to a ?rst approximation can be considered to be an average. The right hand side of equation (1) contains a vector of crosscorrelation components and a matrix of autocorrelation components, i.e.

555_Fixed and Adaptive4.png

Differenting equation (1) with respect to opt and setting the result to zero yields the optimum Wiener ?lter solution which is given by

596_Fixed and Adaptive5.png

Posted Date: 2/27/2013 6:32:29 AM | Location : United States







Related Discussions:- Fixed and adaptive - optimal filtering, Assignment Help, Ask Question on Fixed and adaptive - optimal filtering, Get Answer, Expert's Help, Fixed and adaptive - optimal filtering Discussions

Write discussion on Fixed and adaptive - optimal filtering
Your posts are moderated
Related Questions
Q. Smallest unit of information on a machine? Short for the binary digit the smallest unit of information on a machine. This term was first used in 1946 by the John Tukey, a le

Determine the node voltage by using KCL: Determine the node voltage V and then current flowing through each element by using KCL. Solution Apply KCL at the node whose

Demand Side Management Demand side management refers to programmes implemented through utilities to modify consumer load profile. Energy efficiency programmes decrease energy

Disadvantages of SDR 1. Power consumption is more due to rapid switching of modes 2. Hardware design is not easy 3. Software bugs exist in the system

Explain DAA instruction. DAA: The DAA instruction follows the instruction ADC or ADD to adjust the result in a BCD result. The DAA instruction performs only with the AL registe

explain the waorking principle of function generator

kindly tell me which text book is usefull forlearn the basic electricle.

merits amd demerits of series and shunt clipper

Transistor as a switch: Transistors are generally employed as electronic switches, for both of the high power applications including switched-mode power supplies and low power

Define addressing modes of 8085. a) Immediate addressing b) Register addressing c) Direct addressing d)  Indirect addressing e)  Implicit addressing