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
Single Phase Meters Single phase meters are commonly rated for 240 V AC supply; the current ratings are 5/10, 10/20, 2.5/10 or 5/20 A or are for direct connection to the mains

a) What do you mean by assembly procedures in FEM, discuss by taking suitable example of your choice. b) Write the potential energy equation for particular FE analysis of a prob

Find the power supplied by the voltage source and the power absorbed by the 24 Ω resistor (R3) in the circuit shown below:   Determine the voltage V2 in the circuit shown.

3-phase 180 0 mode VSI In 1800 mode VSI  each thyristor  conduct  for 1800 and two  thyristor  are fired  at 600 interval. For  example  if thyristor  T1  is fired at 00 then

Q.   Define and explain the critical field circuit resistance and critical speed of a DC shunt generator.   Ans. The OCC and R - line for a DC shunt generator. As, R f is

i have to design a project title "Edge determining techniques for Low quality images in different lighting conditions and we use matlab for images simulation by changing different

Q. Explain about Delay System? Delay System: A class of telecommunication networks, like data networks, places the message or call arrivals in a queue in the

Op code Format As we  have seen  in the  section that  the first  byte of all the instruction is the  op code. microprocessors  reads this  op code  and decodes it  to identif

Q. A single-line diagram of a three-phase transformer bank connected to a load is given in Figure. Find the magnitudes of the line-to-line voltages, line currents, phase voltages,

Q. Explain Current-to-Current Amplifier ? The circuit given in Figure is to amplify a current fed to the input of the op amp. Applying KCL at Y, i 1 + i S = i o S