Continuous-Time Wiener Filters

• Approach

• Example 4-1, Continuous-Time Wiener Filter

• Wiener Filters Mean-Square Error

• MSE of Example 4-1

Discrete-Time Wiener IIR Filters

• Overview

• Finding S_d(z) and S_x(z) from R_x(t)

  • GMP

  • Z transform

• Example 4-2, S_d(z) from R_x(t)

  • GMP or can be approx. as a GMP

  • Z transform

• Example 4-3, Discrete Wiener Filter

• Example 4-4, Digital Wiener Filter

• Example 4-5, Discrete Wiener Filter Simulation 
• Mean-Square Error
• Example 4-6, MSE of Example 4-3
  • Z-Domain Approach
  • Time Domain Approach

Discrete-Time Wiener FIR Filters

• Using the Filter Impulse Response 
• Optimal Discrete Wiener Filter Using R_x & R_x
• R_x  Conditioning
• Selection of Number of R_d terms
• Example 4-7, Optimum Wiener FIR Filter

Prediction & Smoothing

• Prediction
• Smoothing
• Example 4-8, One-Step Discrete Predictor

Complimentary (Matched) Filters

• Overview
• Design & Implementation Steps
• Example 4-9, Complimentary Filter Design

Adaptive Linear Filters

Solved Problems

• Continuous-Time Wiener Filter
• IIR Wiener Filter
• FIR Wiener Filter #1
• FIR Wiener Filter #2
• FIR Wiener Filter #3
• IIR One-Stage Predictor
• Adaptive Linear Filter

Chapter 4 Quiz Review

For Questions and Comments on the Structure or Design of this page ,e-mail Rajesh

Overview

Wiener filters expect the signal to be noise like.  Therefore, the shape of the Power Spectral Density of the signal must be determined.  There is a situation where Wiener filter theory can be used to design a Wiener filter if there are two sources from which a deterministic signal + noise or a random signal + noise are available.  For example, one of the signals is from a pitch angle sensor and the other signal is from a pitch rate sensor.  The second pitch angle is found by integrating the pitch rate signal.  The Complimentary Filters are:

From the circuit above:

Of course,

The filter works quite well if  is “low” frequency noise compared to noise . For design purposes, is considered as the desired signal and  is considered the noise going into the Wiener filter, .  Notice that the desired signal, , does not pass through the filter; hence, the estimated desired signal, , is not delayed or phase shifted relative to .