# 4F7 Digital Filters and Spectrum Estimation

## Michaelmas Term

### Sumeetpal S. Singh

The lecture slides will be placed on this website after each lecture.

Need more help or you have comments you would like to share? Why not email me. (For help do so well in advance of the exam.)

## Lecture Notes for Adaptive Filters

Introduction to Adaptive Filtering; Wiener filter and Steepest Descent [ pdf]

Least Mean Square Algorithm [ pdf]

Recursive Least Squares [ pdf]

Kalman Filter [ pdf]

Hidden Markov Model [ pdf]

Examples paper: part 1 [ pdf], part 2 [ pdf]

(Examples class is second half of lecture 7 and lecture 8)

Solutions: part 1 [ pdf], part 2 [ pdf]

### Matlab demo files

Matlab m-file for Lecture 2: Steepest Descent Example Lec2_SDexample.m

Matlab m-file for Lecture 3: Noise Cancellation problem [ noiseCancel.m], Learning AR signal parameters [ misAdjustment.m], NLMS [ nlms.m]

For noise cancellation, you should plot the various signals. Also consider the effect of changing the filter order, the frequency of both the noises, their lags etc.

Matlab m-file for Lecture 4: Learning AR signal parameters using the RLS [ rlsExample.m] algorithm

The Matlab file for Examples Sheet 1, Q4 [ ex1Question4.m]

The Matlab file implementing the scalar KF

The Matlab file for Dishonest Casino

## Lecture Notes for Spectrum Estimation

Power Spectrum Estimation [ pdf]

Periodogram properties [ pdf]

Improving the Periodogram [ pdf]

Parametric methods [ pdf]

Fitting the MA model [ pdf]

Maximum likelihood for ARMA model estimation [ pdf]

Examples paper with solutions [ pdf]

### Matlab demo files

Estimating the PSD with the Periodogram Same demo for periodogram_white_noise.m

Matlab demo of validity of the approximation of the variance of the Periodogram for a more general wide sense stationary process Periodogram variance

Matlab demo for ARMA MLE

Matlab file for Question 17 of Spectrum estimation Examples paper.