4F7 Digital Filters and Spectrum Estimation
Michaelmas Term
Sumeetpal S. Singh
The lecture slides will be placed on this website after each lecture.
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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]
Solutions: part 1 [ pdf], part 2 [ pdf]
Matlab demo files
Matlab m-file for Lecture 2: Steepest Descent Example Lec2_SDexample.mMatlab 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]
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.mMatlab 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.