ECE 510/610: Homework Assignments

Homework 1 (Due Mon., January 23)

Obtain a signal for prediction

1. Describe how the signal was obtained and what it's basic properties are
2. Explain the significance of being able to predict the signal
3. Estimate the auto-correlation using one of the estimators from ECE~5/638. Indicate how much confidence you have in this estimate. Include a plot of the autocorrelation.
4. Pick a filter order $M$ for prediction. Justify this choice.
5. Show a time-domain plot of how well you can predict $L$ steps ahead.
6. Calculate the normalized mean squared error as a function of $L$
7. Discuss and interpret your results.
8. What conclusions can you draw?

Homework 2 (Due Mon., February 6)

Find a pair of signals that can be used for an inverse filtering, deconvolution, channel equalization, or matched filter application (see Sections~6.7--6.9 in the text).

1. Describe how the signals were obtained and what their basic properties are
2. Explain the significance of being able to solve the problem
3. Plot the PSDs and cross-PSD
4. Pick a measure of performance and justify it.
5. Pick a filter order $M$ for prediction. Justify this choice with estimated autocorrelation, partial autocorrelation, or a plot of the estimated NMSE versus $M$.
6. Demonstrate how well the estimator performs by estimating the NMSE.
7. Discuss and interpret your results.
8. What conclusions can you draw?

Homework 3 (Due Mon., February 27)

1. Apply the Kalman filter to an estimation problem of interest
2. Include all the usual elements: Introduction, significance, methodology, results, discussion, and conclusion

Everything Below is Tentative

Project Proposal (Due Wed., Nov. 2)

Complete Draft of Report (Due Nov. 28, 12 pm)

Peer Review (Due Dec. 2, 12 pm)

Oral Presentations (Dec. 7)

Presentation slides due by 11 am on 12/7

Presentations begin at 12:30 pm sharp

Final Paper (Due Dec. 8 at 12 pm)

Revised 2.16.06