The Royal Consortium for DSP

"Giving Digital Signal Processing the Royal Treatment"

The Royal Consortium

Introduction to Our DSP Project - Noise Cancellation

The curriculum for Elec 431, Digital Signal Processing, an Electrical Engineering course at Rice University , requires that class members participate together in groups of four or five to examine, an application of DSP. Material gathered is to be presented in the group's project web page (this document), and in an oral class presentation.

For those interested in how we are coming along with this project, ie., our professor, Richard G. Baraniuk , we have included a Progess Report.

The Royal Consortium for DSP (yes, you may inquire about our name but that doesn't mean you will get an answer) has selected the topic of noise cancellation.

For some specialized applications such as noise cancelling headphones, DSP techniques have been successfully used. It turns out that other applications, such as reducing the noise a jet engine makes are much more complex. We will examine these complexities, and if possible, develop a method of practical implementation for at least one application.

Note: If you have information you can contribute to this project, please contact any of our gang members shown below. We would be grateful for the assistance.

Additional Note: Project is complete as of 12/21/96, but we would still be interested in information or comments. Thank you.

Project Document Format

In addition to the formal report classifications described below, this document contains the following information categories:

Progess Report.
Project Members
Quotable Quotes

We generally follow the organization of a standard formal report, modified as required to take advantage of/work around the facilities/limitations of HTML. One key difference between a paper report and this web page report will be the retention of historical entries within each category below. to enable the reader to follow the development of the project.

Abstract
Introduction
Design Approach and Procedure
Result and Discussion - the meat of the matter - click here if you're in a hurry
Conclusions
References
Acknowledgements

We have also devoted a special page to our DSP professor, Richard G. Baraniuk.

Progress Report

"We're Keeping an Eye on Things"

12/21/96

This will be the final project status report for the project for it has come to a successful conclusion. The following is worthy of note:

We gave our project presentation in class on Monday, December 16, 1996, and we would call it a success. We would opt for a couple of changes for the next group of folks who get to do this. First, given the scope of the typical project, 20 minutes is not enough time to give adequate treatment to the material. We would very much like to have expounded on a few more details, but did not have time to do so. Two other groups expressed similar views. Second, full multi-media materials need to be available on the day(s) of the presentations, including owlnet connections and VGA type overhead projectors that work.
The power of adaptive filters is nothing short of amazing. Given the many tests that we ran using the filters, the ability to remove noise (or define a plant) seemed almost like magic, had we not written the code ourselves to cause the magic to happen. Recognizing that adaptive filtering is a graduate level course of study, we would nevertheless recommend that at least the fundamental techniques and theory be introduced at the undergraduate level.
Finally, the project web pages, as of 12/21/96, do not contain any sound or graphics. As soon as we are able to allocate about 6 megabytes of space, viewers of these pages will be able to hear the experiments and the effects of the filters, and will be able to view animated graphics demonstrating filter operation. We expect to have this material in place by year end.

11/28/96

After further reading, we have elected to implement the "stochastic gradient" method of adaptive filtering. This is a least squares method of minimizing some error. For a system that "listens", such as noise cancellation in a muffler, the error is the difference between what is heard and what is desired. For other applications, one approach to error is to minimize the total power found in the signal.

We are now proceeding with three primary tasks. The first is the modelling of a muffler, a rather simplified muffler, of course. Essentially, we are using the physics of sound in a pipe to create the model.

Our second task is the development of the actual filter. We know now that it will be an FIR filter; further, that it will use least squares to control the weights at each tap. We still need to determine filter length and the "mu" function used in tap weight computation.

Lastly, we are seeking out other adaptive filter models. We have identified two sources: A Simulink model and a model produced in England for teaching purposes. The Simulink model should be available from the Mathworks homepage. The other is more difficult to retrieve.

It goes without saying that we have also updated the project web pages rather substantially.

11/12/96

We have reviewed two textbooks and conducted a fairly exhaustive web search for information relevant to noise cancellation. In summary:

There are two basic approaches to developing linear adaptive filters: Stochastic Gradient Approach (or the least mean square 'LMS' algorithm); and the method of Recursive Least Squares 'RLS' algorithm, a filter embodying the notion of state.
The LMS filter appears to provide all the necessary essentials for understanding the issues of convergence, robustness, and performance, and at the same time it is an algorithm which is relatively simple to implement.
We have obtained the mathematical basis and theory for the operation of the LMS filter.
We have identified approximately four papers which should help us with the next steps in the project.

Based upon the limited information we have to date, we are moving the project in the following direction:

We will focus on the LMS filter in order to fully understand how it works and its limitations. The output of this stage of the project will be the mathematical treatment of LMS filters.
We will attempt to obtain a Matlab like filtering/teaching program to understand how the mathematics are actually implemented. The output of this stage will be the "psuedocode" implementation of the filtering algorithm.
We will decide on exactly the type of real world noise cancellation on which we intend to use our filter(s). The output of this stage will be a detailed analysis of the noise problem, approaches taken in the real world, and other relevant information to insure that we fully understand what it is that we think we are doing. We will also collect/build data which is representative of the problem at hand.
We will implement our filtering system in Matlab. Obviously, the output of this stage will be a demonstration of the effectiveness of our noise cancellation techniques. We intend on designing the system that it will be demonstrable in class.

Quotable Quotes

"There is an old trick question: "If a tree falls in the forest and nobody is there to hear it, does it make any noise?" The answer is "no" because sound cannot be *noise* unless somebody hears it and finds it offensive. However, if the question is phrased "Does it make any *sound*," then you have a deep philosophical question to ponder!"

This page, while nearing completion, has yet to have the last bells and whistles added. It was last modified on December 24, 1996, AD. God bless the Queen. If you have kudos and accolades for this page, contact Wayne Herbert, but if you want to gripe, try Art Farkel.