June 22, 2008
June 22, 2008
June 25, 2008
Computers in Education
13.26.1 - 13.26.18
A Correlation Detector Simulation Abstract
In some detection processes, such as radar, sonar, and seismology, the cross-correlation of a known signal and a time-delayed version of the same signal with additive noise can be used to determine the time delay between the transmitted pulse and the return pulse. Such a procedure is relatively easy to rationalize intuitively. (The scheme may also be viewed as filtering the return signal with a matched filter, but the convolution of the signal with the impulse response of the matched filter may be harder for students, especially those who have studied neither linear systems nor digital filters, to grasp.)
A computer simulation of the cross-correlation detection process was originally assigned as a graphical programming project in a computer software class. The simple model used in the assignment assumed a sinusoidal signal of adjustable duration as the transmitted pulse and a delayed version of the same pulse with added white noise as the received pulse. Two noise models were available to the user: zero-mean uniformly distributed white noise and zero-mean Gaussian white noise of adjustable variance. The amplitude of the added noise was to be adjustable by the user. The transmitted pulse and the received signal were displayed in separate plots, and the cross-correlation of the transmitted pulse and the received signal was displayed in a third plot. Both signals and the cross-correlation were represented by finite length sequences.
A simple view of the detection process is included as part of the assignment. The transmitted signal is a pattern to be compared to the received signal at different time offsets. Since the noise is random and many samples are taken during one period of the sinusoidal pulse, the noise tends to cancel as the terms in the cross-correlation are added. The maximum “match” of the pattern occurs when the pattern is offset by the time delay represented in the received signal. The graphical presentation showed that, even in cases where a visual inspection of the received signal showed no hint of a pulse in the received signal, the cross-correlation clearly indicated the delay time of the received pulse.
The program allowed users to experiment with different noise amplitudes and delay times, and the visual presentation was quite dramatic. The concept seemed useful enough that the authors developed a program with a bit more functionality for use in a random processes course, where the topic of matched filters was part of the course material. In addition to a simple time delay, the pulse in the received signal was attenuated.
The original project was assigned in a computer software course covering C#.NET. Most of the students in the course were computer engineering majors. The focus of the programming aspect of the problem was the graphical user interface and graphics. The problem itself was chosen to include topics from a random processes course. The computer program provided a tool to enhance student understanding of a topic that had appeared difficult for students to grasp in the past.
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