This simulation was constructed by utilizing typical Head Related Trasfer Function (hrtf) measurements provided by MIT Media Lab. (1)
The methodology involved constructing two seperate signals of gaussian noise for the left and right channels. Each channel was divided into chunks
representing five degrees of movement on the azimuth plane. Each chunk was convolved with the corresponding hrtf impulse response. Relevant variables
included the period (the time it took the source to make one full rotation) and the direction (clockwise versus counter-clockwise). The period (T) affected
the number of samples to be produced in the original guassian signal, which was a function of the sampling rate times the period (N*fs). The direction
was reversed easily, by swapping the left and right channels in the final stereo signal.
The source heard in part A was produced with a period of 2 seconds (T=2) and a clockwise direction. The resulting signal was then appended onto
itself to produce the resulting 4 second signal. The appended signal is somewhat flawed, because there is a noticeable break in the signal when the
source circles back around to zero degrees (directly in front of the observer).
The source heard in part B was produced by adjusting the period and direction. This source was designed with a period of 1 second (T=1) and a counter-clockwise direction. The signal was then appended onto itself four times in order to produce a 4 second signal. The resulting signal had the same issue as the signal in part A. There is a noticeable break in the signal when the source circles back around to zero degrees on the azimuth plane.
Part C was produced by using the part A and part B to generate the signals seperately. The signals were then added together, resulting in the final signal simulating the two sources simultaneously. Because the periods of each signal are different, the breaks in the signal that were apparent in parts A and B were less noticeable.
In conclusion, the resulting simulations effectively produced signals that sound as if they are rotating around the observer's head. The results would be improved if the breaks that occur in the signals of parts A and B were eliminated. This break could be avoided by using another method to construct a signal of more than one period instead of just appending the signal onto itself.