SpectralNot as easy as it sounds
The big trick here was to distinguish two similar complex sounds. Fourier could do some of this... or at least get the sounds in a format we could work with. Testing began with learning how to manipulate sounds in Java. With all the wiz-bang of Java this should be a walk in the park. It was not a walk in the park. But between the bugs and missing features the system could record microphone data and play it back.
The next task was to add a buffering system so hold two samples for analysis (click here for screenshot). This quickly required a signal generator to create new signals to test with. The created signal generator (screenshot here) could do basic waves and add, multiply, etc. One could also transfer generated buffers over to the main screen where further analysis could take place. This turned out to have great power for testing different signals and sanity checking the system.
The real heart of the matter is the signal differentiation. The rest of the project is really a learning exercise. The two main buffers are analyzed with fourier analysis to get the signals into frequency domain. The Discrete Fourier Transform is given below.
The imaginary component is essentially ignored as we do not care about phase (in truth, the actual values come from x^2 + i^2 = y^2, where x is the real component, i is the imaginary component, and y is the magnitude of interest). The system was initially setup to subtract the two frequency domain graphs, and use the result to present a graph of the how different the two signals really were. This turned out to be pretty sloppy. Even with multiple samples, performing translations of 1 second samples to frequency domain causes a bit of a harmonic mess.
In an effort to make the system better, the chi-square value was calculated and displayed(screenshot here). This offered a single number representing how different two frequency domain graphs are. This was much better.
In the end, there is still a great debate as to how effective the program is. It does indeed give a definitive sense of the difference between two close signals. However, between ambient noise, thermal characteristics, power line fluctuations and simple human error (how far the microphone was held from the target on day seven, for instance) there is just too much slop to make a definitive judgment. Even with all the math and science this system is still pretty subjective.