

Sampled signal from the microprocessor:A 400Hz signal was sampled from a function generator. The red x's are the actual sampled points and the line is drawn to fit the points. Graph of results from autocorrelation algorithm:Autocorrelation is crosscorrelation of the same signal. This technique is a useful method to find the period of a periodic signal in a large amount of noise. See the Theory section for more information. The graph below show these results. The results were then passed though additional code for signal detection. The blue trace is the autocorrelation result from our microprocessor. The red trace is a simulated result of our optimized autocorrelation code with 64 bit precision. The cyan trace is a Matlab autocorrelation result (positive values shown) of our sampled data from the microprocessor. The results decay rather fast. More storage samples would have extended the decaying quasisinusoidal curve. However, our optimized code still allows for accurate period detection.
Signal from the audio capture circuit (in a noisy environment):The following graphs show a similar 400Hz signal sampled in a noisy environment (after amplification and filtering) and also the autocorrelation results (second graph). The noise can be seen when this graph is compared the graph above (directly from a function generator),
Graph of results from autocorrelation algorithm (in a noisy environment):The autocorrelation still yields clear results in the noisy environment. This is show in the plot below.
Conclusion:With our math, circuit design, microprocessor programming, and hard work, the signals were learned and detected correctly. 
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