Get ready for the most boring animation, ever. EVER! (don’t say I didn’t warn you). I made this for a talk I gave for the MG&G lunch seminar a couple of weeks ago. I wanted to figure out a way to describe how a matched filter works, and found that I was doing lots of crazy hand gestures that weren’t helping me at all. Matlab animation to the rescue!
Let’s say you have your received time series, , and a simulated version of the transmitted call, . The cross correlator output is simply:
The function has peaks that correspond to onset times of the calls in the original time series.
In the top panel, the blue line is the received time series, and the red line is the simulated signal. Buried in the blue time series is the original signal, between seconds 2 and 3. It’s hard to see it by eye, but the matched filter plucks it right out! The black line in the second panel is the output of the cross correlation. The peak aligns exactly with the start time of the signal. Miracle!
I know what you’re dying to ask me, and no, Pixar still has not been in touch.