Abstract:
A matched filter maximizes the signal-to-noise ratio of a signal. In the recent work
of Corron et al. [Chaos 20, 023123 (2010)], a matched filter is derived for the chaotic
waveforms produced by a piecewise-linear system. This system produces a readily
available binary symbolic dynamics that can be used to perform correlations in the
presence of large amounts of noise using the matched filter. Motivated by these
results, we describe a pseudo-matched filter, which operates similarly to the original
matched filter. It consists of a notch filter followed by a first-order, low-pass filter.
We compare quantitatively the matched filter’s performance to that of our pseudomatched
filter using correlation functions. On average, the pseudo-matched filter
performs with a correlation signal-to-noise ratio that is 2.0 dB below that of the
matched filter. Our pseudo-matched filter, though somewhat inferior in comparison
to the matched filter, is easily realizable at high speed (> 1 GHz) for potential radar
applications.