| Popis: |
We show the development of a wideband delay guided by the closed-form, analytic solution of a solvable chaotic oscillator. This delay serves as a crucial component in the design of a matched filter receiver that optimally detects chaotic waveforms in the presence of noise. Unlike most chaotic systems, a special class of solvable chaos permits a closed-form analytic expression that may be used to guide designs. Specifically, we employ a cascade of 7th-order Bessel filter cells to accommodate various bandwidths associated with these oscillators. These bandwidth increments are guided by a closed form expression of the chaotic signals' spectral content. The resulting delay has wideband frequency characteristics while keeping group delay maximally flat within the operating band. Next, we analyze our results through time series comparison of the delayed signals with corresponding, analytically reconstructed chaotic waveforms. Finally, we summarize the trade-off space for these delay designs informed by analytic solution. Our results show that these finite bandwidth delay designs impose a 13% deviation from analytic time series expectations when 4 spectral lobes are considered and 17 % deviation for 3 spectral lobes. |
