We show development of a wideband delay using the closed-form, analytic solution of a solvable chaotic oscillator which serves as a crucial component in the design of a matched filter receiver. We employ a cascade of 7th-order Bessel filter cells to accommodate various degrees of oscillators bandwidth guided by closed form expression of its spectral content. The resulting delay has wideband frequency characteristics while keeping group delay maximally flat within the operating band. Our time series comparison results show that these finite bandwidth delay designs impose a 13% deviation from analytic time series expectations when 4 spectral lobes are considered.