Click modulation

In this paper we show how one may determine a sequence of equal intensity impulses or clicks $$\pi \sum^{\infty}_{-\infty} \delta (t-t_k)$$ such that a desired bandpass signal, f'(t), may be obtained by filtering the clicks; i.e. $$f^{'}(t) = \pi \sum^{\infty}_{-\infty} K(t-t_k),$$ where K(t) is the impulse response of a suitable bandpass filter. The {tk} are found as the zeros of a bandlimited signal s(t), where if f(t), the bandpass signal whose derivative is f'(t), is sufficiently small, we also have $$f(t) = \int^{\infty}_{-\infty} q(x)K(t-x)dx,$$ where q(x) is a square wave simply related to s(t).