Wireless sensor nodes (WSNs) are increasingly used in applications such as environmental monitoring and the Internet of things. However, traditional digital WSNs rely on synchronous Nyquist-Shannon sampling, which leads to high baseline power consumption and system complexity. Event-based sampling offers an alternative approach, where signals are sampled only when an event occurs. This leads to data arriving at the transmitter at unpredictable times with both sparse and dense bursts of activity. This paper analyzes the use of event-based communication for variable bandwidth signals, which are characterized by an instantaneous bandwidth rather than a constant one. An asynchronous frequency-shift keying on-off keying (FSKOOK) transmission and detection scheme is introduced to enable pulse based communication, where events are modulated onto distinct frequencies and are transmitted as short bursts. We analyze the susceptibility of a time-warping reconstruction approach to pulse deletions, insertions and distortion in noisy channels, and we compare its performance to that of piecewise linear interpolation as a baseline. Furthermore, we present a hardware prototype of a FSKOOK transmitter with preliminary transmission results.