Sampling Based on Local Bandwidth

This paper investigates the sampling of continuous-time signals according to time-varying or local bandwidth. A general framework is established for sampling based on local bandwidth. Two specific representations of local bandwidth are subsequently presented. In the first approach, the time-invariant anti-aliasing filter that typically precedes uniform sampling is generalized to a time-varying lowpass filter. A corresponding sampling and re-synthesis method is developed that achieves perfect reconstruction for a class of self-similar input signals; in most cases, however, perfect reconstruction does not result. In the second approach, local bandwidth is represented in terms of time-warping applied to globally bandlimited signals. The use of time-warping is proposed as a pre-conditioning technique to transform the input signal into one that is as close as possible to being globally bandlimited.