Signal approximation using the bilinear transform

This paper explores the approximation properties of a unique basis expansion, which realizes a bilinear frequency warping between a continuous-time signal and its discrete-time representation. We investigate the role that certain parameters and signal characteristics have on these approximations, and we extend the analysis to a windowed representation, which increases the overall time resolution. Approximations derived from the bilinear representation and from Nyquist sampling are compared in the context of a binary detection problem. Simulation results indicate that, for many types of signals, the bilinear approximations achieve a better detection performance.