Bandwidth Efficient Digital Communication with Wavelet Approximations

Based on their shift and scale orthogonality properties, scaling and wavelet functions may be used as signaling functions having good frequency localization as determined by the fractional-out-of-band power (FOOBP). In this paper, application of Daubechies' wavelet and scaling functions as baseband signaling functions is described, with a focus on finding discretely realizable pulse-shaping transfer function circuits whose outputs approximate scaling and wavelet functions when driven by more conventional digital signaling waveforms. It is also shown that the inter-symbol interference (ISI) introduced by the approximation has negligible effect on the performance in terms of signal-to-noise ratio (SNR). Moreover, the approximations are often more bandwidth efficient than the original wavelet functions. These waveforms thus illustrate an example solution of a tradeoff between residual ISI and bandwidth efficiency as a signal design problem.