Power Spectral Density and Hilbert Transform

Report No. ARL-TR-7920
Authors: Patrick Jungwirth
Date/Pages: December 2016; 42 pages
Abstract: This technical report focuses on the Hilbert transform and some of its applications for digital signal processing. Herein we review power spectral density and complex exponentials, and illustrate how the Hilbert transform converts a real signal (real in the sense of a real time domain function and symmetric Fourier transform) into an analytic signal. We then demonstrate how multiplication by a complex exponential is used for frequency translation and provide 2 uses for the Hilbert transform in a software-defined radio: 1) creating an analytic signal and 2) recovering single sideband. Examples of upgrading a software-defined radio architecture with new algorithms (software) are also provided.
Distribution: Approved for public release
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Last Update / Reviewed: December 1, 2016