Power Spectral Density and Hilbert Transform

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.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 2016
Accession Number
AD1023688

Entities

People

  • Patrick Jungwirth

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Amplitude Modulation
  • Analytic Functions
  • Bandwidth
  • Cartesian Coordinates
  • Complex Numbers
  • Delta Functions
  • Digital Signal Processing
  • Dynamic Range
  • Frequency
  • Frequency Shift
  • Modulation
  • Sidebands
  • Signal Processing
  • Software Defined Radio
  • Spectrum Analyzers
  • Square Waves
  • Translations

Fields of Study

  • Engineering

Readers

  • Image Processing and Computer Vision.
  • Radio communications and signal processing.