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Homework 2

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Reading

  • Chapter 8 in Oppenheim & Wilsky

Problems

  • 8.1 Let $ x(t)$ be a signal for which $ X(j\omega) = 0$ when $ \vert\omega\vert>\omega_M$ . Another signal $ y(t)$ is specified as having the Fourier transform $ Y(j\omega) = 2X(j(\omega-\omega_c))$ . Determine a signal $ m(t)$ such that $ x(t) = y(t) m(t)$ .
  • 8.2 Let $ x(t)$ be a real-valued signal for which $ X(j\omega) = 0$ when $ \vert\omega\vert>1,000\pi$ . Supposing that $ y(t) = e^{j\omega_c
t} x(t)$ , answer the following questions:
    1. What constraint should be placed on $ \omega_c$ to ensure that $ x(t)$ is recoverable from $ y(t)$ ?
    2. What constraint should be placed on $ \omega_c$ to ensure that $ x(t)$ is recoverable from $ \Re\{ y(t)\}$ ?
  • 8.3
  • 8.22
  • 8.26
  • 8.28
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 29). Homework 2. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Communication_Systems_I_1/hw2.html. This work is licensed under a Creative Commons License Creative Commons License