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Homework 4

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Reading

  • Chapter 7 in Oppenheim & Wilsky

Problems

  • If a continuous-time co-sinusoidal signal with frequency pi*10000 rads/sec is samples at 3000 Hertz, what is the frequency of the resulting discrete-time co-sinusoid?
  • 7.31
  • 7.34 Besides specifying the L and M values draw sketches to show how the original spectra changes after each step in the upsampling-downsampling process. Assume that the original signal spectrum has a triangular shape.
  • 7.35 ( Downsampling by a factor of 2 )
  • ( Upsampling by a factor of 2 ) Consider the discrete-time sequence x[n] from which we form two new sequences xp[n] and xu[n] . The sequence xp[n] corresponds to x[n] with one zero sampled inserted between each sample of x[n] . The sequence xu[n] is a low-pass filtered version of xp[n] using an ideal low-pass filter with a cutoff frequency of pi/8 .
    1. If x[n] is the sequence illustrated below, then sketch xp[n] and xu[n] .
    2. If X(e^j*w) is as shown below, sketch Xp(e^j*w) and Xu(e^j*w) .

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 29). Homework 4. 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/hw4.html. This work is licensed under a Creative Commons License Creative Commons License