1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How would you match up these Z-transforms?

  1. May 10, 2015 #1
    1. The problem statement, all variables and given/known data
    In Figure Q1b (on the next page), two plots display samples of the continuous-time signal uct(t) = sin(2πt) and two plots display samples of the continuous-time signal vct(t) = e −t sin(2πt). For each signal, the samples in the corresponding plots are obtained with two different sampling times. Associate each of the four plots with the corresponding Z transform in the list and justify your answer:
    Capture2.PNG
    Capture.PNG


    2. Relevant equations

    Table of Z-Transforms

    3. The attempt at a solution
    Ok so using considering the generic denominator of the Z transform of a sinusoid:

    z2+2cdz+d2

    I can see that both equations 2 and 3 have a value of d=1 hence they are both undamped systems, so they are either one of (b) or (c)

    Then from the generic denominator equation:

    for (2) c=-2cos(ωT) =1.9842
    = cos(ωT) = -0.9921

    For (3) c=-2cos(ωT) =-1.9646
    = cos(ωT) = 0.9823

    Its at this point im stuck on what I need to do and how to see which one of b and c is the correct plot?

    Thanks for any tips!
     
    Last edited: May 10, 2015
  2. jcsd
  3. May 10, 2015 #2

    Hesch

    User Avatar
    Gold Member

    In (b) you can count the samples per periode ( about 33.2 samples ). As one period is 360°, (b) matches a polepair = 1 / ±10.84°.

    Now solve the roots in denominator in 2) and 3). See if there is a match.
     
  4. May 24, 2015 #3
    Sorry for the late response, my revision swapped to a different module. That's great thank you managed to solve it for the correct answer using that
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted