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!

Nyquist Sampling Theorem - I just need help understand this.

  1. Mar 17, 2012 #1
    Hello! I am having a difficult time understanding the "Nyquist Sampling Theorem." I was wondering if someone can help me understand this. Below is an example out of my book:

    Q: Suppose that an analog signal is given as
    x(t) = 5cos(2*pi*1000t), for t > 0
    and is sampled at the rate of 8000 HZ

    a.) Sketch the spectrum for the original signal.

    A:
    They do the Euler Identity:
    5cos(2*pi*1000t = (ej*2*pi*1000*t + e-j*2*pi*1000*t) / 2
    5cos(2*pi*1000t)= 2.5*ej*2*pi*1000*t + 2.5*e-j*2*pi*1000*t

    The coefficient is c1 = 2.5 and c2 = 2.5 and they get the following graph:
    graph.jpg
    --------------------------------------------

    According to whats in my book and my course shell, I am trying to do the example problem like it is in my course shell which is something like this:
    I know fs > 2* fmax


    x(t) = 5cos(2*pi*1000t)
    fs = (1 / Ts)

    x(nT) = 5cos((2*pi*1000*n) /fs)
    x(nT) = 5cos((2000*pi*n)/8000)
    x(nT) = 5cos((1/4)*pi*n) <-- This is where I get stuck.

    I don't recall the Euler Method and I don't understand how they get -1 and 1, and it shows 2.5.

    Am I doing this wrong and Eulor Identity is the only way to do this? Or is my procedure right the way I am doing it? Again if its correct, this is where I get stuck at.

    I have homework problems that covers similar materials like this and if someone can help me understand this, that would great.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Nyquist Sampling Theorem - I just need help understand this.
  1. I need help (Replies: 0)

  2. Nyquist Sampling (Replies: 0)

Loading...