1. digantashikerkar

    Thread Starter New Member

    Oct 25, 2013
    Hi i am going through a book called Signals & Systems by Oppenheim and willsky.I have a doubt regarding complex exponential signal e^jωot.
    The difference between continuous time and discrete time exponential signal is mentioned to be that the continuous time signals for each value of ωo are unique whereas they repeat with an interval of 2∏ for discrete time.
    Considering above discursion if we plot exponential signal using eulers theorem if if we plot cos(∏/2) and cos(5∏/2) they should be unique but they appear to be same....how is it?
    Please solve this doubt of mine...
  2. #12


    Nov 30, 2010
    Sine waves repeat every 2Pi radians. Any multiple of 2Pi radians will give the same output from a continuous wave.
  3. digantashikerkar

    Thread Starter New Member

    Oct 25, 2013
    I think u havent got my doubt clearly.....please go thru the book if possibl....
  4. WBahn


    Mar 31, 2012
    You want someone here to go track down a book that you have and then go through it trying to figure out what it is that you don't understand?


    Let me polish off my crystal ball and see if my mind-reading skill might be peaking tonight.

    The key thing that you are missing is that the signals are either unique or repeat. Not just one specific sample, but the entire signal (i.e., ALL samples) repeats.

    One thing that can make playing with this difficult is that, on a computer, you have no choice but to work with discrete-time signals since there is no way to work with a continuous-time signal. The key is to use a sampling rate way higher than any other signal you are playing with.

    So do the following:

    Generate the following sequences at 1ms intervals over a period of 1s:

    1) A signal at ω = 20∏ rad/s.

    2) A signal at ω = 220∏ rad/s

    Plot the two sequences on the same axis.

    Now sample those same two signals at 10ms intervals and plot the two sequences on the same axis.

    What do you notice?

    Now see if you can explain why you are seeing what you are seeing mathematically.

    Generate a sequence of samples taken at 1ms intervals.