Period and Aliasing Problems

Discussion in 'Homework Help' started by josh007, Jul 4, 2016.

  1. josh007

    Thread Starter Member

    Sep 20, 2015
    40
    1
    Good day All,

    I need your valued precious advice and help once again, in correcting my tutorial homework examples.

    Please can you check my work if I am correct or advice where I am going wrong.

    gracias

    Q1)

    If the signal x(t)=4cos(200πt) is sampled at 500 Hz, determine the signal x(n).

    What is the period of the sampled signal?

    MY ANSWER:

    x(t)=4cos((200/500)πt)

    so my signal x(n) = 4cos((2/5)πt)


    P = 2π/w


    Where w is the angular velocity = 2π/5


    P = 2π/(2π/5) = 5 units


    So Period is 5 units



    Q2)

    Determine the minimum sampling rate to avoid aliasing for the signal x(t)=20cos(400πt)+10cos(20πt).

    MY ANSWER:

    I will take the highest frequency to avoid aliasing.


    So P = 2π/w = 2π/400π = 1/200


    Therefore f= 1/T = 1/(1/200) = 200hz


    To avoid aliasing fx2 = 400hz
     
  2. WBahn

    Moderator

    Mar 31, 2012
    17,757
    4,800
    Looks good, except that sampling rates should not be given in Hz (though they often are), since 1 Hz is one cycle per second. Instead, the units should be Sa/s (samples per second).
     
    josh007 likes this.
  3. josh007

    Thread Starter Member

    Sep 20, 2015
    40
    1
    Fantastic, much appreciation WBahn, I will take note of this. You are correct I read in my text book about the Sa/s but completely forgot about it.

    Gracias
     
  4. crutschow

    Expert

    Mar 14, 2008
    13,022
    3,236
    upload_2016-7-4_1-43-59.png
    upload_2016-7-4_1-45-41.png

    So I think it's okay to refer to a sample rate as a sample frequency in Hertz. :)
     
  5. DickCappels

    Moderator

    Aug 21, 2008
    2,656
    632
    Alternative definitions are in common use. e.g.: What is the spatial frequency of this bar pattern?
    |||||||||||||||||||||||||||||||||||||
     
  6. WBahn

    Moderator

    Mar 31, 2012
    17,757
    4,800
    I'd use either bars/inch (or other spatial dimension) or bars/pixel.
     
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