period of signal

Discussion in 'Homework Help' started by bhuvanesh, Feb 26, 2015.

  1. bhuvanesh

    Thread Starter Member

    Aug 10, 2013
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    i am reading signals and system by oppenheim.There they shown way to found how to find period of a signal,but did not show to find the period of signal when it is in sum like x(t)= sin5t-4cos7t .Here i can find period of individual signal(i mean sin5t and cos7t) but with that how can find period of x(t).Thank you
     
  2. WBahn

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    Mar 31, 2012
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    In general, you can't. In this specific case you can. Are you familiar with least common multiples?
     
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  3. bhuvanesh

    Thread Starter Member

    Aug 10, 2013
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    yes i am familiar with that,among common multiples of two or three number we have pick up least common multiple that lcm.

    why is that so
     
  4. WBahn

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    Mar 31, 2012
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    So what is the LCM of the period of sin(5t) and cos(7t)?

    What is the least common multiple of √2 and √3?
     
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  5. bhuvanesh

    Thread Starter Member

    Aug 10, 2013
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    T1=2pi/5 and T2=2pi/7 and lcm of (5,7) is 1 .But here i have irrational number like 2pi/5 and 2pi/7 .so how can i perform lcm among this numbers?

    That cannot be period of signal since for the signal to be period it should rational multiple of 2pi. Your values are irrational
     
  6. WBahn

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    Mar 31, 2012
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    Think of the name - Least Common MULTIPLE.

    The least common multiple of 5 and 7 is 35.

    Where do you get that a signal period has to be a rational multiple of 2pi? The value pi itself is irrational!

    Are you saying that you can't take a square piece of paper and draw a sine wave along the diagonal such that there is one period from one corner to the other?
     
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  7. bhuvanesh

    Thread Starter Member

    Aug 10, 2013
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    sorry ,was little messed up
    5:--5,15,20,25,30,35,40
    7:--7,14,21,27,35,42
    so lcm is ,yes 35

    i need some clarification in below but later i come to that before does the least common multiple a fundamental period
     
  8. WBahn

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    I have no idea what you are trying say or ask. Please try again.
     
  9. bhuvanesh

    Thread Starter Member

    Aug 10, 2013
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    now x(t)= sin(5t)+cos(7t)
    period of x(t)?
    period of sin=2pi/5 and period of cos=2pi/7 and lcm of (5,7) is 35. does 2pi/35 a fundamental period of x(t)?
     
  10. WBahn

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    Mar 31, 2012
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    Yes, though I'm not sure you fully understand it. What would your answer have been had the problem been

    x(t) = sin(4t/7) + cos(3t/5)
     
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  11. bhuvanesh

    Thread Starter Member

    Aug 10, 2013
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    70/6 pi
     
  12. WBahn

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    70/6 pi is, at best, just a number. I can't tell if it is a period or a frequency. Please provide units.
     
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  13. bhuvanesh

    Thread Starter Member

    Aug 10, 2013
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    Its a period
     
  14. bhuvanesh

    Thread Starter Member

    Aug 10, 2013
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    Yet I don't understand clearly

    x(t) = sin(4t/7) + cos(3t/5)

    Here period is( 7/2)pi and (10/3)pi
    If there is integer I can say LCM of them but here it is fraction .any simple way to find LCM of such fractions
     
  15. WBahn

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    Mar 31, 2012
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    What's the LCM of 1/2 and 3/8?

    Hint, what is (1/2)x3? What is (3/8)*4?

    The LCM of two values x and y, is simply the smallest value of z such that

    z = (k1)x = (k2)y

    where k1 and k2 are integers.

    (k1/k2) = (y/x)

    Since k1 and k2 are integers, this requires that (y/x) be rational. But as long as (y/x) is rational, then there DOES exist a pair of values k1 and k2 for which the required relationship holds true.

    Note that this does NOT require that either y or x be rational, merely that their ratio be rational. They can both be irrational as long as the irrational part cancels out in the ratio.
     
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