# period of signal

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

1. ### bhuvanesh Thread Starter Member

Aug 10, 2013
268
2
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 Moderator

Mar 31, 2012
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5,755
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
268
2
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 Moderator

Mar 31, 2012
20,230
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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
268
2
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 Moderator

Mar 31, 2012
20,230
5,755
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
268
2
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 Moderator

Mar 31, 2012
20,230
5,755
I have no idea what you are trying say or ask. Please try again.

9. ### bhuvanesh Thread Starter Member

Aug 10, 2013
268
2
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 Moderator

Mar 31, 2012
20,230
5,755
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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Aug 10, 2013
268
2
70/6 pi

12. ### WBahn Moderator

Mar 31, 2012
20,230
5,755
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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Aug 10, 2013
268
2
Its a period

14. ### bhuvanesh Thread Starter Member

Aug 10, 2013
268
2
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 Moderator

Mar 31, 2012
20,230
5,755
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.