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

 

In general, you can't. In this specific case you can. Are you familiar with least common multiples?

 

Are you familiar with least common multiples?

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

In general, you can't.

why is that so

 

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

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

why is that so

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

 

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

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?

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

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

 

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

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?

 

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

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?

 

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

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

 

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)?

 

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)?

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)

 

70/6 pi

 

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

 

Its a period

 

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

 

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

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.