period of signal

[bhuvaneshnick]

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

 

[Jugurtha]

Hello,

What are the questions you would ask yourself for which the answers would lead to the answer you're looking for?

First, we must define a good core question.

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

Becomes:

- I can find the period of sin(5t) and cos(7t), but not of x(t) = sin(5t) - 4cos(7t).
- sin(5t) and cos(7t) are periodic functions:
- Q: What's the definition of a periodic function? .. Then find that out (hint: f(x) = f(x + ?)) and write that down..

Then write things like:
f(x) = f(x + ?)
g(x) = g(x + ??)

Then let h(x) = (f+g)(x)

And find out the conditions that make h(x) periodic.

x(t) = sin(5t) - 4cos(7t).. In other words, as you said in your post, x(t) is a sum of two periodic functions. This should suggest an excellent questions to search for on Google that look like "Is the sum of two periodic functions periodic?" or "Periodicity of the sum of two periodic functions" or "Sum of two periodic functions".

 

[atferrari]

The sum of two sinusoidal functions results in another sinusoidal one. Always.

 

[Jugurtha]

The sum of two sinusoidal functions results in another sinusoidal one. Always.

Assuming that by sinusoidal you meant periodic (which a sinusoid function is), I don't think you can state that the sum of two periodic functions is always periodic. (As long as we agree that "always" means "for any given/in all cases/with no exceptions").

 

[atferrari]

Hola Jugu

I should have said "as long as they are harmonics". Sorry.

 

[MrAl]

Hello there,

I think he wants to restrict the class of functions to those with integer frequency relationships, such as:
sin(w*t)+sin(3*w*t)+sin(8*w*t)+...+etc., ie sums that include terms like sin(n*w*t), n an integer, and not any that are like sin(x*w*t), where x is any number like pi, sqrt(2), etc.

In the case of integer frequency relationships i think the periodicity is as the inverse of lowest frequency, in this case the lowest is f=w/(2*pi) so it would be Tp=1/f.

If we dont restrict ourselves to the integer cases then we have a monumental task on our hands.

 

[Tony Stewart]

how can find period of x(t)?

This relates to the zero crossing of the signal which changes with the amplitude and frequency of each sin function.

One way is to get zero crossing, you differentiate the result then find the peaks.
If you differentiate again you find the peaks by the point where the result changes polarity.

In practice this is not a linear modulation of the phase but more like the envelope which is a full wave rectified envelope of the difference frequency.

 

[MrAl]

Hi,

I dont think it is that simple unless the signals are already related in some way.
For example, what if the zero crossing is spaced A units apart and then later B units apart.

So i think we have to restrict our functions to integer multiples of some base frequency, or at least multiples that can be made integer multiples by finding a common denominator for all the multipliers.
For example, sin(t)+sin(3.5*t), if we transform this to sin(2*t)+sin(7*t) we can find the period too.

 

[bhuvaneshnick]

i am clear with other concept integral multiples way

but i have no idea of below line.could you bit more detail?

This relates to the zero crossing of the signal which changes with the amplitude and frequency of each sin function.

 

[JimB]

Just draw it out on paper, or on the VDU, like this:

I used Microsoft Excel.
The X axis is t
The red trace is Sin(t)
The greeny blue trace is Sin(5t) - 4.Cos(7t)

Have a look, count the peaks and troughs, find the period.

JimB

 

[bhuvaneshnick]

red period -400 and period also 400,sum of them period is also 400