Frequency domain , Time domain relation.

[ameke3]

I need to go down through the basics of Frequency spectrum and its corresponding Time domain.

I need to know the answer for the following question :

Can I predict the maximum difference between any 2 adjacent values - in time domain signal X(t) -separated by sampling time Ts i.e. Maximum value of [X(t+Ts)-X(t)]. Given that I know only that the signal X(t) has frequency components limited to Fx. ?????

 

[verbatim]

Answer is no.... sounds like youre doing homework, so I cant tell you why.

 

[ameke3]

Answer is no.... sounds like youre doing homework, so I cant tell you why.

First of All , Thank you for reply to my post. But ,

Could you please Why you answered like that to my question ?!!!!

Do you really know I'm doing my homework ?????

Do you really have the reason or a little bit discussion about what you have just answered ????

 

[verbatim]

If you're seriously not doing University / homework, then Im curious as to why you need to know this. ( and why the answer of "no" is not sufficient) . Assuming it IS for university, then giving you a complete explanation to plagiarize into your work is not really going to help either of us. If you could explain what you already understand about the subject matter of the problem, then maybe I can help direct you to an understanding that will help.

 

[ameke3]

Look ,That's what I understood which totally encountered against your answer which is "no" :
frequency domain is really indicates how much the signal in time domain change in time so if it has rapid changes in small time so it has higher frequency components, that may illustrate an impulse has infinite bandwidth (theoretically), Depending on what I've just said, If I know the maximum frequency component at frequency (B Hz) so that may give me an indication of how rapidly it changes over time. and that why I say yes.All I need is mathematical help with an integration relation R = IFT(X(W))-IFT(X(W).exp(j*2*pi*Ts). If I Know the maximum value of R so I got the total solution.

Answering for your question : Why I need this if I'm really don't do my homework?
I need it for idea to use it in another application.You can make sure of that by : I will argue with you without deadline time; I think homework is set to a certain deadline isn't it ?

 

[weetabixharry]

Can I predict the maximum difference between any 2 adjacent values - in time domain signal X(t) -separated by sampling time Ts i.e. Maximum value of [X(t+Ts)-X(t)]. Given that I know only that the signal X(t) has frequency components limited to Fx. ?????

This is an interesting question.

I think the trick is to think about the magnitudes of the frequency terms. For example, let's assume Fx is 1Hz. For simplicity, let's assume that X(t) is just a 1Hz sine wave. You may think 1Hz must vary quite slowly... but what if we assume magnitude of the sine is 1000000000000000000000000000000000000000000000000000000000000?

Now, this 1Hz sine wave can cause very large differences between adjacent values. In other words, the maximum difference depends on both frequency and magnitude.

 

[ameke3]

This is an interesting question.

I think the trick is to think about the magnitudes of the frequency terms. For example, let's assume Fx is 1Hz. For simplicity, let's assume that X(t) is just a 1Hz sine wave. You may think 1Hz must vary quite slowly... but what if we assume magnitude of the sine is 1000000000000000000000000000000000000000000000000000000000000?

Now, this 1Hz sine wave can cause very large differences between adjacent values. In other words, the maximum difference depends on both frequency and magnitude.

You're totally right ,But if you read the above post , I need this idea in another application , means I will never use a sine wave of such amplitude.Let for example I know the maximum amplitude is up to A for simplicity 1

 

[weetabixharry]

You're totally right ,But if you read the above post , I need this idea in another application

If you need help with a specific application, you should describe your application. It is a total waste of everyone's time if you don't state your constraints clearly from the start.

If you have a 1Hz sine wave, its gradient is another 1Hz sine wave (shifted by 90 degrees in phase). The maximum value this gradient can take is 1. This gives you an upper limit on the size of the difference.

 

[verbatim]

The way you have originally presented the problem, then the answer is no, for the reason weetabixharry initially mentions above. If you now say signal is BOTH frequency AND amplitude limited, then the answer is yes. I can think of a situation where both Fx and Ts are really large, so that any [X(t+Ts)-X(t)] is the same as the amplitude limits of X(t), meaning its predictable.
If however, Fx < 1/2Ts , then biggest change between samples should be less than the AMplitude limits, and predictable. Maybe you should present your problem a little more clearly. I have assumed signal X(t) , and its frequency representation is an analog 'real' form (after all, its a real application) .
This is quite different to saying its a set of digital samples, with Fx < Nyquist.