power and energy of discrete signal

[PG1995]

Thank you very much.

Only a constant offset will give an average that is useful information. When you do the integral, you need something that goes up as something proportional to T, so that when you divide by T you get a finite number. Anything that integrates out slower than T (for example sqrt(T)) will give an average of zero. Anything that integrates out faster than T (for example, T^2 or T^(1.1) etc) will have an average of infinity.

I found the above part very useful.

There is also something weird about this definition. Consider the two functions; y=x and y=x+1. The function y=x has an average value of zero, but the function y=x+1 has a average of infinity. Based on what I said above, this doesn't make sense because the second function has a constant offset of 1. But, you can also view this function as being shifted in "x" instead. So why not do the average with limits of -T/2-1 to T/2-1 and then take the limit. Then you will get zero for an answer instead of infinity. So, practically speaking, there needs to be some additional constraints placed on the function you are averaging. Also, consider that in over 30 years of doing math, science and engineering, I've never used this definition of an average. The other definitions are more practical, in my opinion.

Just wanted to be sure about this, which definition are you referring to? Are you referring to the **broken link removed**? Please let me know. Thank you.

Regards
PG

PS: **broken link removed** is for my own personal reference.

 

[steveB]

Just wanted to be sure about this, which definition are you referring to? Are you referring to the **broken link removed**? Please let me know. Thank you.

Yes, that's the one. Basically averaging with the limiting form out to infinity is not often needed. That definition is perfectly fine for periodic signals, but it's more complicated than just averaging over the period.

 

[PG1995]

Yes, that's the one. Basically averaging with the limiting form out to infinity is not often needed. That definition is perfectly fine for periodic signals, but it's more complicated than just averaging over the period.

Thank you for letting me know this. The basic difference between the formula #1 given in the book and formula #3 is that the latter doesn't use square of a function. I haven't analyzed the formula #1 but was wondering if it would overcome the problems found with formula #3. If possible, please let me know. Thank you.



Regards
PG

 

[steveB]

I see those two definitions as very similar. They are both averages. One is an average of the signal, and the other is the average of the signal power. Basically, you are averaging a function in either case. The main difference is that when you average the power, you will always have positive values to deal with. This can avoid the issue I raise with the two functions; y=x and y=x+1.

So, there are differences of course, but the concept of an average is used in both cases. As I mentioned, I personaly haven't found either of these formulas useful in my life, so perhaps someone else who has found them useful might have more to say about this question.

 

[PG1995]

I see those two definitions as very similar. They are both averages. One is an average of the signal, and the other is the average of the signal power. Basically, you are averaging a function in either case. The main difference is that when you average the power, you will always have positive values to deal with. This can avoid the issue I raise with the two functions; y=x and y=x+1.

So, there are differences of course, but the concept of an average is used in both cases. As I mentioned, I personaly haven't found either of these formulas useful in my life, so perhaps someone else who has found them useful might have more to say about this question.

I think you wanted to say average of the signal energy. Would you please confirm this? Thank you.

Regards
PG

 

[steveB]

I think you wanted to say average of the signal energy. Would you please confirm this? Thank you.

Regards
PG

No. Signal energy is the integral of instantaneous power and instantaneous power is x^2.

The definitions we are talking about are average power formulas, which formulated as the integral of signal power (which is signal energy) divided by a time interval for the integral.

 

[PG1995]

No. Signal energy is the integral of instantaneous power and instantaneous power is x^2.

The definitions we are talking about are average power formulas, which formulated as the integral of signal power (which is signal energy) divided by a time interval for the integral.

Hi

I understand your point. But isn't the **broken link removed** (please ignore the queries etc. there)? So far I have found this book a bit out of regular line of thinking. Thanks.

 

[steveB]

Hi

I understand your point. But isn't the **broken link removed** (please ignore the queries etc. there)? So far I have found this book a bit out of regular line of thinking. Thanks.

No, the book isn't saying something else as far as I can tell.

I don't think the book is out of line of usual thinking, but the presentation of the average as a limiting form is more obscure and not seen as often as the other definitions, based on my experience.

 

[MrAl]

Hi

I understand your point. But isn't the **broken link removed** (please ignore the queries etc. there)? So far I have found this book a bit out of regular line of thinking. Thanks.

Hi,

What exactly are you having difficulty with? There are a couple formulas, why cant you just use them, what is wrong with that?

 

[PG1995]

Hi

I'm sorry for all this frustration. **broken link removed**, I have tried to tell what was really confusing me. It's okay even if you skip this post. Thank you for the understanding.

Regards
PG

 

[steveB]

In your highlighted green section, the first paragraph is correct. In the second paragraph you are questioning my wording, but I think my wording is correct. The thing you are averaging with equation 2.17, is whatever is inside the integral. You are adding up (integrating) all the signal powers and then dividing by the number of things you added up, which is the time interval T. The integral itself represents an energy, but the thing inside the integral is the power. I hope this is clear.

The remainder of your comments are about the quantities being positive in value. Obviously anything that is squared is positive. So, signal power is positive and the signal energy is positive. I think you are reading too much into simple comments, but perhaps it is also my fault for making extra comments about obvious things like this. Perhaps I make it sound like there is more to it than there is, but I was just making a simple observation. I hope this helps clarify.

 

[PG1995]

Thank you.

I think you are reading too much into simple comments, but perhaps it is also my fault for making extra comments about obvious things like this. Perhaps I make it sound like there is more to it than there is, but I was just making a simple observation. I hope this helps clarify.

Yes, you are right in that I was reading too much into simple comments and that's the reason in the previous post I said "I'm splitting hairs". But I always strive to learn more and more from whatever you say. Probably, you don't notice that I occasionally update past posts with my own commentary on what you or someone else say; for instance I updated two posts in this thread yesterday. And as far as I can tell you never make it sound like there is more to anything and that's the thing I like about you. You stick to the point and first try to clarify whatever is boggling me. No flattery intended!

Best wishes
PG