Reply to thread

Message

<blockquote data-quote="Water Bear" data-source="post: 8603638" data-attributes="member: 673826">I did some research to settle this question.<a href="http://www.ece.iit.edu/~biitcomm/research/references/Other/Tutorials%20in%20Communications%20Engineering/TUTORIAL%201%20-%20Basic%20concepts%20in%20signal%20processing.pdf" target="_blank">Energy and power of a signal.</a>If T is allowed to be any unit of time, the powers may differ.&nbsp; The power integral works out to be:1/2 - sin(2kT)/4kT.If T is very large, then the power of two different sine waves approaches the same value.&nbsp; If time has units of seconds, then even after 1 second the power of a roughly 32 hertz sine wave minus the power of a roughly 60 hertz sine wave is not more than 1/40.&nbsp; Since both powers are close to 1/2, the powers are already pretty close even after a second.&nbsp; (In other words both waves have a power which is about 20 times larger than the difference between their powers).Note:&nbsp; Power here is in units of Watts, and as long as the amplitudes of the two waves are the same, the results of these calculations doesn&#039;t change *much*.&nbsp; I assumed the amplitude was 1 for simplicity.&nbsp; If the amplitude is A, then the power becomes A^2 times the above function:&nbsp; A^2 [ 1/2-sin(2kT)/4kT ].&nbsp; So the ratio of the difference of the waves&#039; powers to their actual power would still be 1/20 after 1 second.</blockquote>

[QUOTE="Water Bear, post: 8603638, member: 673826"] I did some research to settle this question. [URL="http://www.ece.iit.edu/~biitcomm/research/references/Other/Tutorials%20in%20Communications%20Engineering/TUTORIAL%201%20-%20Basic%20concepts%20in%20signal%20processing.pdf"]Energy and power of a signal.[/URL] If T is allowed to be any unit of time, the powers may differ. The power integral works out to be: 1/2 - sin(2kT)/4kT. If T is very large, then the power of two different sine waves approaches the same value. If time has units of seconds, then even after 1 second the power of a roughly 32 hertz sine wave minus the power of a roughly 60 hertz sine wave is not more than 1/40. Since both powers are close to 1/2, the powers are already pretty close even after a second. (In other words both waves have a power which is about 20 times larger than the difference between their powers). Note: Power here is in units of Watts, and as long as the amplitudes of the two waves are the same, the results of these calculations doesn't change *much*. I assumed the amplitude was 1 for simplicity. If the amplitude is A, then the power becomes A^2 times the above function: A^2 [ 1/2-sin(2kT)/4kT ]. So the ratio of the difference of the waves' powers to their actual power would still be 1/20 after 1 second. [I][/I] [/QUOTE]

Verification