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Changed variable in limits from x to T
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Arty
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I have to find the power of the following signal and would like to know if I'm doing this right or, if I'm doing it wrong, how to do it.

The equation for power in my textbook is \$\overline{m^2(t)} = \lim_{x\to\infty} \frac{1}{T} \int_{\frac{-T}{2}}^{\frac{T}{2}} m^2(t) dt\$\$\overline{m^2(t)} = \lim_{T\to\infty} \frac{1}{T} \int_{\frac{-T}{2}}^{\frac{T}{2}} m^2(t) dt\$

This signal periodically has the equation \$m(t) = \frac{t}{\pi/4} \$

From the picture, \$T=\pi\$

Therefore, this can be simplified to: \$\overline{m^2(t)} = \lim_{x\to\infty} \frac{1}{\pi} \int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} (\frac{t}{\pi/4})^2 dt\$\$\overline{m^2(t)} = \lim_{T\to\infty} \frac{1}{\pi} \int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} (\frac{t}{\pi/4})^2 dt\$, right?

If the above is correct, then \$\overline{m^2(t)} = \frac{1}{6}\$

I believe this is correct, but only for the part of the signal that exists. Since half of the signal has no value or is zero, does this mean I have to divide the answer I just got by 2? So that \$\overline{m^2(t)} = \frac{1}{12}\$?

Find the power of this signal

I have to find the power of the following signal and would like to know if I'm doing this right or, if I'm doing it wrong, how to do it.

The equation for power in my textbook is \$\overline{m^2(t)} = \lim_{x\to\infty} \frac{1}{T} \int_{\frac{-T}{2}}^{\frac{T}{2}} m^2(t) dt\$

This signal periodically has the equation \$m(t) = \frac{t}{\pi/4} \$

From the picture, \$T=\pi\$

Therefore, this can be simplified to: \$\overline{m^2(t)} = \lim_{x\to\infty} \frac{1}{\pi} \int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} (\frac{t}{\pi/4})^2 dt\$, right?

If the above is correct, then \$\overline{m^2(t)} = \frac{1}{6}\$

I believe this is correct, but only for the part of the signal that exists. Since half of the signal has no value or is zero, does this mean I have to divide the answer I just got by 2? So that \$\overline{m^2(t)} = \frac{1}{12}\$?

Find the power of this signal

I have to find the power of the following signal and would like to know if I'm doing this right or, if I'm doing it wrong, how to do it.

The equation for power in my textbook is \$\overline{m^2(t)} = \lim_{T\to\infty} \frac{1}{T} \int_{\frac{-T}{2}}^{\frac{T}{2}} m^2(t) dt\$

This signal periodically has the equation \$m(t) = \frac{t}{\pi/4} \$

From the picture, \$T=\pi\$

Therefore, this can be simplified to: \$\overline{m^2(t)} = \lim_{T\to\infty} \frac{1}{\pi} \int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} (\frac{t}{\pi/4})^2 dt\$, right?

If the above is correct, then \$\overline{m^2(t)} = \frac{1}{6}\$

I believe this is correct, but only for the part of the signal that exists. Since half of the signal has no value or is zero, does this mean I have to divide the answer I just got by 2? So that \$\overline{m^2(t)} = \frac{1}{12}\$?

Find the power of this signal

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Arty
  • 43
  • 6

Calculating Power of a Non-Continuous Signal

I have to find the power of the following signal and would like to know if I'm doing this right or, if I'm doing it wrong, how to do it.

The equation for power in my textbook is \$\overline{m^2(t)} = \lim_{x\to\infty} \frac{1}{T} \int_{\frac{-T}{2}}^{\frac{T}{2}} m^2(t) dt\$

This signal periodically has the equation \$m(t) = \frac{t}{\pi/4} \$

From the picture, \$T=\pi\$

Therefore, this can be simplified to: \$\overline{m^2(t)} = \lim_{x\to\infty} \frac{1}{\pi} \int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} (\frac{t}{\pi/4})^2 dt\$, right?

If the above is correct, then \$\overline{m^2(t)} = \frac{1}{6}\$

I believe this is correct, but only for the part of the signal that exists. Since half of the signal has no value or is zero, does this mean I have to divide the answer I just got by 2? So that \$\overline{m^2(t)} = \frac{1}{12}\$?

Find the power of this signal