(New page: Category:ECE301Spring2011Boutin Category:problem solving = Compute the energy <math class="inline">E_\infty</math> and the power <math class="inline">P_\infty</math> of the follo...)
 
Line 10: Line 10:
 
----
 
----
 
===Answer 1===
 
===Answer 1===
write it here.
+
<math>
 +
\begin{align}
 +
E_{\infty}&=\lim_{T\rightarrow \infty}\int_{-T}^T |j|^2 dx
 +
&= \lim_{T\rightarrow \infty}\int_{-T}^T {(\sqrt{jj*})}^2 dx
 +
&= \lim_{T\rightarrow \infty}\int_{-T}^T {(\sqrt{-j^2})}^2 dx
 +
& = \lim_{T\rightarrow \infty}\int_{-T}^T 1 dx
 +
&= \lim_{T\rightarrow \infty} t \Big| ^T _{-T}
 +
&=\infty.  
 +
\end{align}
 +
</math>
 +
 
 +
So <math class="inline">E_{\infty} = \infty</math>.
 +
 
 +
<math>
 +
\begin{align}
 +
P_{\infty}&=\lim_{T\rightarrow \infty} {1 \over {2T}} \int_{-T}^T |j|^2 dx
 +
&= \lim_{T\rightarrow \infty} {1 \over {2T}} \int_{-T}^T 1 dx
 +
& = \lim_{T\rightarrow \infty} {1 \over {2T}} t \Big| ^T _{-T}
 +
& = \lim_{T\rightarrow \infty} {1 \over {2T}} T - {1 \over {2T}}
 +
& = \lim_{T\rightarrow \infty} {1 \over {2}} + {1 \over {2}}
 +
&= 1
 +
\end{align}
 +
</math>
 +
 
 +
So <math class="inline">P_{\infty} = 1 </math>.
 +
 
 +
--[[User:Rgieseck|Rgieseck]] 21:35, 12 January 2011 [[Category:ECE301Spring2011Boutin]]
 
===Answer 2===
 
===Answer 2===
 
write it here.
 
write it here.

Revision as of 18:34, 12 January 2011

Compute the energy $ E_\infty $ and the power $ P_\infty $ of the following discrete-time signal

$ x[n]= j  $

What properties of the complex magnitude can you use to check your answer?


Share your answers below

You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!


Answer 1

$ \begin{align} E_{\infty}&=\lim_{T\rightarrow \infty}\int_{-T}^T |j|^2 dx &= \lim_{T\rightarrow \infty}\int_{-T}^T {(\sqrt{jj*})}^2 dx &= \lim_{T\rightarrow \infty}\int_{-T}^T {(\sqrt{-j^2})}^2 dx & = \lim_{T\rightarrow \infty}\int_{-T}^T 1 dx &= \lim_{T\rightarrow \infty} t \Big| ^T _{-T} &=\infty. \end{align} $

So $ E_{\infty} = \infty $.

$ \begin{align} P_{\infty}&=\lim_{T\rightarrow \infty} {1 \over {2T}} \int_{-T}^T |j|^2 dx &= \lim_{T\rightarrow \infty} {1 \over {2T}} \int_{-T}^T 1 dx & = \lim_{T\rightarrow \infty} {1 \over {2T}} t \Big| ^T _{-T} & = \lim_{T\rightarrow \infty} {1 \over {2T}} T - {1 \over {2T}} & = \lim_{T\rightarrow \infty} {1 \over {2}} + {1 \over {2}} &= 1 \end{align} $

So $ P_{\infty} = 1 $.

--Rgieseck 21:35, 12 January 2011

Answer 2

write it here.

Answer 3

write it here.


Back to ECE301 Spring 2011 Prof. Boutin

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood