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===Answer 1=== | ===Answer 1=== | ||
a) <math>|e^{2n}|=\sqrt{(e^{2n})^2}=e^{2n}</math> | a) <math>|e^{2n}|=\sqrt{(e^{2n})^2}=e^{2n}</math> | ||
| + | :<span style="color:green"> Instructor's comments: Yes, this is correct, but I would like to propose an alternative justification: </span> | ||
| + | :<math>{\color{green}|e^{2n}|=\sqrt{(e^{2n})(e^{2n})^*}=\sqrt{e^{2n}e^{2n}}=e^{2n}}</math> | ||
| + | :<span style="color:green">where <math>{\color{green}~^*}</math> denotes the complex conjgate.-pm </span> | ||
b) <math>|e^{2jn}|=|cos(2n)+jsin(2n)|=\sqrt{cos(2n)^2+sin(2n)^2}=\sqrt{1}=1</math> | b) <math>|e^{2jn}|=|cos(2n)+jsin(2n)|=\sqrt{cos(2n)^2+sin(2n)^2}=\sqrt{1}=1</math> | ||
Revision as of 14:14, 11 January 2011
Contents
Compute the Magnitude of the following discrete-time signals
a) $ x[n]=e^{2n} $
b) $ x[n]=e^{2jn} $
c) $ x[n]=j^n $
What properties of the complex magnitude can you use to check your answer?
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
a) $ |e^{2n}|=\sqrt{(e^{2n})^2}=e^{2n} $
- Instructor's comments: Yes, this is correct, but I would like to propose an alternative justification:
- $ {\color{green}|e^{2n}|=\sqrt{(e^{2n})(e^{2n})^*}=\sqrt{e^{2n}e^{2n}}=e^{2n}} $
- where $ {\color{green}~^*} $ denotes the complex conjgate.-pm
b) $ |e^{2jn}|=|cos(2n)+jsin(2n)|=\sqrt{cos(2n)^2+sin(2n)^2}=\sqrt{1}=1 $
c) $ |j^n|=|e^{nj\pi/2}|=|cos(n\pi/2)+jsin(n\pi/2)|=\sqrt{cos(n\pi/2)^2+sin(n\pi/2)^2}=\sqrt{1}=1 $
Answer 2
write it here.
Answer 3
write it here.
