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=Discussion for [[HW4_ECE301_Spring2011_Prof_Boutin|HW4], [[ECE301]], Spring 2011, Prof. [[user:mboutin|Boutin]]=
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=Discussion for [[HW4_ECE301_Spring2011_Prof_Boutin|HW4]], [[ECE301]], Spring 2011, Prof. [[user:mboutin|Boutin]]=
 
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Write your questions/comments here.
 
Write your questions/comments here.
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Question 1 i's) I am a little shaky as to the mathematical procedure for proving an LTI system is memoryless using its impulse response. The notes say <math class="inline"> h(t) = k\delta(t), k \in {\mathbb C}</math>, but I am not sure how to use this...
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:Just check if h(t) has the correct form. Say, for example if h(t)=<math>\delta(t+7)</math>, then it does not have the right form, so the system is not memoryless. -pm
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Question 2 h)  No matter how I think about this signal, I think that it's always 1, and therefore not periodic, so it doesn't have fourier coefficients. What am I doing wrong?
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:Nothing! There was a typo in the question. It has been corrected now. -pm
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Question 6) Should there be j's in parts c,d,e? Because if not, they're not periodic...
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:You are absolutely right. This has been corrected. -pm
 
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[[HW4_ECE301_Spring2011_Prof_Boutin|Back to HW4]],
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Question from an email sent by a student:
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:My friend and I were having a disagreement last night about one of the homework problems and we're hoping you can resolve this. For 2g the function is already in its Fourier series. So to find the a_k values you need to manipulate the exponential terms. I changed all the e's to e^(k*2pi/N*n)and tried to find a k such that it would equal the given e. For example e^(j4/7*pi*n) = e^(j*k*2pi/N*n), N was found to equal 35 therefore k must equal 10. When doing this for the other term k = 7. My friend however disagrees, she says that pi/35 is the LCD related between the two terms and thus k should be 20 and 14. Who is right?
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Instructor's reply:
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:I am going to show you how to sort it out by yourself: <br> Ask yourself what is the period N of the signal, according to your argument. Then check whether the signal is truly period with that period. To do this, a) make sure it is an integer, b) check that x[n+N]=x[n] for all n. <br> Then repeat with your friends argument.  <br> What do you find?-pm
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[[HW4_ECE301_Spring2011_Prof_Boutin|Back to HW4]]
  
 
[[2011 Spring ECE 301 Boutin|Back to 2011 Spring ECE 301 Boutin]]
 
[[2011 Spring ECE 301 Boutin|Back to 2011 Spring ECE 301 Boutin]]

Latest revision as of 04:50, 14 February 2011


Discussion for HW4, ECE301, Spring 2011, Prof. Boutin


Write your questions/comments here.

Question 1 i's) I am a little shaky as to the mathematical procedure for proving an LTI system is memoryless using its impulse response. The notes say $ h(t) = k\delta(t), k \in {\mathbb C} $, but I am not sure how to use this...

Just check if h(t) has the correct form. Say, for example if h(t)=$ \delta(t+7) $, then it does not have the right form, so the system is not memoryless. -pm

Question 2 h) No matter how I think about this signal, I think that it's always 1, and therefore not periodic, so it doesn't have fourier coefficients. What am I doing wrong?

Nothing! There was a typo in the question. It has been corrected now. -pm

Question 6) Should there be j's in parts c,d,e? Because if not, they're not periodic...

You are absolutely right. This has been corrected. -pm

Question from an email sent by a student:

My friend and I were having a disagreement last night about one of the homework problems and we're hoping you can resolve this. For 2g the function is already in its Fourier series. So to find the a_k values you need to manipulate the exponential terms. I changed all the e's to e^(k*2pi/N*n)and tried to find a k such that it would equal the given e. For example e^(j4/7*pi*n) = e^(j*k*2pi/N*n), N was found to equal 35 therefore k must equal 10. When doing this for the other term k = 7. My friend however disagrees, she says that pi/35 is the LCD related between the two terms and thus k should be 20 and 14. Who is right?

Instructor's reply:

I am going to show you how to sort it out by yourself:
Ask yourself what is the period N of the signal, according to your argument. Then check whether the signal is truly period with that period. To do this, a) make sure it is an integer, b) check that x[n+N]=x[n] for all n.
Then repeat with your friends argument.
What do you find?-pm

Back to HW4

Back to 2011 Spring ECE 301 Boutin

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