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
