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

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang