Extra Problems

A few students have asked me for more practice problems. I will try to post a few more problems than what has been considered in the homework. This will be a great way to practice for the upcoming midterm. I will not promise to provide written or typed solutions to these problems. However, I will be happy to go through your solutions to the problems if you bring them to my office.

The advantage of using a wiki is that students can share or contribute some problems they tried either from a book or found elsewhere that they think will be useful to the whole class. It is in fact a great exercise to try to come up with your own problem. I hope at least a few students would take the initiative to contribute one or two problems.

  • Problem1: (From Proakis 4e): Problem 5.24 - This is simple problem and illustrates all the concepts that we dealt so far…
  • Problem 2: (Multiplicative White Gaussian Noise -MWGN): Consider a MWGN channel which is used to transmit two equally like signals s(t) = {K1,K2}. Derive the structure for optimum receiver? (I am not sure of this problem, just trying something different)
  • Problem 3: Consider the signal $s(t) = sin(8 \pi t)/8 \pi t$. Find a frequency $f_0$ such that the I and Q components of the baseband signal with respect to $f_0$ are such that the I component is the Hilbert transform of the Q component
  • Problem 4: Pulse width modulation: Consider three signals given by
\begin{align} s_1(t) = 1, \ \ \, 0 \leq t < T \end{align}
\begin{align} s_2(t) = 1, \ \ \, 0 \leq t < 2T \end{align}
\begin{align} s_3(t) = 1, \ \ \, 0 \leq t < 3T \end{align}

Find the signal space and a vector representation for these signals. Compute a union bound on the probability of error when these signals are transmitted through an AWGN channel with PSD $N_0/2$

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