FM Homework Assignment Questions
Introduction
Please feel free to use this page like a message board to ask any questions you like about the FM homework assignment.
Questions and Answers (Q&A)
Question 1: I have been trying for days, using the bilinear transform (matlab: bilinear) to convert the filters from continuous time domain to discrete time domain. For the butterworth filter, I even used the butterworth function provided by matlab (matlab: butter). Nothing worked, the frequency responses always showed a difference of about a factor of 10. I then stumbled across another discretisation method from the Control Systems Toolbox: c2d. For the first two filters, I simply used a bilinear tustin approximation ( Hn = c2d(Hn_a,ts,'tustin') ) and for the third filter, I used the bilinear tustin approximation with prewarping, as with higher frequencies, the prewarping effect is more visible ( H3=c2d(H3_a,ts,'prewarp',omega_c3) ) The approximation using a zero order hold also works, but the prewarp is more accurate. My question now: Is it mandatory that we use the bilinear() function, or is the above described method okay?
- Answer 1: <blah blah>
Question 2: Is the equation for the reference signal at the top of page 3 of the assignment? (v(t) = ...) I'm trying to integrate to get phi(t) but the integral of the message signal is always zero.
- >> syms t;
- >> sin_m_of_t = sin(2*pi*2000*t);
- >> int(sin_m_of_t, 0, 277775)
- ans = 0
so that implies that for the sinusoidal input v(t) = A + n_c(t) + j*n_s(t)? It is just a sine wave though, so I suppose it does make sense that its integral over a whole number multiples of 2*pi is zero. Also, is my upper limit on the integral correct? ( = delta * (number of samples - 1))
- Answer 2: <blah blah>
Question 3:
- Answer 3: <blah blah>
Question 4: The assignment seems a little ambiguous, as the specs just indicate that the maximum absolute value of the message signal must be less than 1.
- Answer 4: You are right. In fact, the random message signal should be normalised so that its maximum absolute value is always 1. Therefore please do this in your simulation.
Question 5: For the theoretical SNR I'm using the equation on slide 43 of section 5 (and factoring in for the non-ideal filter by dividing it by the scaling factor before converting it to dB). It just seems a bit strange to me that my simulated SNR goes up and down and that it is so far below the theoretical value (assuming my theoretical value is correct, that is). Looking a bit closer the amplitude of my s_o(t) is around 2 x 10^-3, whilst n_o(t) is about 0.15V and v_o is about 2.5 volts so the signal that is demodulated is healthy as far as I can see. What is strange is that the value of lambda changes a fair bit.
This is for increasing values of Pr_over_NoW.
- Answer 5:
Question 6: I'm having difficulty trying to set the seed of the Gaussian random number generator at the begginning of my simulation. I take it you need to declare a variable such that:
- >> seed = "some prime number";
...then go into the source block parameter for Random Number and change the inital seed parameter to "seed" and play around with seed values from your code as the assignment suggests (if you want to). But the problem I'm having is matlab won't let me change this parameter.. in fact I can't even change "mean" or "variance" not that I need but how can I gain access to change this?
