Assignment 2 -- Signals & Spectra

March 17, 2004

Review and study:

Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7

Construction should be completed by Wednesday, April 7th:

Save all your work on your own work disk!

Task 5: Sampling an analog signal.

As discussed in lecture, I would like you to build a SIMULINK configuration in which a specified analog signal is sampled as the first step in a communication process.
  1. Using as input a "clock" module taken from the SIMULINK 'Sources" library, generate an arbitrary, but interesting analog temporal function by entering "cos(u)*sin(u/2)*cos(u/4)*sin(u/8)" into a "MATLAB function" module from the SIMULINK "User-Defined Functions " library.  Under "Parameters" in the "Simulation" menu choose, as a start, "Type" = Fixed-step, "Fixed step size" = 0.1, and "Stop time" = 500.  Execute the simulation and examine the generated function with a "Scope" module from the SIMULINK "Sinks" library and a "Average Power Spectral Density" module from the SIMULINK Extras "Sink" library. (Suggested configuration) 

  2. Sample this analog signal by multiplying it (use the "product" module from the SIMULINK "Nonlinear" library) with the output of a "Pulse Generator" module from the SIMULINK "Sources" library.  Choose the "Duty Cycle" of the pulse to be, say, 10%.  By choosing various values of the pulse "Period", examine the sampled output and spectrum as a function of the period.

  3. A pulse generator period of one second works pretty well - check it out.  Remember, according to  the Nyquist or sampling theorem the sampling rate must be equal or greater than twice the bandwidth of the analog signal.  Does a one second period satisfy this condition.
      
  4. When you think you are doing a good job of sampling, save your signal sampling configuration as a ".mdl" file.

Task 6: Filtering a sampled analog signal

As was discussed in lecture, we find that we can "smooth-out" a sampled signal by passing it through a low-pass frequency filter -- i.e., a device which removes high frequency components from a signal.   To demonstrate this key signal processing notion:
  1. Examine the following suggested SIMULINK configuration.
    2.  
  2. As in Task 5, use analog temporal function  "cos(u)*sin(u/2)*cos(u/4)*sin(u/8)".

  3. After "appropriately filtering" the sampled analog signal - i.e.by choosing a suitable low pass filter compare it with the original analog signal.  Note that the filtered signal is time delayed with respect to the original signal.  A signal gain of 10 has been inserted after the low-pass filter to restore signal strength lost in the sampling and filtering processes.

  4. To implement the Butterworth low-pass filter see the discussion in Filter Resources

Task 7: Model of a DSB-AM Communication Link.

In lecture, we have discussed amplitude modulation in some detail and in Assignment 1 you were asked to build a DSB-AM modulator.  In this assignment I would like you to build and study a model of a complete DSB-AM communication link.  The linked sketch is annotated with a set of reasonably good starting simulation parameters, but you may be able to enhance system performance by varying a parameter or two.  If no parameter is specified, use the library default value.
  1. To implement the Butterworth low-pass filter see the discussion in Filter Resources.
  2.  Follow the temporal and spectral evolution of the signals through each phase of the communication process and make sure that you understand each phase.

  3. Note how the DSB-AM spectrum varies with the amplitude of the modulating signal.
    4.  
  4. Also note once again the critical role that multiplication (i.e., a nonlinear operation) plays in the modulation (encoding) and demodulation (decoding) processes.

  5. When you think you are doing a good job of AM communicating, save your configuration as a ".mdl" file.

Task 8: Model of a FM Communication Link

In lecture, we also have discussed frequency modulation in some detail and in Assignment 1 you were asked to build a FM modulator.  In this assignment I would like you make use of this modulator as starting point to build and study a model of a complete FM communication link.  The linked sketch is annotated with a set of reasonably good starting simulation parameters, but you may be able to enhance system performance by varying a parameter or two.  If no parameter is specified, use the library default value.

Of course, the communication starts with the modulation process.  The modulated signal is then transmited though a medium with loss and signal delay.  After reception the signal is injected into a model FM discriminator configured from two back-to-back band-pass filters. (see an illustration of a FM discriminator from FM Generation Demo).  The discriminator converts the FM signal to a SSB-AM signal -  observe signal displayed by Post discrimination power spectral density.  Finally, the initial input is recoved with SSB-AM heterodyne detector.
  1. To implement the various filters see the discussion in Filter Resources.
  2.  Follow the temporal and spectral evolution of the signals through each phase of the communication process and make sure that you understand each phase.

  3. Observe the he temporal and spectral signal throughout the system a function of the The “FM spectral density” as a function of the moduation index beta (e.g., for beta = 0.1, 0.5, 1.0, 1.5, 3.0, 5.0 and 10.0).

  4. When you think you are doing a good job of FM communicating, save your configuration as a ".mdl" file.



This page was prepared and is maintained by R. Victor Jones
Comments to: jones@deas.harvard.edu.

Last updated March 20, 2004