Lecture Outline for Fall 2004

1. Wednesday 8/25

   • Sections 1.1, 1.2: Introduction to the course. Time-domain representation of continuous-time signals. Simple continuous-time signals: step, impulse, ramp and pulse. Using MATLAB to plot continuous-time signals.
     • MATLAB M-file for making a simple plot
     • MATLAB plot

2. Friday 8/27

   • Finish Secion 1.2.
   • Section 1.3: Time-domain representation of discrete-time signals. Simple discrete-time signals: step, impulse, ramp and pulse. Using MATLAB to plot discrete-time signals.
     • MATLAB M-file for plotting signals defined interval by interval
     • MATLAB plot
     • MATLAB M-file for plotting a discrete time signal
     • MATLAB plot

3. Monday 8/30

   • Section 1.4: Examples of simple continuous-time and discrete-time systems.

4. Wednesday 9/1

   • Section 1.5: Basic properties of systems: causality, linearity, time invariance, dimensionality.

5. Friday 9/3

   • Section 2.1: Solution of linear constant-coefficient differential equations
     • Method for time-domain solution of linear constant-coefficient differential equations

6. Wednesday 9/8

   • Section 2.1, 2.2: More on solution of linear constant-coefficient differential equations

7. Friday 9/10

   • Sections 2.3: Solution of linear constant-coefficient difference equations
     • A useful summation formula

8. Monday 9/13

   • Sections 2.3: Solution of linear constant-coefficient difference equations
     • Method for time-domain solution of linear constant-coefficient difference equations
   • Section 2.4: Discretization in time of differential equations

9. Wednesday 9/15

   • Finish Section 2.4: Discretization in time of differential equations
     • m-file for Problem 2.30
   • Section 2.4: Discretization in time of differential equations
   • Section 3.1: Convolution representation of linear time-invariant discrete-time systems

10. Friday 9/17

    • Sections 3.1, 3.2: Convolution of discrete-time signals
      • m-file for determining correct indices when doing a discrete-time convolution

11. Monday 9/20

    • Sections 3.1, 3.2: Convolution of discrete-time signals
      • How to find impulse response for differences equations
      • Properties of discrete-time convolution
      • Computation of system output from input and impulse response

12. Wednesday 9/22

    • Exam 1

13. Friday 9/24

    • Sections 3.1, 3.2: Convolution of discrete-time signals
      • How to find impulse response for second order discrete-time system with complex roots
    • Section 3.3: Convolution representation of continuous-time systems

14. Monday 9/27

    • Sections 3.3, 3.4: Convolution of continuous-time signals
      • How to find impulse response for first-order differential equations
      • Computation of convolution integral

15. Wednesday 9/29

    • Sections 3.4: Convolution of continuous-time signals
      • Properties of discrete-time convolution
      • Computation of system output from input and impulse response
      • Sections 3.5: Numerical convolution of continuous-time signals

16. Friday 10/1

    • Appendix A: A brief review of complex numbers
      • Polar representation of complex numbers
      • Addition of complex numbers
    • Sections 4.1, 4.2: Fourier series representation of periodic sequences

17. Monday 10/4

    • Sections 4.2: Fourier series representation of periodic sequences
      • How to find calculate Fourier coefficients
      • Time shift of a signal results in phase change of the Fourier coefficients
      • Parseval's Theorom
    • Section 4.3: Introduction to the Fourier transform
      • From the Fourier series to the Fourier transform

18. Wednesday 10/6

    • Sections 4.3: Fourier transform
      • Computation of Fourier transform and inverse Fourier transform

19. Friday 10/8

    • Section 4.4: Properties of the Fourier transform
    • Sections 4.5: The generalized Fourier transform
      • Fourier transfrom of impulse, cos(wt), sin(wt), 1
      • Fourier transfrom of real-valued function
      • Fourier transfrom of even and odd functions

20. Monday 10/11

    • Section 4.4: Properties of the Fourier transform

21. Wednesday 10/13

    • Section 5.1: Response to a sinusoidal input
      • Response of a low-pass filter to x(t) = 1 + cos(t) + cos(100 t)

22. Friday 10/15

    • Section 5.1: Response to a sinusoidal input

23. Monday 10/18

    • Section 5.2: Response to periodic inputs
      • Fourier series coefficients for a rectified sine wave

24. Wednesday 10/20

    • Section 5.4: Analysis of ideal filters

25. Monday 10/25

    • Review for Exam 2

26. Wednesday 10/27

    • Exam 2 covering Chapters 3 and 4

27. Friday 10/29

    • Section 5.4: Analysis if ideal filters
    • Section 5.5: Sampling

28. Monday 11/1

    • Section 5.5: Sampling
      • Aliasing -- two signals with different frequencies sampled at the same rate result in the same output
      • Fourier transforms of a exp(-t) u(t), and Fourier transform of the signal sampled at 1 Hz
      • Sampled signal from above after filtering with an ideal low-pass filter with a bandwidth of 5 rad/sec.

29. Wednesday 11/3

    • Section 6.1: Applications to communications: Analog modulation

30. Friday 11/5

    • Section 6.1: Analog modulation
    • Section 6.2: Demodulation of analog signals
    • Section 6.3: Simultaneous transmission of signals

31. Monday 11/8

    • Section 6.4: Digital modulation

32. Wednesday 11/10

    • Section 6.4: More on digital modulation

33. Fiday 11/12

    • Guest lecture on communications by Dr. El-Osery
      • Spread Spectrum
      • Multiple Access
      • Cellular Systems

34. Wednesday 11/17

    • Section 7.1: Discrete time Fourier transform
      • DTFT of (0.5)^n u[n]
      • DTFT of (0.5)^n u[n] plotted for frequencies from -pi to pi
      • DTFT of (-0.5)^n u[n]
      • DTFT of (0.9)^n cos(pi n/6) u[n]
      • DTFT of (0.9)^n cos(pi n/6) u[n]
      • DTFT of (0.9)^n cos(pi n/3) u[n]
      • DTFT of (0.9)^n cos(7 pi n/3) u[n] -- same as (0.9)^n cos(pi n/3) u[n]
      • DTFT of (0.9)^n cos(7 pi n/3) u[n] plotted for frequencies from -4 pi to 4 pi

35. Friday 11/19

    • Review for Exam 3

36. Monday 11/22

    • Exam 3 covering Chapters 5 and 6

37. Wednesday 11/24

    • Section 7.2: More on the Discrete Fourier Transform (DFT)
      • M-file to plot DTFT and DFT
      • Plot of DTFT and DFT

38. Monday 11/29

    • Results from Exam 3
    • Section 7.2: More on the Discrete Fourier Transform (DFT)
      • Calculation of the DFT and inverse DFT

39. Wednesday 12/1

    • Section 7.3: Properties of the DFT
      • Circular Convolution

40. Friday 12/3

    • Section 7.4: System analysis via the DTFT and DFT
    • Section 7.5: FFT algorithm
      • 20th order low-pass filter
      • 200th order low-pass filter
      • 200th order high-pass filter

41. Monday 12/6

    • Section 7.4: More on system analysis via the DTFT and DFT
      • 200th order non-causal low-pass filter
      • 200th order causal low-pass filter
      • 200th order causal low-pass filter, using MATLAB unwrap function to make the phase look linear
      • 200th order causal high-pass filter
      • 200th order causal band-pass filter
      • Impulse of frequency response for system from Problem 7.30
      • MATLAB m-file for example of relationship between discrete-time and continuous-time frequencies
      • Plot from above m-file
    
    

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    Bill Rison, <rison@nmt.edu >