**Lecture Outline for Fall 2004**

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.

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.

Monday 8/30

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

Wednesday 9/1

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

Friday 9/3

- Section 2.1: Solution of linear constant-coefficient differential equations

Wednesday 9/8

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

Friday 9/10

- Sections 2.3: Solution of linear constant-coefficient difference equations

Monday 9/13

- Sections 2.3: Solution of linear constant-coefficient difference equations
- Section 2.4: Discretization in time of differential equations

Wednesday 9/15

- Finish Section 2.4: Discretization in time of differential equations
- Section 2.4: Discretization in time of differential equations
- Section 3.1: Convolution representation of linear time-invariant discrete-time systems

Friday 9/17

- Sections 3.1, 3.2: Convolution of discrete-time signals

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

- Sections 3.1, 3.2: Convolution of discrete-time signals
Wednesday 9/22

- Exam 1

Friday 9/24

- Sections 3.1, 3.2: Convolution of discrete-time signals
- Section 3.3: Convolution representation of continuous-time systems

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

- Sections 3.3, 3.4: Convolution of continuous-time signals
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

- Sections 3.4: Convolution of continuous-time signals
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

- Appendix A: A brief review of complex numbers
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

- Sections 4.2: Fourier series representation of periodic sequences
Wednesday 10/6

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

- Sections 4.3: Fourier transform
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

Monday 10/11

- Section 4.4: Properties of the Fourier transform

Wednesday 10/13

- Section 5.1: Response to a sinusoidal input

Friday 10/15

- Section 5.1: Response to a sinusoidal input

Monday 10/18

- Section 5.2: Response to periodic inputs

Wednesday 10/20

- Section 5.4: Analysis of ideal filters

Monday 10/25

- Review for Exam 2

Wednesday 10/27

- Exam 2 covering Chapters 3 and 4

Friday 10/29

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

Monday 11/1

- Section 5.5: Sampling

Wednesday 11/3

- Section 6.1: Applications to communications: Analog modulation

Friday 11/5

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

Monday 11/8

- Section 6.4: Digital modulation

Wednesday 11/10

- Section 6.4: More on digital modulation

Fiday 11/12

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

- Guest lecture on communications by Dr. El-Osery
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

- Section 7.1: Discrete time Fourier transform
Friday 11/19

- Review for Exam 3

Monday 11/22

- Exam 3 covering Chapters 5 and 6

Wednesday 11/24

- Section 7.2: More on the Discrete Fourier Transform (DFT)

Monday 11/29

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

Wednesday 12/1

- Section 7.3: Properties of the DFT
- Circular Convolution

- Section 7.3: Properties of the DFT
Friday 12/3

- Section 7.4: System analysis via the DTFT and DFT
- Section 7.5: FFT algorithm

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

*Bill Rison, <rison@nmt.edu >*- Section 7.4: More on system analysis via the DTFT and DFT