ECE 301 Fall 2020 -- Krogmeier Section

Course Information

1. Main Course Web Page
2. Recitation schedule below indicates the topics from the asynchronous video lectures that will be amplified during the indicated session.
3. Last revised: 9/14/2020.

Topic Schedules and Notes

1. Week 1 (MWF 10:30-11:20 am starting 8/24)
   • Sessions 1, 2, 3 (identical): Linear discrete-time signals and systems interpreted as matrix (system) multiplied by vector (signal).
   • Notes
2. Week 2 (MWF 10:30-11:20 am starting 8/31)
   • Sessions 1, 2, 3 (identical): Transformations of time index, periodic signals, even/odd signals, illustraction of time delay with transmission line example, exponential signals in continuous time and discrete time and observations about periodicity.
   • Notes
3. Week 3 (MWF 10:30-11:20 am starting 9/7)
   • Sessions 1, 2, 3 (identical): The harmonically related complex exponential signals in discrete time, using them as a basis for the vector space of length N signals, properties of the discrete Fourier transform matrix.
   • Notes
4. Week 4 (MWF 10:30-11:20 am starting 9/14)
   • Sessions 1, 2, 3 (identical): The continuous time delta function, meaning only inside of an integral operator, definition of delta as a limit of a family of tall and skinny pulse of unit area, examples of such, the smoothing properties of physical systems via a simple circuit example.
   • Notes
5. Week 5 (MWF 10:30-11:20 am)
   • Session 1 (9/21): Linear and time invarient systems via impulse response and convolution, properties of LTI systems via properties of the impulse response, example of convolution in discrete-time, example of convolution in continuous time.
   • Notes
   • Session 2 (9/23): Linear and time invarient systems via impulse response and convolution, properties of LTI systems via properties of the impulse response, review the solutions of homogeneous linear differential/difference equations with constant coefficients, solving for the discrete time impulse response directly from a difference equation description.
   • Notes
   • Session 3 (9/25): Linear and time invarient systems via impulse response and convolution, properties of LTI systems via properties of the impulse response, solving for the continuous time impulse response directly from a differential equation description.
   • Notes
6. Week 6 (MWF 10:30-11:20 am)
   • Session 1 (9/28): Response of LTI systems to complex exponential inputs, Fourier Series representation of periodic signals in continuous time.
   • Notes
   • Session 2 (9/30): Calculation of the Fourier Series coefficients, an example for a periodic sawtooth wave, convergence in mean-square, convergence pointwise at points of continuity.
   • Notes
   • Session 3 (10/2): Fourier series properties, proofs of 1) the multiplication property, 2) Parseval's relation, and 3) the periodic convolution property.
   • Notes
7. Week 7 (MWF 10:30-11:20 am)
   • Session 1 (10/5): Finish proof of the periodic convolution property, Fourier Series for a periodic pulse train, Matlab examples.
   • Notes
   • Matlab m-file
   • Matlab published run of m-file
   • Session 2 (10/7): Limiting form of the periodic pulse train and its limiting Fourier Series, Fourier series of a train of impulses, example of using properties of the Fourier series to compute the Fourier series of a periodic triangular wave.
   • Notes
   • Session 3 (10/9): Finishing the example from previous class, generic periodic pulse trains, example of a periodic train of decaying exponentials.
   • Notes
8. Week 8 (MWF 10:30-11:20 am)
   • Session 1 (10/12): A generic Fourier series (i.e., not interpreting signal as a time function, observation that time and frequency may be reversed to create a transform from a discrete-time signal to a periodic function of a continuous frequency variable - this is the discrete-time Fourier transform, using Fourier series to compute the output of an LTI system, discrete-time periodic signals and the discrete-time Fourier series.
   • Notes
   • Session 2 (10/14): The discrete-time Fourier series and examples. An example related to periodic signals input to LTI systems.
   • Notes
   • Session 3 (10/16): Revision of Fourier series in both discrete and continuous time. Proof of discrete-time periodic convolution property.
   • Notes
9. Week 9 (MWF 10:30-11:20 am)
   • Session 1 (10/19): The continuous-time Fourier transform as the limit of a continuous-time Fourier series as the period goes to infinity; Example of decaying exponential pulse in time; Example of a nasty little pulse.
   • Notes
   • Session 2 (10/21): Fourier transform of real-valued time signal; Fourier transform of flat topped pulse in time; Inverse Fourier transform of flat topped frequency function; the sinc function; Gaussian pulse in time <--> Gaussian pulse in frequency.
   • Notes
   • Session 3 (10/23): What to do when the transform or inverse transform results in an integral that doesn't exist as a well-behaved function -- use delta functions; A tricky student question; Fourier transforms of periodic signals.
   • Notes
10. Week 10 (MWF 10:30-11:20 am)
    • Session 1 (10/26): Finish answering the ``tricky student question,'' Fourier transform properties.
    • Notes
    • Session 2 (10/28): Solution to Midterm 2 problem 1. Partial solution to Midterm 2 problem 6.
    • Notes
    • Session 3 (10/30): No class for reading day.
11. Week 11 (MWF 10:30-11:20 am)
    • Session 1 (11/2): Finishing CTFT properties. Discussion of duality.
    • Notes
    • Session 2 (11/4): Solving LTI systems by multiply input FT by transfer function and then inverse transforming using partial fraction expansion and the transform tables; amplitude modulation.
    • Notes
    • Session 3 (11/6): Communication systems, amplitude modulation.
    • Notes
    • Notes on Comm Systems
12. Week 12 (MWF 10:30-11:20 am)
    • Session 1 (11/9): Introduction to Discrete Time Fourier Transform, working sample exam questions for old MT3s.
    • Notes
    • Session 2 (11/11): Working more sample exam questions for old MT3s.
    • Notes
    • Session 3 (11/13): DTFT for sinusoidal signal, DTFT of periodic discrete-time signal, solving a difference equation or convolution problem using frequency domain multiplication of transforms and a table of discrete-time Fourier transforms.
    • Notes
13. Week 13 (MWF 10:30-11:20 am)
    • Session 1 (11/16): The sampling theorem.
    • Notes
    • Session 2 (11/18): Zero-order hold sampling.
    • Notes
    • Session 3 (11/20): Discrete-time processing of continuous-time signals.
    • Notes
14. Week 14 (MWF 10:30-11:20 am)
    • Session 1 (11/23): The Laplace and Z Transforms.
    • Notes
    • Session 2 (11/25): No class.
    • Session 3 (11/27): No class.
15. Week 15 (online)
    • Session a: Bilateral Laplace Transform Calculations.
    • Notes
    • Video
    • Session b: A two pole bilateral Laplace Transform Example.
    • Notes
    • Video
    • Session c: Bilateral Z transform calculations; Comparison of ROCs for Bilateral Laplace and Bilateral Z.
    • Notes
    • Video
    • Session d: Inversion formula for bilateral LT.
    • Notes
    • Video
    • Session e: Inversion formula for bilateral ZT.
    • Notes
    • Video