ECE 301 Fall 2020 -- Krogmeier Section
Course Information
- Main Course Web Page
- Recitation schedule below indicates the topics from the asynchronous video lectures
that will be amplified during the indicated session.
- Last revised: 9/14/2020.
Topic Schedules and Notes
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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.
- 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
- 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
- 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
- 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.
- 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