ECE 301: Signals and Systems

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Relevant Tables of Formulas

• Complex Number Identities and Formulas
• Power Series
• basic signals and functions
• Signal Metrics Definitions and Formulas
• Laplace Transform Pairs and Properties
• Continuous-time Fourier Transform Pairs and Properties (function of ω in radians)
• Discrete-time Fourier Transform Pairs and Properties

Review of pre-requisites

• A hub page about Complex numbers

Main Topics in ECE301

• Continuous-time signal energy and power
• Discrete-time signal energy and power
• Periodic and non-periodic signals
• Systems properties
• Computing the output of a DT system using the Convolution sum
• Computing the output of a CT system using the Convolution Integral
• Fourier Series
• Continuous-time Fourier transform
• Discrete-time Fourier transform
• Modulation
• Sampling Theorem
• DT processing of CT signals
• About Laplace transform

Practice Problems

• Review of complex numbers
  • Compute the magnitude of these three complex numbers
  • Compute the magnitude of these two CT signals
  • Compute the magnitude of these three DT signals
• Signal Power and Energy
  • Compute the power and energy of the following CT signal
  • Compute the power and energy of the following DT signal
• Transformation of the independent variable
  • Cascade the following time delay and time scaling
• Basic Signal Properties
  • Is the following system invertible?
  • Is the following system stable?
• Linearity and time invariance
  • Is the following system time-invariant?
  • Is the following system linear?
    • Please comment on the following solution to a related problem
      • Time-invariance of a system proved by a previous student
• Computing the output of an LTI system by convolution
  • Compute the output of the following DT LTI system
    • Another one like this
    • And another one
    • And another one
    • And another one
    • And another one
    • And another one
    • And another one
  • Compute the output of the following CT LTI system
• Computing the Fourier series coefficients of a CT signal
  • Obtain the Fourier series coefficients of this CT sinusoidal
  • Obtain the Fourier series coefficients of this CT pulse-train
• Computing the Fourier series coefficients of a DT signal
  • Obtain the Fourier series coefficients of this DT sinusoidal
  • Obtain the Fourier series coefficients of this DT pulse-train

Interesting pages in the ECE301 category

• Cascading transformations of the independent variable, a video tutorial
• 301 students playing music with Matlab
• Animated example of periodic function
• Two things you should know about periodic and on-periodic signals
• What are all these symbols? (from Fall 2008)
• A mystery about complex number: why is e^j2πt not equal to one? More precisely, why can't one say that e^j2πt = (e^j2π)^t = 1^t = 1? Please discuss here.
• Some practice exam problems
• Practice problem on proving time-invariance
• A collective page to practice computing Fourier series of a CT signal
• A collective page to practice computing Fourier series of a DT signal

Semester/Instructor specific pages

• ECE301: Spring 2011, Prof. Boutin
• ECE 301 Fall 2010 Professor Pollak
• ECE 301 Fall 2009 Prof. Bouman
• ECE 301 Summer 2009 Landis Huffman
• ECE 301 Spring 2009 Prof. Lehnert
• ECE 301 Fall 2008 Professor Boutin
• ECE 301 Summer 2008 Aung San
• ECE 301 Fall 2007 Prof. Boutin
• ECE 301 Fall 2008 Professor Wang

Related Courses

• Systems and Fourier Transforms are going to be very important in ECE438.

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