Signals and Systems

From JonWiki

Big Idea

The big idea of Signals and Systems is that you can construct things out of a well-selected set of basis vectors.

The duality of multiplication and convolution in the time and frequency domains is a by-product of this idea, but it is not the whole idea.

Additionally, the transform between the time and frequency domain follows the Uncertainty Principle. A sharp-sloped function in the time domain results in an infinite or close to infinite. In fact, if we look at the variance of both the time and frequency domains, their product is the constant in the Uncertainty Principle.

The time required to resolve a band-passed signal is inversely proportional to the sharpness of the cutoff of the filter.

Topics to Cover

• Polar and Complex Exponential Math (Very Quick Review)
• Bilateral Laplace Transform
  • Convergence
  • Fourier Transform
  • Fourier Series
• Step and Impulse Response
• Convolution
• 1st, 2nd order systems
• System: differential equations <-> H(s) <-> s-plane
  • Laplace transform as a transformation between differential equations and H(s)
  • Fourier series as they interact with Laplace
  • z-transform
  • How these concepts tie into energy and power.
• Discrete Time
  • FIR
  • IIR
  • z-plane
• Basis vectors
  • Sines, Cosines, Exponentials
  • Random Variables
  • Functions
  • Random Process
  • Taylor Series

Assessment Methods

• Three Exams
  • Final Exam will be cumulative
• Weekly Problem Sets
  • MATLAB "labs" at the end
• Pre-class problems