Summary of Information for the Final

ABET Outcomes

(a) an ability to classify signals (e.g. periodic, even) and systems (e.g. causal, linear) and an understanding of the difference between discrete and continuous time signals and systems. [1,2;a]

(b) an ability to determine the impulse response of a differential or difference equation. [1,2;a]

(c) an ability to determine the response of linear systems to any input signal convolution in the time domain. [1,2,4;a,e,k]

(d) an understanding of the deffnitions and basic properties (e.g. time-shifts,modulation, Parseval's Theorem) of Fourier series, Fourier transforms, bi-lateral Laplace transforms, Z transforms, and discrete time Fourier trans-forms and an ability to compute the transforms and inverse transforms of basic examples using methods such as partial fraction expansions. [1,2;a]

(e) an ability to determine the response of linear systems to any input signal by transformation to the frequency domain, multiplication, and inverse transformation to the time domain. [1,2,4;a,e,k]

(f) an ability to apply the Sampling theorem, reconstruction, aliasing, and Nyquist theorem to represent continuous-time signals in discrete time so that they can be processed by digital computers. [1,2,4;a,e,k]

Chapter 1: CT and DT Signals and Systems

Chapter 2: Linear Time-Invariant Systems

Chapter 3: Fourier Series Representation of Period Signals

Chapter 4: CT Fourier Transform

Chapter 5: DT Fourier Transform

Chapter 7: Sampling

Chapter 8: Communication Systems

Chapter 9: Laplace Transformation

Chapter 10_ECE301Fall2008mboutin: z-Transformation

Summary

1. The z-Transform

$ X(z) = \sum_{n = -\infty}^{+\infty}x[n]z^{-n} $

2. Region of Convergence for the z-Transform

3. The Inverse z-Transform

$ x[n] = \frac{1}{2\pi j} \oint X(z)z^{n-1}\,dz $

4. z-Transform Properties

5. z-Transform Pairs