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3. '''The Inverse z-Transform''' | 3. '''The Inverse z-Transform''' | ||
:<math>x[n] = \frac{1}{2\pi j} \oint X(z)z^{n-1}\,dz</math> | :<math>x[n] = \frac{1}{2\pi j} \oint X(z)z^{n-1}\,dz</math> | ||
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| + | 4. '''z-Transform Properties''' | ||
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| + | 5. '''z-Transform Pairs''' | ||
Revision as of 05:34, 8 December 2008
Contents
- 1 Summary of Information for the Final
- 1.1 ABET Outcomes
- 1.2 Chapter 1: CT and DT Signals and Systems
- 1.3 Chapter 2: Linear Time-Invariant Systems
- 1.4 Chapter 3: Fourier Series Representation of Period Signals
- 1.5 Chapter 4: CT Fourier Transform
- 1.6 Chapter 5: DT Fourier Transform
- 1.7 Chapter 7: Sampling
- 1.8 Chapter 8: Communication Systems
- 1.9 Chapter 9: Laplace Transformation
- 1.10 Chapter 10_ECE301Fall2008mboutin: z-Transformation
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
