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=Summary of Information for the Final= | =Summary of Information for the Final= | ||
| − | ==ABET Outcomes== | + | ===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] | :(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] | :(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] | :(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 | + | :(d) an understanding of the deffinitions 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 transforms and an ability to compute the transforms and inverse transforms of basic examples using methods such as [[partial fraction expansion_ECE301Fall2008mboutin]]. [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] | :(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 | + | :(f) an ability to apply the [[Sampling theorem_ECE301Fall2008mboutin]], reconstruction, aliasing, and [[Nyquist_ECE301Fall2008mboutin]] 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 | + | ===[[Chapter 1_ECE301Fall2008mboutin]]: CT and DT Signals and Systems=== |
| − | ==Chapter | + | ====Summary==== |
| − | ==Chapter | + | ===[[Chapter 2_ECE301Fall2008mboutin]]: Linear Time-Invariant Systems=== |
| − | ==Chapter | + | ====Summary==== |
| − | ==Chapter | + | ===[[Chapter 3_ECE301Fall2008mboutin]]: Fourier Series Representation of Period Signals=== |
| − | ==Chapter | + | ====Summary==== |
| − | ==Chapter | + | ===[[Chapter 4_ECE301Fall2008mboutin]]: CT Fourier Transform=== |
| − | ==Chapter | + | ====Summary==== |
| − | ==[[Chapter 10_ECE301Fall2008mboutin]]: z-Transformation== | + | ===[[Chapter 5_ECE301Fall2008mboutin]]: DT Fourier Transform=== |
| − | ===Summary=== | + | ====Summary==== |
| − | 1. '''The z-Transform''' | + | ===[[Chapter 7_ECE301Fall2008mboutin]]: Sampling=== |
| + | ====Summary==== | ||
| + | ===[[Chapter 8_ECE301Fall2008mboutin]]: Communication Systems=== | ||
| + | ====Summary==== | ||
| + | ===[[Chapter 9_ECE301Fall2008mboutin]]: Laplace Transformation=== | ||
| + | ====Summary==== | ||
| + | :1. '''The Laplace Transform''' | ||
| + | |||
| + | ::<math>X(s) = \int_{-\infty}^{+\infty}x(t)e^{-st}\, dt</math> | ||
| + | |||
| + | ::<math> \mathcal{F}\lbrace x(t)e^{-\sigma t} \rbrace = \mathcal{X}(\omega) = \int_{-\infty}^{+\infty}x(t)e^{-\sigma t}e^{-j\omega t}\, dt</math> | ||
| + | |||
| + | :2. '''The Region of Convergence for Laplace Transforms''' | ||
| + | |||
| + | |||
| + | :3. '''The Inverse Laplace Transform''' | ||
| + | |||
| + | ::<math> x(t) = \frac{1}{2\pi}\int_{\sigma - j\infty}^{\sigma + j\infty} X(s)e^{st}\,ds</math> | ||
| + | ===[[Chapter 10_ECE301Fall2008mboutin]]: z-Transformation=== | ||
| + | ====Summary==== | ||
| + | :1. '''The z-Transform''' | ||
:<math>X(z) = \sum_{n = -\infty}^{+\infty}x[n]z^{-n}</math> | :<math>X(z) = \sum_{n = -\infty}^{+\infty}x[n]z^{-n}</math> | ||
| − | 2. '''Region of Convergence for the z-Transform''' | + | :2. '''Region of Convergence for the z-Transform''' |
| − | 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> |
| − | 4. '''z-Transform Properties''' | + | :4. '''z-Transform Properties''' |
| − | 5. '''z-Transform Pairs''' | + | :5. '''z-Transform Pairs''' |
Revision as of 06:54, 8 December 2008
Contents
- 1 Summary of Information for the Final
- 1.1 ABET Outcomes
- 1.2 Chapter 1_ECE301Fall2008mboutin: CT and DT Signals and Systems
- 1.3 Chapter 2_ECE301Fall2008mboutin: Linear Time-Invariant Systems
- 1.4 Chapter 3_ECE301Fall2008mboutin: Fourier Series Representation of Period Signals
- 1.5 Chapter 4_ECE301Fall2008mboutin: CT Fourier Transform
- 1.6 Chapter 5_ECE301Fall2008mboutin: DT Fourier Transform
- 1.7 Chapter 7_ECE301Fall2008mboutin: Sampling
- 1.8 Chapter 8_ECE301Fall2008mboutin: Communication Systems
- 1.9 Chapter 9_ECE301Fall2008mboutin: 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 deffinitions 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 transforms and an ability to compute the transforms and inverse transforms of basic examples using methods such as partial fraction expansion_ECE301Fall2008mboutin. [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_ECE301Fall2008mboutin, reconstruction, aliasing, and Nyquist_ECE301Fall2008mboutin 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_ECE301Fall2008mboutin: CT and DT Signals and Systems
Summary
Chapter 2_ECE301Fall2008mboutin: Linear Time-Invariant Systems
Summary
Chapter 3_ECE301Fall2008mboutin: Fourier Series Representation of Period Signals
Summary
Chapter 4_ECE301Fall2008mboutin: CT Fourier Transform
Summary
Chapter 5_ECE301Fall2008mboutin: DT Fourier Transform
Summary
Chapter 7_ECE301Fall2008mboutin: Sampling
Summary
Chapter 8_ECE301Fall2008mboutin: Communication Systems
Summary
Chapter 9_ECE301Fall2008mboutin: Laplace Transformation
Summary
- 1. The Laplace Transform
- $ X(s) = \int_{-\infty}^{+\infty}x(t)e^{-st}\, dt $
- $ \mathcal{F}\lbrace x(t)e^{-\sigma t} \rbrace = \mathcal{X}(\omega) = \int_{-\infty}^{+\infty}x(t)e^{-\sigma t}e^{-j\omega t}\, dt $
- 2. The Region of Convergence for Laplace Transforms
- 3. The Inverse Laplace Transform
- $ x(t) = \frac{1}{2\pi}\int_{\sigma - j\infty}^{\sigma + j\infty} X(s)e^{st}\,ds $
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
