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===[[Chapter 1_ECE301Fall2008mboutin]]: CT and DT Signals and Systems=== | ===[[Chapter 1_ECE301Fall2008mboutin]]: CT and DT Signals and Systems=== | ||
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===[[Chapter 2_ECE301Fall2008mboutin]]: Linear Time-Invariant Systems=== | ===[[Chapter 2_ECE301Fall2008mboutin]]: Linear Time-Invariant Systems=== | ||
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===[[Chapter 3_ECE301Fall2008mboutin]]: Fourier Series Representation of Period Signals=== | ===[[Chapter 3_ECE301Fall2008mboutin]]: Fourier Series Representation of Period Signals=== | ||
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===[[Chapter 4_ECE301Fall2008mboutin]]: CT Fourier Transform=== | ===[[Chapter 4_ECE301Fall2008mboutin]]: CT Fourier Transform=== | ||
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===[[Chapter 5_ECE301Fall2008mboutin]]: DT Fourier Transform=== | ===[[Chapter 5_ECE301Fall2008mboutin]]: DT Fourier Transform=== | ||
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===[[Chapter 7_ECE301Fall2008mboutin]]: Sampling=== | ===[[Chapter 7_ECE301Fall2008mboutin]]: Sampling=== | ||
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#'''Sampling''' | #'''Sampling''' | ||
##Impulse Train Sampling | ##Impulse Train Sampling | ||
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===[[Chapter 8_ECE301Fall2008mboutin]]: Communication Systems=== | ===[[Chapter 8_ECE301Fall2008mboutin]]: Communication Systems=== | ||
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===[[Chapter 9_ECE301Fall2008mboutin]]: Laplace Transformation=== | ===[[Chapter 9_ECE301Fall2008mboutin]]: Laplace Transformation=== | ||
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:1. '''The Laplace Transform''' | :1. '''The Laplace Transform''' | ||
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::<math> x(t) = \frac{1}{2\pi}\int_{\sigma - j\infty}^{\sigma + j\infty} X(s)e^{st}\,ds</math> | ::<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=== | ===[[Chapter 10_ECE301Fall2008mboutin]]: z-Transformation=== | ||
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:1. '''The z-Transform''' | :1. '''The z-Transform''' | ||
Revision as of 06:10, 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
Chapter 2_ECE301Fall2008mboutin: Linear Time-Invariant Systems
Chapter 3_ECE301Fall2008mboutin: Fourier Series Representation of Period Signals
Chapter 4_ECE301Fall2008mboutin: CT Fourier Transform
Chapter 5_ECE301Fall2008mboutin: DT Fourier Transform
Chapter 7_ECE301Fall2008mboutin: Sampling
- Sampling
- Impulse Train Sampling
- The Sampling Theorem and the Nyquist
- Signal Reconstruction Using Interpolation: the fitting of a continuous signal to a set of sample values
- Sampling with a Zero-Order Hold (Horizontal Plateaus)
- Linear Interpolation (Connect the Samples)
- Undersampling: Aliasing
- Processing CT Signals Using DT Systems (Vinyl to CD)
- Analog vs. Digital: The Show-down (A to D conversion -> Discrete-Time Processing System -> D to A conversion
- Sampling DT Signals (CD to MP3 albeit a complicated sampling algorithm, MP3 is less dense signal)
Chapter 8_ECE301Fall2008mboutin: Communication Systems
Chapter 9_ECE301Fall2008mboutin: Laplace Transformation
- 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
- 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
