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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

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Chapter 3_ECE301Fall2008mboutin: Fourier Series Representation of Period Signals

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Chapter 4_ECE301Fall2008mboutin: CT Fourier Transform

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Chapter 5_ECE301Fall2008mboutin: DT Fourier Transform

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Chapter 7_ECE301Fall2008mboutin: Sampling

Summary

1. Sampling
   1. Impulse Train Sampling
   2. The Sampling Theorem and the Nyquist
2. Signal Reconstruction Using Interpolation: the fitting of a continuous signal to a set of sample values
   1. Sampling with a Zero-Order Hold (Horizontal Plateaus)
   2. Linear Interpolation (Connect the Samples)
3. Undersampling: Aliasing
4. Processing CT Signals Using DT Systems (Vinyl to CD)
   1. Analog vs. Digital: The Show-down (A to D conversion -> Discrete-Time Processing System -> D to A conversion
5. Sampling DT Signals (CD to MP3 albeit a complicated sampling algorithm, MP3 is less dense signal)

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