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[[Category:ECE438Spring2009mboutin]][[Category:ECE438Spring2009mboutin:CourseNotes]]
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[[Category:ECE]]
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[[Category:ECE438]]
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[[Category:signal processing]]
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[[Category:ECE438Spring2009mboutin]]
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[[Category:lecture notes]]
  
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== ECE438 Course Notes January 14, 2009 ==
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=Lecture Notes for [[ECE438]] Spring 2009, [[user:mboutin|Prof. Boutin]]=
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*[[CourseNotes1_(BoutinSpring2009)|Course Notes Lecture 1 Jan. 14, 2009]]
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1)Definitions
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*[[CourseNotes2_(BoutinSpring2009)|Course Notes Lecture 2 Jan. 16, 2009]]
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*[[CourseNotes3_(BoutinSpring2009)|Course Notes Lecture 3 Jan. 21, 2009]]
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ECE438 is about digital signals and systems
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*[[CourseNotes4_(BoutinSpring2009)|Course Notes Lecture 4 Jan. 23, 2009]]
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*[[CourseNotes6_(BoutinSpring2009)|Course Notes Lecture 6 Jan. 28, 2009]]
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2) Digital Signal = a signal that can be represented by a sequence of 0's and 1's.
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*[[CourseNotes16_(BoutinSpring2009)|Course Notes Lecture 16 Feb. 23, 2009]]
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so the signal must be DT X(t) = t, i.e. need x(n), n belongs to Z
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*[[CourseNotes20_(BoutinSpring2009)|Course Notes Lecture 20 Mar. 11, 2009]]
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*[[CourseNotes30_(BoutinSpring2009)|Course Notes Lecture 30 Apr. 17, 2009]]
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Signal values must be discrete
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----
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[[ECE438_(BoutinFall2009)|Back to ECE438, Spring 2009]]
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-<math>x(n) \in {0,1}</math> <-- binary valued signal
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<br/><math>x(n) \in {0,1,2,...,255}</math> <-- gray scale valued signal
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Another example of digital signal
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-the pixels in a bitmap image (grayscale) can have a value of 0,1,2,...,255 for each individual pixel.
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--If you concatenate all the rows of the image you can convert it to a 1 dimensional signal.
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i.e. <math>x = (row1,row2,row3)</math>
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2D Digital signal = signal that can be represented by an array of 0's and 1's
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<u>example</u>: 128x128 gray scale image<br/>
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<math>p_{ij} \in {0,...,255}</math>
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matrix <math>A_{ij} = p_{ij}</math> of size 128x128 <br/>
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<strong>Digital Systems</strong> = system that can process a ditital signal.<br/>
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E.g.
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<ul>
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<li>Software (MATLAB,C, ...) </li>
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<li>Firmware</li>
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<li>Digital Hardware</li>
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</ul>
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== Advantages of Digital Systems ==
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<ul>
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<li>precise,reproducable</li>
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<li>easier to store data</li>
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<li>easier to build:
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  <ul>
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    <li>just need to represent 2 states instead of a continuous range of values</li>
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  </ul>
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</li>
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</ul>
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<strong>Software based digital systems</strong>
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<ul>
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<li>easier to build</li>
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<li>cheap to build</li>
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<li>adaptable</li>
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<li>easy to fix/upgrade</li>
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</ul>
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<strong>Hardware-based digital systems</strong>
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<ul>
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<li>fast.</li>
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</ul>
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<table border="1px">
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<tr>
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<td  width="50%" align="center" valign="top">
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<strong>Continuous time world</strong>
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<ul>
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<li>most natural signals live here</li>
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<li>things are easy to write, understand, conceptualize</li>
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</ul>
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</td>
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<td width="50%" align="center" valign="top">
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<strong>Digital World</strong>
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<ul>
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<li>digital media signals live here along with computers, MATLAB, digital circuits</li>
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</ul>
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</td>
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</tr>
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</table>
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<p>These world are brought together using sampling & quantization, as well as reconstruction</p>
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== Signal Characteristics ==
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<ul>
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  <li>Deterministic vs. random
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    <ul>
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      <li>x(t) well defined , s.a. <math>x(t) =  e^{j\pi t}</math></li>
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      <li>x(n) well defined , s.a. <math>x(n) = j^{n}</math> <br/>ex: Lena's image</li>
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    </ul>
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  </li>
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  <li>Random
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    <ul>
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      <li>x(t) drawn according to some distribution</li>
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      <li>example: x(t) white noise<br/>x = rand(10) (almost) random</li>
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    </ul>
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  </li>
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</ul>
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<ul>
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  <li>Periodic vs. non-periodic
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  <ul><li> if <math>\exists</math> positive T such that x(t+T) = x(t),<math>\forall t</math> then we say that x(t) is periodic with period T</li></ul>
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  </li>
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</ul>
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Latest revision as of 05:37, 16 September 2013


Lecture Notes for ECE438 Spring 2009, Prof. Boutin

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