(20 intermediate revisions by 5 users not shown)
Line 1: Line 1:
−
[[Category:ECE438Spring2009mboutin]][[Category:ECE438Spring2009mboutin:CourseNotes]]
+
[[Category:ECE]]
 +
[[Category:ECE438]]
 +
[[Category:signal processing]]
 +
[[Category:ECE438Spring2009mboutin]]
 +
[[Category:lecture notes]]
  
−
== ECE438 Course Notes January 14, 2009 ==
+
=Lecture Notes for [[ECE438]] Spring 2009, [[user:mboutin|Prof. Boutin]]=
−
 
+
*[[CourseNotes1_(BoutinSpring2009)|Course Notes Lecture 1 Jan. 14, 2009]]
−
1)Definitions
+
*[[CourseNotes2_(BoutinSpring2009)|Course Notes Lecture 2 Jan. 16, 2009]]
−
 
+
*[[CourseNotes3_(BoutinSpring2009)|Course Notes Lecture 3 Jan. 21, 2009]]
−
ECE438 is about digital signals and systems
+
*[[CourseNotes4_(BoutinSpring2009)|Course Notes Lecture 4 Jan. 23, 2009]]
−
 
+
*[[CourseNotes6_(BoutinSpring2009)|Course Notes Lecture 6 Jan. 28, 2009]]
−
2) Digital Signal = a signal that can be represented by a sequence of 0's and 1's.
+
*[[CourseNotes16_(BoutinSpring2009)|Course Notes Lecture 16 Feb. 23, 2009]]
−
so the signal must be DT X(t) = t, i.e. need x(n), n belongs to Z
+
*[[CourseNotes20_(BoutinSpring2009)|Course Notes Lecture 20 Mar. 11, 2009]]
−
 
+
*[[CourseNotes30_(BoutinSpring2009)|Course Notes Lecture 30 Apr. 17, 2009]]
−
Signal values must be discrete
+
----
−
 
+
[[ECE438_(BoutinFall2009)|Back to ECE438, Spring 2009]]
−
-<math>x(n) \in {0,1}</math> <-- binary valued signal
+
−
<br/><math>x(n) \in {0,1,2,...,255}</math> <-- gray scale valued signal
+
−
 
+
−
 
+
−
Another example of digital signal
+
−
 
+
−
-the pixels in a bitmap image (grayscale) can have a value of 0,1,2,...,255 for each individual pixel.
+
−
--If you concatenate all the rows of the image you can convert it to a 1 dimensional signal.
+
−
i.e. <math>x = (row1,row2,row3)</math>
+
−
 
+
−
2D Digital signal = signal that can be represented by an array of 0's and 1's
+
−
 
+
−
<u>example</u>: 128x128 gray scale image<br/>
+
−
<math>p_{ij} \in {0,...,255}</math>
+
−
 
+
−
matrix <math>A_{ij} = p_{ij}</math> of size 128x128 <br/>
+
−
 
+
−
<strong>Digital Systems</strong> = system that can process a ditital signal.<br/>
+
−
E.g.
+
−
<ul>
+
−
<li>Software (MATLAB,C, ...) </li>
+
−
<li>Firmware</li>
+
−
<li>Digital Hardware</li>
+
−
</ul>
+
−
 
+
−
== Advantages of Digital Systems ==
+
−
<ul>
+
−
<li>precise,reproducable</li>
+
−
<li>easier to store data</li>
+
−
<li>easier to build:
+
−
  <ul>
+
−
    <li>just need to represent 2 states instead of a continuous range of values</li>
+
−
  </ul>
+
−
</li>
+
−
</ul>
+
−
 
+
−
<strong>Software based digital systems</strong>
+
−
<ul>
+
−
<li>easier to build</li>
+
−
<li>cheap to build</li>
+
−
<li>adaptable</li>
+
−
<li>easy to fix/upgrade</li>
+
−
</ul>
+
−
 
+
−
<strong>Hardware-based digital systems</strong>
+
−
<ul>
+
−
<li>fast.</li>
+
−
 
+
−
</ul>
+
−
<table border="1px">
+
−
<tr>
+
−
<td  width="50%" align="center" valign="top">
+
−
<strong>Continuous time world</strong>
+
−
<ul>
+
−
<li>most natural signals live here</li>
+
−
<li>things are easy to write, understand, conceptualize</li>
+
−
 
+
−
</ul>
+
−
</td>
+
−
<td width="50%" align="center" valign="top">
+
−
<strong>Digital World</strong>
+
−
<ul>
+
−
<li>digital media signals live here along with computers, MATLAB, digital circuits</li>
+
−
</ul>
+
−
</td>
+
−
</tr>
+
−
</table>
+
−
<p>These world are brought together using sampling & quantization, as well as reconstruction</p>
+
−
 
+
−
== Signal Characteristics ==
+
−
<ul>
+
−
  <li>Deterministic vs. random
+
−
    <ul>
+
−
      <li>x(t) well defined , s.a. <math>x(t) =  e^{j\pi t}</math></li>
+
−
      <li>x(n) well defined , s.a. <math>x(n) = j^{n}</math> <br/>ex: Lena's image</li>
+
−
    </ul>
+
−
  </li>
+
−
  <li>Random
+
−
    <ul>
+
−
      <li>x(t) drawn according to some distribution</li>
+
−
      <li>example: x(t) white noise<br/>x = rand(10) (almost) random</li>
+
−
    </ul>
+
−
  </li>
+
−
</ul>
+
−
 
+
−
<ul>
+
−
  <li>Periodic vs. non-periodic
+
−
  <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>
+
−
  </li>
+
−
</ul>
+

Latest revision as of 06:37, 16 September 2013


Lecture Notes for ECE438 Spring 2009, Prof. Boutin

Back to ECE438, Spring 2009

Retrieved from "https://www.projectrhea.org/rhea/index.php?title=ECE_438_Spring_2009_mboutin_Course_Notes&oldid=58285"
Shortcuts
Help Main Wiki Page Random Page Special Pages Log in
Search

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett