| Line 1: | Line 1: | ||
| − | <center><font size= 4> | + | <center><font size="4"></font> |
| − | DTFT of a Cosine Signal Sampled Above and Below the Nyquist Frequency | + | <font size="4">DTFT of a Cosine Signal Sampled Above and Below the Nyquist Frequency </font> |
| − | </font | + | |
| − | A [https://www.projectrhea.org/learning/slectures.php slecture] by [[ECE]] student Andrew Pawling | + | A [https://www.projectrhea.org/learning/slectures.php slecture] by [[ECE]] student Andrew Pawling |
| − | Partly based on the [[ | + | Partly based on the [[2014 Fall ECE 438 Boutin|ECE438 Fall 2014 lecture]] material of [[User:Mboutin|Prof. Mireille Boutin]]. |
| − | </center> | + | </center> |
---- | ---- | ||
---- | ---- | ||
| − | + | <font size = '3'> | |
In this slecture we will look at an example that illustrates the Nyquist condition. When a signal is sampled, frequencies above half the sampling rate cannot be properly represented and result in aliasing. | In this slecture we will look at an example that illustrates the Nyquist condition. When a signal is sampled, frequencies above half the sampling rate cannot be properly represented and result in aliasing. | ||
| + | |||
| + | ---- | ||
| − | + | Lets look at a pure tone frequency F4 = 349Hz | |
| − | Lets look at a pure tone frequency F4 = 349Hz | + | |
| − | We will represent this tone as a cosine signal, <math> | + | We will represent this tone as a cosine signal, <math>cos*(2\pi349t)</math> |
| − | For this signal <math> f_{s} > 2f_{m} = 2(349)Hz = 698Hz</math> | + | For this signal <math>f_{s} > 2f_{m} = 2(349)Hz = 698Hz</math>, so we will choose a sampling frequency of 800 Hz |
Revision as of 18:02, 1 October 2014
DTFT of a Cosine Signal Sampled Above and Below the Nyquist Frequency
A slecture by ECE student Andrew Pawling
Partly based on the ECE438 Fall 2014 lecture material of Prof. Mireille Boutin.
In this slecture we will look at an example that illustrates the Nyquist condition. When a signal is sampled, frequencies above half the sampling rate cannot be properly represented and result in aliasing.
Lets look at a pure tone frequency F4 = 349Hz
We will represent this tone as a cosine signal, $ cos*(2\pi349t) $
For this signal $ f_{s} > 2f_{m} = 2(349)Hz = 698Hz $, so we will choose a sampling frequency of 800 Hz
