Chapter 6: Continuous-time Fourier Methods Dr. Kalyana Veluvolu Example 1 (Find the Fourier Series Pair) 1
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
Example 1 (Find the Fourier Series Pair)
1
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
Example 2
2
Find the Fourier Series pair for the periodic function defined in one period
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
Example 2 Cond…
3
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
Example 3
4
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
Example 3 Cond..
5
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
Example 3 Cond..
6
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
Example 4
7
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
Example 5
8
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
Fourier Transform Properties
9
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
Fourier Transform Properties
10
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
Example 6 - CTFT
11
rect(t) sinc(f)F
Linearity 25 rect(t) 25 sinc(f)F
Time Scaling 25 rect(t/10) 250 sinc(10f)F
Time Shifting 25 rect((t-4)/10) 250 sinc(10f)F 8j fe
Find CTFT of x(t)= 25 rect((t-4)/10)
We can find the CTFT of the unit rectangle function
in the table of Fourier Transforms
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
Example 7 - CTFT
12
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
If x(t)= 10 Sin(t) find
(a) The CTFT of x(t) ; b) The CTFT of x(2(t-1));
c) The CTFT of x(2t-1)
Better to use radian-frequency form of CTFT
Example 8 - CTFT
13
a)
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu
Example 8 – CTFT contd..
14
b) The CTFT of x(2(t-1));
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu 15
Example 8 – CTFT contd..
c) The CTFT of x(2t-1);
Chapter 6: Continuous-time Fourier Methods
Dr. Kalyana Veluvolu 16
Example 9 – CTFT
Related Documents
