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*The sampling of a signal in the time domain <math> x(t) </math> is basically the repetition of the sampled signal <math> x(t) </math> or the <math> rep </math> function in the frequency domain. The graphical interpretation for this relationship can be seen in the picture below | *The sampling of a signal in the time domain <math> x(t) </math> is basically the repetition of the sampled signal <math> x(t) </math> or the <math> rep </math> function in the frequency domain. The graphical interpretation for this relationship can be seen in the picture below | ||
| − | [[Image:Sl1.jpg| | + | [[Image:Sl1.jpg|400px|relationship view for the sampling signal between time domain and frequency domain]] |
*From the picture above, I should point out that this relationship goes both ways, if we try to sample a signal from the frequency domain the sampled signal that will be produced in the time domain will also be in the form a of <math> rep </math> function. | *From the picture above, I should point out that this relationship goes both ways, if we try to sample a signal from the frequency domain the sampled signal that will be produced in the time domain will also be in the form a of <math> rep </math> function. | ||
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Revision as of 09:56, 6 October 2014
Frequency domain view of the relationship between a signal and a sampling of that signal
A slecture by ECE student Talha Takleh Omar Takleh
Partly based on the ECE438 Fall 2014 lecture material of Prof. Mireille Boutin.
Outline
- Introduction
- Main Points
- Conclusion
Introduction
This Slecture will look into the relationship between a signal and the sampling of that signal in the view of the frequency domain. The signal that will be sampled will be in the time domain $ x(t) $ and after it was Fourier transformed, the sampled signal $ X(f) $ will be in the frequency domain. Here, we will see the relationship between this two signals and what rules need to be obeyed in order to create a good sampling signal within the frequency domain.
Main Points
- The sampling of a signal in the time domain $ x(t) $ is basically the repetition of the sampled signal $ x(t) $ or the $ rep $ function in the frequency domain. The graphical interpretation for this relationship can be seen in the picture below
- From the picture above, I should point out that this relationship goes both ways, if we try to sample a signal from the frequency domain the sampled signal that will be produced in the time domain will also be in the form a of $ rep $ function.
