Slecture Topic 7 ECE438 - Rhea

Outline

1. Introduction
2. Main Points
3. 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

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 $ rep $ function.