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==Derivation== | ==Derivation== | ||
| − | The first thing which need to be clarified is that there two different types of sampling signal: <math> x_s(t) </math> and <math> x_d[n] </math>. <math> x_s(t) </math> is created by multiplying a impulse train <math> P_T(t) </math> with the original signal <math> x(t) </math> | + | The first thing which need to be clarified is that there two different types of sampling signal: <math> x_s(t) </math> and <math> x_d[n] </math>. <math> x_s(t) </math> is created by multiplying a impulse train <math> P_T(t) </math> with the original signal <math> x(t) </math> and actually <math> x_s(t) </math> is a <math> comb_T(x(t)) </math> |
Revision as of 20:26, 5 October 2014
Frequency domain view of the relationship between a signal and a sampling of that signal
A slecture by ECE student Botao Chen
Partly based on the ECE438 Fall 2014 lecture material of Prof. Mireille Boutin.
Outline
- Introduction
- Derivation
- Example
- Conclusion
Introduction
In this slecture I will discuss about the relations between the original signal $ X(f) $ , sampling continuous time signal $ X_s(f) $ and sampling discrete time signal $ X_d(\omega) $ in frequency domain and give a specific example showing the relations.
Derivation
The first thing which need to be clarified is that there two different types of sampling signal: $ x_s(t) $ and $ x_d[n] $. $ x_s(t) $ is created by multiplying a impulse train $ P_T(t) $ with the original signal $ x(t) $ and actually $ x_s(t) $ is a $ comb_T(x(t)) $
