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In this slecture I will discuss about the relations between the original signal <math> X(f) </math> , sampling continuous time signal <math> X_s(f) </math> and sampling discrete time signal <math> X_d(\omega) </math> in frequency domain and give a specific example showing the relations. | In this slecture I will discuss about the relations between the original signal <math> X(f) </math> , sampling continuous time signal <math> X_s(f) </math> and sampling discrete time signal <math> X_d(\omega) </math> in frequency domain and give a specific example showing the relations. | ||
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| + | ==Derivation== | ||
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| + | 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 with the original signal which is known as a <math> comb_T(x(t)) </math> | ||
Revision as of 21:22, 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 with the original signal which is known as a $ comb_T(x(t)) $
