Frequency Domain View of Downsampling
A Text slecture by ECE David Klouda
Partly based on the ECE438 Fall 2014 lecture material of Prof. Mireille Boutin.
Contents
Outline
- Introduction
- Derivation
- Example
- Conclusion
1. Introduction
In this slecture, the Frequency Domain view of Downsampling will be discussed. It will begin with the derivation of the formulas and explaining the terms involved. It will then show an example using the DTFT and finish with an explanation as to why filtering is necessary when decimating.
2. Derivation
Begin with x(t) as a continuous time signal with $ x_1[n]= x(T_1*n) $ being its discrete time sampling.
Let $ x_2[n]=x(T_2*n)=x_1[T_2/T_1*n] $
with Downsampling factor $ D=T_2/T_1 $
3. Example
4. Conclusion
T
Questions and comments
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