Frequency Domain View of Upsampling
Why Interpolator needs a LPF after Upsampling
A slecture by ECE student Chloe Kauffman
Partly based on the ECE438 Fall 2014 lecture material of Prof. Mireille Boutin.
Outline
- Introduction
- Derivation
- Example
- Conclusion
Introduction
For real world application, higher sampling rates are preferred because reconstruction doesn't require filter to be as close to the ideal (sharper cutoff). **add picture & source**
Assume $ {x}_{c}(t) $ is a bandlimited CT signal,
$ {x}_{1}[n] $ is a DT sampled signal of $ {x}_{c}(t) $ with sampling period $ {T}_{1} $
This leads to the question, can you use
$ {x}_{1}[n] = x_{c}(n{T}_{1}) $
to obtain
$ {x}_{u}[n] = {x}_{c}(n{T}_{u}) $, a signal sampled at a HIGHER sampling frequency than $ {x}_{1}[n] $, without having to fully reconstruct $ {x}_{c}(t) $
Derivation
