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#Example | #Example | ||
#Conclusion | #Conclusion | ||
| + | |||
| + | ---- | ||
| + | |||
| + | ---- | ||
| + | <font size = 2> | ||
| + | |||
| + | == 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). | ||
| + | This leads to the question, can you use | ||
| + | |||
| + | <math> {x}_{1}[n] = x_{c}(n{T}_{1})</math> | ||
| + | |||
| + | to obtain | ||
| + | |||
| + | <math>{x}_{u}[n] = {x}_{c}(n{T}_{u})</math> | ||
| + | without having to fully reconstruct <math> {x}_{c}(t) </math> | ||
| + | |||
| + | assume <math> {x}_{c}(t) </math> is a bandlimited CT signal, | ||
| + | <math> {x}_{1}[n] </math> is a DT sampled signal of <math> {x}_{c}(t) </math> with sampling period <math> {T}_{1} </math> | ||
| + | |||
| + | ---- | ||
| + | ---- | ||
| + | |||
| + | == Derivation == | ||
| + | |||
---- | ---- | ||
Revision as of 13:16, 14 October 2014
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). 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}) $ without having to fully reconstruct $ {x}_{c}(t) $
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} $
Derivation
