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m (rearrange into) |
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== Introduction == | == 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). | + | 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 <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> | ||
| + | |||
| + | |||
This leads to the question, can you use | This leads to the question, can you use | ||
| − | <math> {x}_{1}[n] = x_{c}(n{T}_{1})</math> | + | <math> {x}_{1}[n] = x_{c}(n{T}_{1})</math> |
to obtain | to obtain | ||
| − | <math>{x}_{u}[n] = {x}_{c}(n{T}_{u})</math> | + | <math>{x}_{u}[n] = {x}_{c}(n{T}_{u})</math>, a signal sampled at a HIGHER sampling frequency than <math> {x}_{1}[n]</math>, |
without having to fully reconstruct <math> {x}_{c}(t) </math> | without having to fully reconstruct <math> {x}_{c}(t) </math> | ||
| − | + | ||
| − | + | ||
---- | ---- | ||
Revision as of 13:27, 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). **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
