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</center> | </center> | ||
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− | ==outline== | + | == outline == |
*Introduction | *Introduction | ||
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*References | *References | ||
− | ==Introduction== | + | == Introduction == |
− | Consider a CT cosine signal (a pure frequency), and sample that signal with a rate above or below Nuquist rate. In this slecture, I will talk about how does the discrete-time Fourier transform of the sampling of this signal look like. | + | Consider a CT cosine signal (a pure frequency), and sample that signal with a rate above or below Nuquist rate. In this slecture, I will talk about how does the discrete-time Fourier transform of the sampling of this signal look like. Suppose |
− | ==Sampling rate above Nyquist rate== | + | the cosine signal is <math>x(t)=cos(2*pi*440t)</math> |
+ | == Sampling rate above Nyquist rate == | ||
− | ==Sampling rate below Nyquist rate== | + | == Sampling rate below Nyquist rate == |
− | ==Conclusion== | + | == Conclusion == |
− | ==References== | + | == References == |
[1].Mireille Boutin, "ECE438 Digital Signal Processing with Applications," Purdue University August 26,2009 | [1].Mireille Boutin, "ECE438 Digital Signal Processing with Applications," Purdue University August 26,2009 | ||
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Revision as of 12:12, 27 September 2014
Discrete-time Fourier transform (DTFT) of a sampled cosine
A slecture by ECE student Yijun Han
Partly based on the ECE438 Fall 2014 lecture material of Prof. Mireille Boutin.
Contents
outline
- Introduction
- Sampling rate above Nyquist rate
- Sampling rate below Nyquist rate
- Conclusion
- References
Introduction
Consider a CT cosine signal (a pure frequency), and sample that signal with a rate above or below Nuquist rate. In this slecture, I will talk about how does the discrete-time Fourier transform of the sampling of this signal look like. Suppose the cosine signal is $ x(t)=cos(2*pi*440t) $
Sampling rate above Nyquist rate
Sampling rate below Nyquist rate
Conclusion
References
[1].Mireille Boutin, "ECE438 Digital Signal Processing with Applications," Purdue University August 26,2009
Questions and comments
If you have any questions, comments, etc. please post them on this page.