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Wednesday March 9, 2011 (Week 9) - See [[Lecture Schedule ECE301Spring11 Boutin|Course Schedule]]. | Wednesday March 9, 2011 (Week 9) - See [[Lecture Schedule ECE301Spring11 Boutin|Course Schedule]]. | ||
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| − | Today we explained how to recover a signal from its samples. To understand how things work, we looked at the sampling process in the frequency domain. We observed that, when Nyquist's condition is satisfied, the Fourier transform of the sampling of a band-limited signal consists of copies of the Fourier transform of the original signal. Satisfying Nyquist's condition insures that there is "space" between the copies, so that one can recover the initial signal by low-pass-filtering. | + | Today we explained how to recover a signal from its samples. To understand how things work, we looked at the sampling process in the frequency domain. We observed that, when Nyquist's condition is satisfied, the Fourier transform of the sampling of a band-limited signal consists of copies of the Fourier transform of the original signal. Satisfying Nyquist's condition insures that there is "space" between the copies, so that one can recover the initial signal by low-pass-filtering. This actually proves Nyquist's theorem. |
== Action items before the next lecture: == | == Action items before the next lecture: == | ||
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==Relevant Rhea Pages== | ==Relevant Rhea Pages== | ||
*[[ECE_301_Fall_2007_mboutin_Sampling_Theorem|The sampling theorem explained by a student]] | *[[ECE_301_Fall_2007_mboutin_Sampling_Theorem|The sampling theorem explained by a student]] | ||
| − | *[[Student_Statements_Sampling_Theorem_from_Exam|Students' answer to the question "state the sampling theorem in your own words"]] (from an exam | + | *[[Student_Statements_Sampling_Theorem_from_Exam|Students' answer to the question "state the sampling theorem in your own words"]] (from an exam) |
Previous: [[Lecture24ECE301S11|Lecture 24]] | Previous: [[Lecture24ECE301S11|Lecture 24]] | ||
Latest revision as of 08:37, 30 March 2011
Lecture 25 Blog, ECE301 Spring 2011, Prof. Boutin
Wednesday March 9, 2011 (Week 9) - See Course Schedule.
Today we explained how to recover a signal from its samples. To understand how things work, we looked at the sampling process in the frequency domain. We observed that, when Nyquist's condition is satisfied, the Fourier transform of the sampling of a band-limited signal consists of copies of the Fourier transform of the original signal. Satisfying Nyquist's condition insures that there is "space" between the copies, so that one can recover the initial signal by low-pass-filtering. This actually proves Nyquist's theorem.
Action items before the next lecture:
- Work on HW7.
Relevant Rhea Pages
- The sampling theorem explained by a student
- Students' answer to the question "state the sampling theorem in your own words" (from an exam)
Previous: Lecture 24
Next: Lecture 26
