HW13 DFT/Sampling Assignment: Difference between revisions
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===Problem Statement=== |
===Problem Statement=== |
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1.Sample <math>sin(2*\pi*t)\!</math> at <math> 3 Hz;\!</math> |
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Sample |
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<br>2.Take the DFT |
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<br>3.Explain the results. |
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The Nyquist theorem states: "Exact reconstruction of a continuous-time baseband signal from its samples is possible if the signal is bandlimited and the sampling frequency is greater than twice the signal bandwidth." |
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<math>sin(2*\pi*t)\!</math> |
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is a sine wave with a frequency of 1 Hz. This signal is bandlimited, because it consists of a single frequency sine wave, and the requested sampling frequency, <math> 3 Hz;\!</math> |
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at 3 Hz; take the DFT; explain the results. |
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is greater than twice the signal bandwidth, as required in the Nyquist Theroem. |
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Latest revision as of 14:19, 5 December 2007
Problem Statement
1.Sample at
2.Take the DFT
3.Explain the results.
Solution
The Nyquist theorem states: "Exact reconstruction of a continuous-time baseband signal from its samples is possible if the signal is bandlimited and the sampling frequency is greater than twice the signal bandwidth."
is a sine wave with a frequency of 1 Hz. This signal is bandlimited, because it consists of a single frequency sine wave, and the requested sampling frequency, is greater than twice the signal bandwidth, as required in the Nyquist Theroem.