HW13 DFT/Sampling Assignment: Difference between revisions
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===Problem Statement=== | ===Problem Statement=== | ||
Sample | 1.Sample <math>sin(2*\pi*t)\!</math> at <math> 3 Hz;\!</math> | ||
<br>2.Take the DFT | |||
<br>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." | |||
<math>sin(2*\pi*t)\!</math> | |||
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> | |||
is greater than twice the signal bandwidth, as required in the Nyquist Theroem. | |||
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.