HW13 DFT/Sampling Assignment: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| (11 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
Problem Statement: Sample <math>sin(2*pi*t)</math> at 3 Hz; take the DFT; explain the results. |
|||
===Problem Statement=== |
===Problem Statement=== |
||
Sample <math>sin(2\pi*t)</math> at 3 Hz; |
1.Sample <math>sin(2*\pi*t)\!</math> at <math> 3 Hz;\!</math> |
||
<br>2.Take the DFT |
|||
<br>3.Explain the results. |
|||
===Solution=== |
===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 13:19, 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.