HW13 DFT/Sampling Assignment

Problem Statement

1.Sample $sin(2*\pi *t)$ at $3Hz;$
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."

$sin(2*\pi *t)$

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, $3Hz;$ is greater than twice the signal bandwidth, as required in the Nyquist Theroem.