Student Center

Problem: Investigate the behavior of sampling a signal and reconstruct it

Sampling Theory:

Suppose we sample a signal, such as the one in Figure 1, which is band-limited to frequencies between 0 Hz and fn Hz. If we want to reconstruct the signal later, we must ensure that the sample rate, fs, is strictly greater than 2*fn. A signal sampled at fs = 2*fn is said to be Nyquist sampled, and fs = 2*fn is called the Nyquist frequency.

Note that information may be lost if a signal is sampled exactly at the Nyquist frequency. For example, the sine wave in Figure 1 has a frequency of 1/2 Hz. The Nyquist frequency is therefore 1 Hz. If we sample the sine wave at a rate of 1 Hz, say at t=0, t=1, t=2, and so on, all the sample values will be 0. The signal will look is if it were identically 0, and no reconstruction method will be able to recreate the 1/2 Hz sine wave. This is why fs must be strictly greater than 2*fn.

Figure 1: Sine Wave Signal.

Figure 2: Sampled Sine Wave Signal.

Design Criteria: Investigate the behavior of sampling a signal and then reconstruct it.

Objective: Using MATLAB, create and plot several graphs that show what happens when one sample is below, at, and above the Nyquist frequency.

Given: fs= 0.5, 1, 2, 4, 8 Hz, fn = 0.5 Hz, t = 0:4 seconds, A = 5, and the signal is a sine wave.

See Solution