Contents
SAMPLING PART 1
Basic Definition of Sampling
Sampling is the extraction of values of a continuous signal at fixed intervals. We learn more about the frequency spectrum of a signal the faster we sample it. Naturally, if the signal changes much faster than the sampling rate, these changes will not be captured accurately and aliasing occurs.
Nyquist Sampling Theorem
The Nyquist Sampling theorem says that in order to capture all the frequency information of a bandlimited signal, the sampling frequency must be twice the maximum frequency of the signal. In other words, each frequency component must be sampled at least twice per period.
<insert nyquist sampling rate conditions here>
The Sampling Process
In theory, here is how we would like to sample our signals.
Step 1: Begin with a continuous function x(t).
Step 2: Sample x(t) using an impulse generator or comb function.
Step 3: Discretize the signal.
After Step 3, the signal is ready to be put through a discrete filter.
