sampling process video lecture from NPTEL

The signals we use in the real world, such as our voices, are called "analog" signals.  To process these signals in computers, we need to convert the signals to "digital" form.  While an analog signal is continuous in both time and amplitude, a digital signal is discrete in both time and amplitude.  To convert a signal from continuous time to discrete time, a process called sampling is used.  The value of the signal is measured at certain intervals in time. Each measurement is referred to as a sample.  (The analog signal is also quantized in amplitude, but that process is ignored in this demonstration.  See the Analog to Digital Conversion page for more on that.)

When the continuous analog signal is sampled at a frequency F, the resulting discrete signal has more frequency components than did the analog signal.  To be precise, the frequency components of the analog signal are repeated at the sample rate.  That is, in the discrete frequency response they are seen at their original position, and are also seen centered around +/- F, and around +/- 2F, etc.


How many samples are necessary to ensure we are preserving the information contained in the signal?  If the signal contains high frequency components, we will need to sample at a higher rate to avoid losing information that is in the signal.  In general, to preserve the full information in the signal, it is necessary to sample at twice the maximum frequency of the signal.  This is known as the Nyquist rate.  The Sampling Theorem states that a signal can be exactly reproduced if it is sampled at a frequency F, where F is greater than twice the maximum frequency in the signal.

What happens if we sample the signal at a frequency that is lower that the Nyquist rate?  When the signal is converted back into a continuous time signal, it will exhibit a phenomenon called  aliasing.  Aliasing is the presence of unwanted components in the reconstructed signal.  These components were not present when the original signal was sampled.  In addition, some of the frequencies in the original signal may be lost in the reconstructed signal.  Aliasing occurs because signal frequencies can overlap if the sampling frequency is too low.  Frequencies "fold" around half the sampling frequency - which is why this frequency is often referred to as the folding frequency.

Sometimes the highest frequency components of a signal are simply noise, or do not contain useful information.  To prevent aliasing of these frequencies, we can filter out these components before sampling the signal.  Because we are filtering out high frequency components and letting lower frequency components through, this is known as low-pass filtering.