Nyquist – Shannon Sampling Theorem
The theorem states that for reconstructing a sampled signal accurately from the available samples, the sampling frequency should be at least twice as much as the highest frequency component of the signal.
It can be understood by the following expression:
[Tex]2 \times f_{max} \leqslant f_{s} [/Tex]
Where,
[Tex]f_{max} [/Tex] = maximum frequency component of the original signal
[Tex]f_{s} [/Tex]= sampling frequency
“A signal can be exactly reproduced if it is sampled at the rate fs which is greater than twice the maximum frequency (f_{max} ).”
- If [Tex] f_{s} < 2 \times f_{max} [/Tex], then it is the case of undersampling.
- If [Tex]f_{s} = 2 \times f_{max} [/Tex], then it is the case of sampling at Nyquist Rate and it is perfect sampling.
- If [Tex]f_{s} > 2 \times f_{max} [/Tex], then it is the case of oversampling.
Sampling in Digital Communication
Sampling in digital communication is converting a continuous-time signal into a discrete-time signal. It can also be defined as the process of measuring the discrete instantaneous values of a continuous-time signal.
Digital signals are easier to store and have a higher chance of repressing noise. This makes sampling an important step in converting analog signals to digital signals with its primary purpose as representing analog signals in a discrete format.
- Sampling Process in Digital Communication
- Nyquist – Shannon Sampling Theorem
- Oversampling & Undersampling
- Aliasing
- Why Sampling is Required?
- Methods of Sampling
- Scope of Fourier Transform
- Solved Examples on Sampling