Solved Examples on Sampling
Question 1: Given the signal, what will be the sampling frequency for which the signal can be reconstructed
[Tex]x(t) = cos(2\pi10t) [/Tex]
Solution:
Comparing the given signal with [Tex]cos(2\pi ft) [/Tex]
[Tex]f_{max} = 10 Hz [/Tex]
then according to the sampling theorem, the sampling frequency will be [Tex]2 \times f_{max} \leqslant 2 \times 10 \leqslant 20 Hz [/Tex].
Question 2: Sample the given signal at 60Hz
[Tex]x(t) = cos(2 \pi 50 t) [/Tex]
Solution:
We know that x[n] = [Tex]cos(2 \pi \frac{f_{max}}{f_{s}} n ) [/Tex]
Here, x[n] = [Tex](2 \pi \frac{50}{60} n) [/Tex]
Finally, we get the discrete time signal as: [Tex]x[n] = cos(2 \pi \frac{5}{6} n) [/Tex]
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