Nyquist Sampling Rate Determination
The Nyquist-Shannon sampling theorem states that to perfectly reconstruct a signal from its samples, the sampling frequency must be at least twice the highest frequency component present in the signal. This minimum sampling frequency is known as the Nyquist rate.
Applying the Nyquist Theorem
Let the maximum frequency component of the signal be denoted by $f_{max}$. According to the theorem, the minimum sampling frequency, $f_s$, required is:
$f_s \ge 2 f_{max}$The question provides the maximum frequency component in terms of angular frequency, $\omega_m$. The relationship between angular frequency ($\omega$) and frequency ($f$) is $\omega = 2\pi f$. Therefore, the maximum angular frequency is $\omega_m = 2\pi f_{max}$.
The sampling frequency in terms of angular frequency, $\omega_s$, must satisfy:
$\omega_s \ge 2 \omega_{max}$Substituting $\omega_{max}$ with the given $\omega_m$, the minimum sampling angular frequency ($\omega_s$) is:
$\omega_s \ge 2 \omega_m$Thus, the minimum sampling frequency (Nyquist sampling rate) needed is $2\omega_m$.
Important Questions from Physics
What is the colour of the light emitted by the Sun?
Lightning occur in the sky when two clouds:
With reference to street-lighting, how do sodium lamps differ from LED lamps?
1. Sodium lamps produce light in 360 degrees but it is not so in the case of LED lamps.
2. As street lights, sodium lamps have a longer life span than LED lamps.
3. The spectrum of visible light from sodium lamps is almost monochromatic while LED lamps offer significant colour advantages in street lighting.
Select the correct answer using the code given below.
Which one of the following is a reason why astronomical distances are measured in light-years?
In a pressure cooker, the temperature at which the food is cooked depends mainly upon which of the following?
1. Area of the hole in the lid
2. Temperature of the flame
3. Weight of the lid
Select the correct answer using the code given below.
