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
On the basis of which principle does soap clean surfaces?
Which one of the following devices is used to measure atmospheric pressure?
Which one of the following energy is stored in the links between the atoms?
Who among the following has explained the phenomenon of photoelectric effect?
What special name is given to the frictional force exerted by a fluid?
