Max nyquist sampling rate hznyquist sampling interval secondsthe signal the form sinc

Solved Step by Step With Explanation- Nyquist Sampling Rates

Questions

b) 5sinc² (2007)

c) sinc (2100лt) + sinc² (200πt)

To determine the Nyquist sampling rate and the Nyquist sampling interval for each signal, we need to understand the concept of Nyquist-Shannon sampling theorem. The Nyquist-Shannon sampling theorem states that to accurately reconstruct a continuous signal from its samples, the sampling rate must be at least twice the highest frequency present in the signal. Mathematically, the Nyquist sampling rate (fs) is given by:

fs = 2 * f_max

The signal is of the form sinc(ωt), where ω = 2100π. The highest frequency component in this signal is ω_max = 2100π. Therefore:

Nyquist sampling rate (fs) = 2100π = 2100π Hz

Nyquist sampling rate (fs) = 2 * 100π = 200π Hz

Nyquist sampling interval (Ts) = 1 / (200π) seconds

c) Answer

sinc(2100πt) + sinc²(200πt)

Nyquist sampling rate (fs) = 2100π = 2100π Hz

Nyquist sampling interval (Ts) = 1 / (2100π) seconds

The highest frequency component in sinc(200πt) is ω_max2 = 200π.

The highest frequency component after multiplication is ω_max_product = ω_max1 + ω_max2 = 2100π + 200π = 2300π.