Question

A baseband signal g(t) with bandwidth 50 Hz is sampled at the Nyquist rate and the resulting sampled values are

{ −1 n=−1,−2
g(nTs​)= { 1​, n=1,2
{ 0 otherwise
Find g(0.015) from its reconstruction.

Answer 1

To find g(0.015) from the reconstructed baseband signal, we can use the Nyquist rate formula and linear interpolation.

Step-by-step explanation:

To find g(0.015) from the reconstructed baseband signal, we need to determine the value of g(t) at that specific time. Since g(t) is a baseband signal with a bandwidth of 50 Hz, it means the highest frequency component of the signal is 25 Hz. Therefore, we can use the Nyquist rate formula to determine the sampling rate:

Sampling rate = 2 * maximum frequency component = 2 * 25 = 50 samples per second

Since the samples are given at nTs intervals, where Ts is the sampling period, we have:

g(-1*Ts) = -1, g(1*Ts) = 1, and g(2*Ts) = 1

Using the linear interpolation formula, we can find the value of g(0.015) as:

g(0.015) = g(Ts) + 0.015/Ts * (g(2*Ts) - g(Ts)) = 1 + 0.015/0.01 * (1 - 1) = 1