Did you know?
Did you know that in signal processing, sampling is the process of converting a continuous-time signal into a discrete-time signal? In this case, an analog input signal x(t) = 1.5 + 0.5 sin(100t) is being sampled with a sampling frequency of 2 kHz.
To determine the value of the sample x [20], we need to calculate the value of the signal at t = 0.01 seconds (since 20 samples are equivalent to 20/2000 = 0.01 seconds).
Plugging in t = 0.01 in the equation x(t) = 1.5 + 0.5 sin(100t), we get:
x(0.01) = 1.5 + 0.5 sin(1)
This simplifies to:
x(0.01) = 1.5 + 0.5 (sin(1))
Calculating sin(1) ≈ 0.84, we find:
x(0.01) = 1.5 + 0.5 (0.84)
x(0.01) = 1.5 + 0.42
x(0.01) = 1.92
Therefore, the value of the sample x [20] is 1.92.
Now, to determine the sampling period Ts, we know that the sampling frequency fs = 2 kHz, which implies that Ts = 1/fs.
Plugging in the value of fs into the equation, we get:
Ts = 1/2000 Hz
Ts = 0.0005 seconds
So, the sampling period is 0.0005 seconds.
Sampling at a higher frequency allows for more accuracy in representing the original continuous signal, but it also requires more storage and processing power. Balancing the sampling frequency is crucial in capturing the necessary information from the analog signal while maintaining efficiency in digital systems.
