Did you know?
Did you know that in signal processing, an analog input signal can be sampled to convert it into a digital signal? Let's consider an example.
Given an analog input signal x(t) = 1.5 + 0.5 sin(100t), where t represents time, and a sampling frequency fs of 2 kHz (2000 samples per second), we can determine the value of the sample x[20].
To find the value of x[20], we need to calculate the time at which the 20th sample occurs. As sampling starts at t = 0 and the sampling frequency is 2 kHz, each sample is taken every 1/fs seconds, which is 1/2000 seconds.
Therefore, the 20th sample occurs at 20 * (1/2000) seconds or 0.01 seconds.
Substituting this time value into the original analog signal expression, we get:
x[20] = 1.5 + 0.5 sin(100 * 0.01)
= 1.5 + 0.5 sin(1)
Evaluating sin(1) to be approximately 0.841, we find:
x[20] ≈ 1.5 + 0.5 * 0.841
≈ 1.92
Hence, the value of the sample x[20] is approximately 1.92.
