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An analog input signal x(t) = 1.5 + 1.5sin(5t) is

sampled with 1 kHz sampling frequency fs.
Assuming that sampling starts at t = 0 compute the
value of the sample x[6]. Show your work.

x[6] = 1.5 + 1.5sin(5*6/1000)

= 1.5 + 1.5sin(0.03)
= 1.5 + 1.5(0.0299957)
= 1.5 + 0.4499855
= 1.9499855

Did you know?

Did you know that in digital signal processing, the process of sampling involves converting analog signals into discrete-time signals? In the given example, an analog input signal is sampled with a frequency of 1 kHz, meaning that 1000 samples are taken per second. To compute the value of the sample x[6], we need to determine the time at which the sixth sample is taken. Since the sampling starts at t = 0, we can calculate the time using the formula: t = n / fs Where: t is the time at which the sample is taken, n is the sample number (in this case, 6), and fs is the sampling frequency (1 kHz or 1000 samples per second). Plugging in the values, we have: t = 6 / 1000 We can find the value of the sample x[6] by substituting this time value into the given formula for the analog input signal x(t): x(t) = 1.5 + 1.5sin(5t) After calculating the value of x(t), we can determine x[6] as the corresponding sampled value at time t. By understanding the concept of sampling and performing these calculations, we can effectively convert continuous analog signals into discrete digital signals for digital signal processing.