Question

The signal; x(t) = 3 cos 100πt is sampled at the rate, 75 Hz, what is the discrete-time signal?

Answer 1

Given

x(t) = 3cos100πt

For a signal x(t) sampled with a sampling interval T_s, the discrete sequence can be written as 

\(x(n) = x(t)|_{t=nT_s}\)

T_s = sampling interval

\(f_s = 75Hz\)

\(T_s = \frac 1{75}\)

\(x(n) = 3\cos 100\pi (\frac n{75})\)

\(x(n) = 3\cos (\frac{4\pi n}3)\)