A function has the form ft 5 sin 10 pi t 3 cos 40 pi t and

A function has the form f(t) = 5 sin 10 pi t + 3 cos 40 pi t and is sampled at a rate of 30 samples per second. What false alias frequency(ies) would you expect in the discrete data?

Solution

Consider the given function

f(t) = 5sin(10t) + 3cos(40t)

f(t) = 5sin( 2 5t) + 3cos(2 20t)

The function has frequencies of 5Hz and 20 Hz. The minimum sampling rate would then be 40 Hz to avoid aliasing. Sampling at 30 Hz would not produce aliases for the 5 Hz signal but would for the 20 Hz signal.

The alias frequency can be evaluated as follows :

f_a = 30 - 20 = 10 Hz

This is the difference between the sampling rate and the signal frequency