What is targeted sampling in research studies?

I would like to sample the signal Xa(t) =1+cos(10 *pi*t) using sampling frequency fs=8 Hz. How can I calculate this?

ANSWER:

Your signal has a frequency component of 5hz (from the equation: 2*pi*f*t = 10*pi*t, therefore f=5). The Nyquist rate for this signal (the minimum sampling rate required to reconstruct the signal) is then 10Hz, and even at that rate the amplitude of the sampled signal will be reduced unless you can somehow synchronize the sampling with the peaks/troughs of the cosine signal.

If you sample at 8Hz you will not be able to reconstruct the signal at all.