To satisfy the sampling theorem, a 100 Hz sine wave should be sampled at

Nyquist Sampling Theorem:

A continuous-time signal can be represented in its samples and can be recovered back when sampling frequency fs is greater than or equal to twice the highest frequency component of the message signal, i.e.

fs ≥ 2fm

Therefore when we want to convert continuous signals to discrete signals, the sampling must be done at the Nyquist rate.

Calculation:

With f_m = 100 Hz, the minimum sampling frequency will be:

fs = 2fm = 2 × 100

f_s = 200 Hz