Question

If seismic signals of periods greater than 10 s are of interest, the minimum sampling frequency should be ________ Hz. (Round off to one decimal place).

Hint:

To avoid aliasing in signal processing, always sample at least twice the highest frequency in the signal.

Answer 1

Step 1: Sampling theorem. 
According to the Nyquist-Shannon sampling theorem, the minimum sampling frequency \(f_s\) should be at least twice the highest frequency component of the signal. 
Step 2: Relation between frequency and period. 
The frequency \(f\) is the reciprocal of the period \(T\): \[ f = \frac{1}{T} \] Given the period is greater than 10 s, the frequency corresponding to the maximum period (10 s) is: \[ f = \frac{1}{10} = 0.1 \, {Hz} \] Step 3: Minimum sampling frequency. 
To satisfy the Nyquist criterion, the minimum sampling frequency should be: \[ f_s = 2 \times 0.1 = 0.2 \, {Hz} \] Thus, the minimum sampling frequency should be \(0.2\) Hz.