## Solution

The sampling rate of the signal will change based on the desired measurement being the frequency or the shape of the signal. To accurately measure the frequency of a signal, we need a sampling rate of at least twice the highest frequency in the signal. This concept is known as Nyquist's theorem. To get the shape of the signal, you will need a sampling rate of at least ten times higher than the highest frequency in the signal.

- The equation for frequency measurement is found below:

- where:

*f*_{max} is the maximum resolvable frequency

*f*_{Nyquist} is the Nyquist frequency

*f*_{s} is the sampling frequency

To measure the shape of the signal, *f*_{s }will need to be divided by 10 instead of 2.

To get a full picture of the signal, sample for at least one full period of the waveform. The number of samples that corresponds to can be shown through frequency resolution:

The frequency resolution (df) is dictated by the acquisition time:

where:

*T* is the period of the signal

*N* is the number of samples acquired

*f*_{s} is the sampling frequency

For example, a signal with frequency 50 Hz, there will need to be at least 0.02(1/50) seconds of data for a full period of the signal. At a sampling rate of 100 Hz for a frequency measurement, N will be 5000.