Question

A strain gauge is used to measure the strain on a vibrating beam which can vibrate up to a maximum frequency of 60 Hz. The strain gauge analog signal is converted in to a digital signal via an Analog to Digital Converter (ADC) in order to store the data on a computer hard drive. The engineer responsible for this measurement mistakenly selects a sampling frequency of 90 Hz for the ADC. (a) Determine the alias frequency due to the small sampling frequency. (b) Propose a sampling frequency that will not result into aliasing of the analog signal (make sure to provide your rationale for selecting this frequency)

Answer 1

The aliased frequency that is due to small sampling frequency is 675 Hz.

The proposed sampling frequency is 2f = 120

How to solve for the aliased frequency

The signal frequency that is given in the question is 60Hz

The sampling frequency is 90Hz

a. Using Nyquist frequency,

fn = 0.5*90Hz = 45Hz

The aliased frequency =  |n*fn - fs|

aliased frequency = |n*fn - fs|

We have  n >= 1/Fs = 17ms

Then the aliased frequency is = 17 x 45 - 90

= 675 Hz

b) The Nyquist sampling theorem

In order to avoid aliasing the sampling frequency, this has to be at least two times the highest frequency.

Therefore Fs =

2xF = 120Hz

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