Question

6. A signal from a sensor has its largest amplitude component at 3 kHz frequency. A co-worker of yours said he sampled the signal with a data acquisition device at 5 kHz, and analyzed the frequency components of the sampled signal. He said that the largest amplitude component was not at 3 kHz. a. What frequency do you expect that your co-worker saw as the largest amplitude component in the sampled frequency spectrum? b. What could your co-worker have done to avoid being misled as he was?

Answer 1

Given: The signal from a sensor has its largest amplitude component at 3KHz frequency. Which means that the maximum frequency with which the sensor can generate the output is 3KHz (i.e., the signal from a sensor is bandlimited to 3KHz)

Solution:

A. The co-worker will see the largest amplitude component at 2.5KHz. Please refer to the justification given below:

As the maximum frequency of the signal is 3KHz, the minimum sampling frequency required to sample the signal should be 6KHz according to Nyquist criteria (i.e., twice the maximum frequency = 2*3KHz).

In the given question, co-worker used the sampling frequency of 5KHz to sample the signal which is less than the frequency specified by the Nyquist criteria (i.e., 6KHz). Therefore in the sampled signal, the co-worker will see the largest amplitude component at 2.5KHz (i.e., half of the sampling frequency used = 5KHz/2) instead of 3KHz.

B. The co-worker should have sampled the signal at a frequency greater than or equal to the frequency specified by the Nyquist criteria i.e., 6KHz. This way the largest component will be seen at 3KHz (i.e., half of the sampling frequency used =6KHz/2)