The following frequencies are present in a continuous time signal: 20 Hz, 60 Hz, 110 Hz. The signal is sampled in discrete time. To avoid aliasing, the signal should be sampled at a rate (Hz) of at least most nearly:
A. 40
B. 120
C. 160
D. 220
The following frequencies are present in a continuous time signal: 20 Hz, 60 Hz, 110 Hz. The signal is sampled in discrete time. To avoid aliasing, the signal should be sampled at a rate (Hz) of at least most nearly:
A. 40
B. 120
C. 160
D. 220
1 Answer
James Dowd
Updated on December 29th, 2020Aliasing occurs when multiple signals are sampled in discrete time and, due to the sample frequency, the signals are indistinguishable of the original continuous time sinusoids.
In order to sample a continuous time signal in discrete time and avoid aliasing, we must follow the Nyquist Sampling Theorem. It states that aliasing can be prevented if we choose a sampling rate over twice as fast as its highest frequency component.
Once we are aware of this theorem, our problem becomes straight forward. 110 Hz is the highest frequency present in our continuous time signal. Therefore:
We must sample at least at a rate of 220Hz (Answer D) to avoid aliasing.
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