Calculate aliasing of $x_a(t) = \cos{(2\pi300t)} + \cos(2\pi600t)$ when sampled with $F_s = 1000$

1. How do you calculate aliasing?
2. How do you calculate sampling rate to avoid aliasing?
3. What is aliasing in sampling theory?
4. What is aliasing in FFT?

How do you calculate aliasing?

where f_N is the folding frequency, f_s is the signal frequency, and m is an integer such that f_a < f_N. For example, suppose that f_s = 65 Hz, f_N = 62.5 Hz, which corresponds to 8-ms sampling rate. The alias frequency then is f_a = |2 × 62.5 − 65| = 60 Hz.

How do you calculate sampling rate to avoid aliasing?

According to the Shannon Sampling Theorem, use a sampling frequency at least twice the maximum frequency component in the sampled signal to avoid aliasing.

What is aliasing in sampling theory?

Aliasing is the effect of new frequencies appearing in the sampled signal after reconstruction, that were not present in the original signal. It is caused by too low sample rate for sampling a particular signal or too high frequencies present in the signal for a particular sample rate.

What is aliasing in FFT?

Recognizing Aliasing in the FFT

It is common to have acquired signals with a fundamental frequency less than half the sample rate, but the harmonics of that signal may be greater than half the sample rate and they will alias. This shows up in the FFT as frequencies that fold back into the display.