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Explain sampling theorem for bandpass signals with proof. And also explain anti-aliasing filter?
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How to eliminate aliasing? (Antialiasing filter):

  • Aliasing can be completely eliminated by taking the following actions:

  • Use a bandlimiting low pass filter and pass the signal x (t) through it before sampling as shown in fig.

  • This filter has a cut-off frequency at $f_C$ =W, therefore it will strictly bandlimit the signal x (t) before sampling takes place. This filter is also called as Antialiasing filter or prealias filter.

enter image description here

enter image description here

  • Increase the sampling frequency $f_S$ to a great extend i.e. $f_S$>>>2W. Due to this, even though x (t) is not strictly bandlimited, the spectrums will not overlap. A guard band is created between the adjacent spectrums as shown in fig.

  • Thus aliasing can be prevented by,

  1. Using an Antialiasing or prealiasing filter and

  2. Using the sampling frequency $f_S$>2W.

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