Anti-aliasing filter in the frequency domain

An analog low-pass filter with sufficient attenuation at half the sampling frequency must precede the A/D converter in order to remove unwanted activity prior to digitizing.

A properly filtered signal can be digitized without producing aliasing artefacts. The digital representation is equivalent to the filtered input signal.

Note that the analog anti-aliasing filter can not be substituted by digital filtering after digitizing the signal!

Example: All activity exceeding half the sampling frequency was cut off before A/D conversion of the signal.