It is easy to design an op amp circuit to simultaneously handle frequencies between 0.01 Hz and 100 kHz. When this is tried with a digital system, the computer becomes swamped with data.
If you want to use a digital filter you have to digitize the signal first. If you do that you have to make sure your input signal does not exceed the Nyquist frequency (to avoid ambiguousities). This is usually done by adding an "anti-aliasing" low-pass filter in front of your analog-to-digital converter.
If you convert back to analog using a digital-to-analog converter you need another low-pass filter to remove high frequency components caused by the fact that the output of the DAC is not smooth but time discrete (this results in a lot of steps).
Analog filters are the reference for designing a digital filter theoretically. If you design a discrete filter its much more easier to carry out the analysis and have control better control over your design. The general procedure to design a digital filter is: discritize your analog input which obeys Nyquist rate and then pass it to a filter. And revert back to analog mode if required. Refer digital filter design text for more details.
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