Mathematics Versus Physics

The characteristics of an analog filter are directly attributable
to the physics of the device that implements it. In contrast,
the characteristics of a digital filter are only indirectly
attributable to the physics of the device that implements it.
A digital filter’s passband ripple, shape factor, stopband
attenuation, and phase characteristics are all functions of
the order and type of polynomial used to approximate the
ideal impulse response, the number of bits used in
performing the arithmetic, and the type of architecture used
to implement the arithmetic. Actual frequencies have no
meaning in a digital filter except in their relation to the
sampling frequency. This is because the impulse response is
generated as a function of z-1, the sample interval (the time
between samples). For a smaller shape factor, the order of
the filter and the number of bits in the arithmetic can be
increased. The only physical limitation is the amount of
arithmetic processing that can be integrated on a device or
devices given the filter order and the input sampling rate.