The output of our digital filter is . We have not so far
provided a mechanism to input a series of samples of a time function
into the filter. An input is necessary if we wish to use the filter
in a traditional way--that is, to ``filter'' samples of a sound wave.
A number of possibilities exist for adding input samples to our
difference equation. We have chosen to add input samples to .
With this modification, Equations (2-3) become
We have compared both the sound and the spectrum of our filter output with the outputs of other filter difference equations realizations and we have detected no differences.
We may alternatively add the input samples
on the right-hand side of Eq.(13)
to obtain the transfer function