# Cost of FIR Filtering

Although it seems we have a workable filter to identify the modem answer tone,
our work is not done until we evaluate the cost of this solution. Recall
that an FIR filter with *M+1* coefficients requires *M+1* multiplications
and *M* additions to calculate each output sample (at least, if the convolution
sum is implemented directly).

In a modem, this filter would typically be implemented by a programmable DSP processor. The FIR realization may be too costly, both in the number of cycles required and in the amount of memory needed to store the coefficients and the data in the delay line. Fortunately, less expensive solutions exist.