Let denote the desired reverberation time at radian frequency , and let denote the transfer function of the lowpass filter to be placed in series with the th delay line which is samples long. The problem we consider now is how to design these filters to yield the desired reverberation time. We will specify an ideal amplitude response for based on the desired reverberation time at each frequency, and then use conventional filter-design methods to obtain a low-order approximation to this ideal specification.
In accordance with Eq. (3.6), the lowpass filter in series with a length delay line should approximate
Taking of both sides gives
Now that we have specified the ideal delay-line filter in terms of its amplitude response in dB, any number of filter-design methods can be used to find a low-order which provides a good approximation to satisfying Eq. (3.9). Examples include the functions invfreqz and stmcb in Matlab. Since the variation in reverberation time is typically very smooth with respect to , the filters can be very low order.