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Operating Manual-4048A digital signal processor
Butterworth
Butterworth filters individually are always -3dB at the displayed crossover frequency and are used because
they have a "maximally flat" passband and sharpest transition to the stopband. When a Butterworth HPF and LPF of
the same crossover frequency are summed, the combined response is 3dB. With 12dB per octave Butterworth
crossover filters, one of the outputs must be inverted or else the combined response will result in a large notch at the
crossover frequency.
Bessel
These filters, as implemented on the 4048A, are always -3dB at the displayed crossover frequency. Bessel
filters are used because they have a maximally flat group delay. Stated another way, Bessel filters have the most linear
phase response. When a Bessel HPF and LPF of the same crossover frequency are summed, the combined response is
+3dB for 12dB/oct and 18dB/oct Bessel filters, and -3dB for 24dB/oct Bessel filters. One of the outputs must be
inverted when using either 12dB/oct or 18dB/oct Bessel crossover filters or else the combined response will have a
large notch.
Linkwitz-Riley
The 12 dB/oct and 24dB/oct Linkwitz-Riley filters individually are always -6dB at the displayed crossover
frequency, however the 18dB/oct Linkwitz filters individually are always -3dB at the displayed crossover frequency.
The reason for this is that Linkwitz-Riley filters are defined in terms of performance criterion on the summing of two
adjacent crossover HPF and LPF filters, rather than defined in terms of the pole-zero characteristics of individual
filters. The 18dB/oct Linkwitz-Riley individually are 18dB/oct Butterworth filters in that they have Butterworth pole-
zero characteristics and also satisfy the criterion for Linkwitz-Riley filters.
When a Linkwitz-Riley HPF and LPF of the same displayed crossover frequency are summed, the combined
response is always flat. With 12dB/oct Linkwitz-Riley crossover filters, one of the outputs must be inverted or else the
combined response will have a large notch at the crossover frequency.