A simplified digital implementation of a fourth order Linkwitz-Riley crossover network is provided using approximations and transformations of the classical form. The approximation is particularly beneficial when the crossover frequency is low relative to the digital sampling rate, such as when an audio stream is split between bass and treble at about 30-300 Hz and the sampling frequency is about 100 times the cutoff frequency or higher. Rather than merely cascading two sets of second order filters, such as Butterworth filters, a fourth order transfer function is more directly implemented. Conventional transfer functions are simplified through approximations resulting in the elimination of all except one parameter, c, which is a linear function of the cutoff frequency. Additionally, multipliers are moved in line with the integrator elements. A modulator may be inserted in the processing path at the output of each integrator element if limited fixed precision of the operators is desired while maintaining high performance. A crossover of the inventive design requires a fewer number of state variables, multipliers and adders.
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