PurePath Console Digital Filter design uses analog filter design techniques and transposes them to the digital domain. The analog filters are represented in the S-domain. Through the bilinear transformation, these analog filters are converted from the S-domain to the digital Z-domain. In these filters, each pole of the filter provides a –6 dB per octave or –10 dB per decade slope in the frequency response. Each zero of the filter provides a +6 dB per octave or +10 dB per decade slope in the frequency response. Table 11-1 shows the S-domain transfer function of the PurePath Console filter design. Note that Q = f_c / Bandwidth, where f_c is the center frequency.

Table 11-1 PurePath™ Console Filter Transfer Function

FILTER TYPE	TRANSFER FUNCTION	WHEN TO USE
Band Pass		Filters a set of frequencies given by bandwidth and center frequency
Bass Shelf		Applies the specified gain at low frequency up to the specified cutoff frequency
Equalizer (Bandwidth)		Band-pass filter at the specified center frequency and passband width, with the specified gain
Equalizer (Q Factor)		Band-pass filter at the specified center frequency and quality factor, with the specified gain. The quality factor is the center frequency divided by the passband width.
Gain		All pass filter at the specified gain
High-Pass Butterworth 1		Flat passband and stopband response with a –10 dB / decade slope past the cutoff frequency
High-Pass Butterworth 2		Flat passband and stopband response with a –20 dB / decade past the cutoff frequency
High-Pass Bessel 2		Maximally flat magnitude and phase in passband with constant group delay at the expense of the greatest transition band
High-Pass Linkwitz Riley 2		Use in crossover systems with the same cutoff frequency for low pass and high pass. These filters overall gain is 0 dB at the crossover point.
High-Pass Variable Q 2		Second-order high-pass filter at the specified center frequency, gain and quality factor. The quality factor is the center frequency divided by the passband width.
High-Pass Chebyshev		Sharper transition band than Butterworth at the expense of ripple in the passband.
Low-Pass Butterworth 1		Flat passband and stopband response with a –10 dB / decade slope up to the cutoff frequency
Low-Pass Butterworth 2		Flat passband and stopband response with a –20 dB / decade up to the cutoff frequency
Low-Pass Bessel 2		Maximally flat magnitude and phase in passband with constant group delay at the expense of the greatest transition band
Low-Pass Linkwitz Riley 2		Use in crossover systems with the same cutoff frequency for low pass and high pass. These filters overall gain is 0 dB at the crossover point.
Low-Pass Variable Q 2		Second-order low-pass filter at the specified center frequency, gain and quality factor. The quality factor is the center frequency divided by the passband width.
Low-Pass Chebyshev		Sharper transition band than Butterworth at the expense of ripple in the passband
Notch		Filter or null a specific frequency
Phase Shift		Change the phase of a signal
Treble Shelf		Applies the specified gain at the high frequency past the specified cutoff frequency