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 bi-linear 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 A-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 A-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 pass-band 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 pass-band width.
Gain		All pass filter at the specified gain
High-Pass Butterworth 1		Flat pass-band and stop-band response with a –10 dB / decade slope past the cutoff frequency
High-Pass Butterworth 2		Flat pass-band and stop-band response with a –20 dB / decade past the cutoff frequency
High-Pass Bessel 2		Maximally flat magnitude and phase in pass band 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 pass-band width.
High-Pass Chebyshev		Sharper transition band than Butterworth at the expense of ripple in the pass band.
Low-Pass Butterworth 1		Flat pass-band and stop-band response with a –10 dB / decade slope up to the cutoff frequency
Low-Pass Butterworth 2		Flat pass-band and stop-band response with a –20 dB / decade up to the cutoff frequency
Low-Pass Bessel 2		Maximally flat magnitude and phase in pass band 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 pass-band width.
Low-Pass Chebyshev		Sharper transition band than Butterworth at the expense of ripple in the pass band
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