DAFX: Digital Audio Effects, Second Edition

2.2 Basic Filters

2.2.1 Filter Classification in the Frequency Domain

The various types of filters can be defined according to the following classification (see Figure 2.1):

• Lowpass (LP) filters select low frequencies up to the cut-off frequency fc and attenuate frequencies higher than fc. Additionally, a resonance may amplify frequencies around fc.
• Highpass (HP) filters select frequencies higher than fc and attenuate frequencies below fc, possibly with a resonance around fc.
• Bandpass (BP) filters select frequencies between a lower cut-off frequency fcl and a higher cut-off frequency fch. Frequencies below fcl and frequencies higher than fch are attenuated.
• Bandreject (BR) filters attenuate frequencies between a lower cut-off frequency fcl and a higher cut-off frequency fch. Frequencies below fcl and frequencies higher than fch are passed.
• Allpass filters pass all frequencies, but modify the phase of the input signal.

Figure 2.1 Filter classification.

The lowpass with resonance is very often used in computer music to simulate an acoustical resonating structure; the highpass filter can remove undesired very low frequencies; the bandpass can produce effects such as the imitation of a telephone line or of a mute on an acoustical instrument; the bandreject can divide the audible spectrum into two bands that seem to be uncorrelated.

2.2.2 Canonical Filters

There are various ways ...