Basic Analog Filter Information
Filters are normally used to remove specific frequency components from a complex sound, hence the technique is often called subtractive synthesis. This is not an entirely accurate description, since filters may also add energy to portions of the spectrum. Most analog synthesizers of the '70's and '80's came with the following four basic filter types (they are carried forward today on digital instruments with many variations):
Looking at the graphs above, you will notice that most filters do not suddenly cut off sound at a specific frequency. Rather, they "roll off" the frequencies gradually, for example 12 dB's per octave. We specify a cutoff frequency (c.o.f.) at the point a specific frequency component would have lost approximately half the amplitude (-3 dB) of unaffected frequencies. A common synthesis technique is to sweep the cutoff frequency up or down to provide a 'spectral shape' to a sound over time. Cutoff frequencies are usually controlled by an envelope generator or an oscillator (timbre modulation).
Many filters come with a control called 'Q' or resonance, which feeds a portion of the output back into the input. In the case of a lowpass filter, increasing the 'Q' would cause any frequencies present near the cutoff frequency to be emphasized. This makes sweeping the filter even more apparent.
Too much 'Q' can cause a howling noise or excessive feedback.
In the case of
a bandpass filter, 'Q' is often used to express the sharpness
(narrowness) or broadness of the band. The formula is:
Q = center frequency / bandwidth.
A high value for Q denotes a narrow filter. It also indicates
that as one sweeps a filter higher, the bandwidth needs to widen
to maintain the same value of Q. As the band narrows, energy
previously spread out over a broader range is concentrated on a
smaller range of frequencies and can be very intense when a
strong component of the input signal is centered on the passband.
Filters can be combined in various ways for various purposes.
Filters can be connected in a series or cascade, so that the output of one is fed into the next. This arrangement steepens the rolloff and narrows the passband if the center frequencies are identical.
Filters
can be connected in parallel so the a single
source is fed independently into several filters whose
outputs are then summed. This arrangement is ideal for
creating multiple areas of resonance or formants.
For example, a complex sound source can be shaped to
sound like a soprano's vowel 'A' with multiple bandpass
filters. Their frequencies (Hz), relative amplitude (dB)
and bandwidth (Bw in Hz) would be:
| Freq | dB | Bw |
| 800 | 0 | 80 |
| 1150 | -6 | 90 |
| 2900 | -32 | 120 |
| 3900 | -20 | 130 |
| 4950 | -50 | 140 |
Areas of resonance are referred to as poles whereas areas of non-resonance are referred to as zeroes. A four-pole filter, therefore, might consist of four bandpass filters connected in parallel.
Controllable
parameters for filters usually include:
The most common mistake in using filters is to try filtering
frequencies that are not present in the source signal. Instead, use a rich
signal like noise or a complex waveform rich in partials (i.e.,
not a sine wave). The second most common mistake is to have the
cutoff frequency set so low that all the signal is attenuated (no
sound) or so high that no frequencies are affected (no
filtering).
This document is prepared and maintained by the
Indiana University School of Music
Center for Electronic and Computer Music
Prof. Jeffrey Hass
Last updated: 14 October 2001
URL: http://www.indiana.edu/~emusic/filters.htm
Comments: cecm@indiana.edu
†Copyright 1995-2001, Jeffrey Hass and The Trustees of
Indiana University
