Introduction to Computer Music: Volume One

3. Filters | page 2

Many filters come with a control called 'Q' or resonance (sometime called feedback, emphasis, quality or regeneration), 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. The lowpass filter on the left has a Q near 1, while the lowpass filter on the right has a Q of 5.

In the case of a bandpass filter, 'Q' is often used to express the sharpness (narrowness) or broadness of the band.

The bandpass formula for Q is:

Q = center frequency / bandwidth

A high value for 'Q' denotes a narrow filter. 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. Too much 'Q' can cause a howling noise or excessive feedback, particularly when energetic frequency components fall within 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. With series connections, it is important that some frequency components be passed from the first to subsequent filters for treatment, as is the case with the series or EQ peak/notch filters discussed on the previous page.

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 as pictured below.

Controllable parameters for filters usually include:

  • the initial frequency -- where the cutoff frequency starts before any controls are added to it
  • the attenuator -- how far the cutoff frequency will be swept by the control signal
  • the amount of Q or resonance

The most common mistake in using filters is to try filtering frequencies that are not present in the source signal. When learning how to use filters, use a spectrally rich signal like noise or a complex waveform (i.e., not a sine wave). The second most common mistake is to have the cutoff frequency set so low (for a lowpass) that all the signal is attenuated (no sound) or so high that no frequencies are affected (no filtering).

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