Basics: Filters

by Jim Aikin

From the very beginning, filters have been a vital part of how synthesizers make and shape sound. You don't have to hang around the pages of Keyboard for very long before you hear about the distinctive sound of those early Moog and Oberheim filters. The filter is arguably the most essential ingredient in the sound of a synth.

If you don't know what a filter sounds like, please feel free to turn on your synthesizer right now. Choose a sound that has a bright, buzzy tone. Go into edit mode, locate the filter cutoff parameter, and lower this parameter (bring it down toward zero) while playing notes on the keyboard. You should hear the sound get progressively darker and more muted as the cutoff is lowered.

If you don't hear this effect, check to make sure the filter is set to lowpass mode. You may also need to lower the filter envelope amount; on some synths, this envelope can push the filter cutoff up very high even when the cutoff parameter itself is turned all the way down.

For you to understand what you've just heard, we have to back up a step and talk a little about the nature of sound itself.

THE FREQUENCY SPECTRUM

Let's start from the very beginning: Sound consists of vibrations in the air or some other medium. If we take the broadest possible view of the whole idea, we can identify two kinds of vibrations — periodic and non-periodic. Non-periodic (random) vibrations are known by the technical term "noise." Periodic vibrations, on the other hand, are those in which there are repeating (that is, non-random) cycles.

Sound cycles are measured in terms of their frequency — that is, by the speed with which the cycles repeat. If, for example, the vibration repeats at a rate of 100 cycles per second, we say it has a frequency of 100 Hz. ("Hz" is an abbreviation for "Hertz," which is just another way of saying "cycles per second.") Curiously, we can also talk about the frequency spectrum of noise, but that discussion can get pretty technical, and it isn't relevant to this topic.

The lowest sounds that human ears can perceive as sound have a frequency of about 20Hz, while the highest sounds we can hear have a frequency of about 20,000 Hz. (The latter number is usually printed as 20 kHz. The abbreviation "kHz" stands for "kiloHertz," which is just another way of saying "thousand Hertz.")

Most sounds — both in nature and in synthesizers — are not pure tones that vibrate at a single frequency. Most sounds are composites in which a number of frequencies are blended together. This is even true of noise, by the way: We can talk about high-frequency noise or low-frequency noise, even though the noise waveform itself doesn't have repeating cycles. There's a lot more to the story than this, and we're not going to get into the whole business of overtones, the harmonic series, and Fourier analysis. At this point, what you need to understand is that the sound you're feeding into a filter, even when it presents itself to your ears as a single tone, will most likely consist of a blend of frequencies from low to high.

LOWPASS & HIGHPASS

A filter shapes the sound that it receives by reducing the loudness of certain frequencies. It can also boost the loudness of other frequencies. The boost is accomplished with a form of controlled feedback; we'll have more to say about this below.

A common music electronics term for "reducing the loudness" is attenuating. So when we say, for instance, that a filter attenuates the frequencies above 1 kHz, what we're saying is that whenever a sound passes through the filter, any vibrations within the sound that have a frequency of 1,000 Hz or greater are reduced in level. ("Amplitude" is another term for level. When we're talking about audio signals, amplitude is the same as loudness or volume.)

The most common type of synth filter is called a lowpass filter. A lowpass filter, as its name implies, allows low frequencies to pass through without being attenuated. But high frequencies are attenuated — that is, they're filtered out of the sound. It's a bit like looking at the world through rose-colored glasses. Red light passes through the lenses, but anything that's mainly green in color will look dark gray or black, because the green light is being filtered out.

"Low" and "high" are relative terms. We need to be more specific. A synthesizer filter has a parameter called the cutoff frequency. This parameter defines, at any given moment, what "low" and "high" mean. In a lowpass filter, frequencies below the cutoff frequency are low, so they pass through without being filtered. Frequencies above the cutoff are attenuated. In a highpass filter, it's the other way around: Frequencies below the cutoff are attenuated, while those above it pass through.

THE ROLLOFF SLOPE

The question is, if frequencies above the cutoff are being attenuated (that is, reduced in level), how much are they being attenuated? For technical reasons, it's not easy to build a filter that completely stops all frequencies above the cutoff while having no effect on those below. (Such a filter is called a "brick wall" filter, by the way. They're used in some digital audio devices, for reasons we'll get to next year.) In a synthesizer, the filter is designed to kick in gradually, in such a way that the amount of filtering depends on the frequency of the input. Frequencies near the cutoff are attenuated only slightly. The farther beyond the cutoff a particular sound is, the more it will be attenuated. This idea is illustrated in Figure 1.

(see figure #1)

You may have heard the terms "two-pole" and "four-pole" being slung around when filters are being discussed. The terms "12 dB per octave" and "24 dB per octave" are also common. The term "pole" is a way of describing the response of a filter mathematically. Without getting too technical, the more poles a filter has, the steeper its rolloff slope. Each pole creates 6 dB per octave of rolloff. A 24 dB-per-octave (four-pole) rolloff is twice as steep as a 12 dB-per-octave (two-pole) rolloff, as you can see in Figure 1.

The number of dB per octave is a measure of how much a frequency will be attenuated for each octave that it falls beyond the cutoff frequency. For reference, each musical octave represents a doubling of the frequency: A sound at 1,000 Hz, for instance, is exactly one octave higher than a sound at 500 Hz.

When it comes to shaping the tone in a synthesizer or sampler, the tool for the job is the filter. The classic analog synth sound would be impossible without filter resonance. If possible, you should turn on your synth, find the parameters we're covering, and experiment with them. This kind of hands-on experience is the best way to get a firm grasp of filtering (or anything else).

RESONANCE

First-generation analog synth filters incorporated a circuit that had the effect of boosting the frequencies near the cutoff frequency. This circuit created the type of filter response shown in Figure 2.

(see figure #2)

Several terms were used to describe this type of response; the most common were resonance, emphasis, and Q. Today the term "resonance" seems to have won out. Early digital filters didn't have a resonance control, but today's chips are fast enough to support the extra computation needed to model analog filter resonance, so just about all digital filters, whether they're found on conventional sample playback instruments or modeled "analog" synths, have analog-style resonance.

The sound of filter resonance is difficult to describe, but it's unmistakable. As the resonance is increased the sound will develop a pronounced peak. The character of this peak will depend on the cutoff frequency. If the cutoff is low, the sound will be "woofy" or "honky." With a higher cutoff, the sound will be more nasal, and with a high cutoff there will be a pronounced sizzle or a laser-like cutting edge.

Quite often, the cutoff will be swept up or down during the course of each note by an envelope generator. A quick envelope sweep sounds like a "blip," a medium-length one has a "wah" or "oww" sound, and a slow one has a broad, spacey quality. We'll have a lot more to say about envelope generators in the next couple of issues.

On some filters, especially true analog filters, the resonance amount can be set so high that the filter will self-oscillate. When it does this, you'll hear a whistling sound at the pitch of the cutoff frequency. Except when the filter is self-oscillating, you won't hear the resonant peak unless there is sound energy in the filter's input in that part of the frequency spectrum. For example, if you set the cutoff to 1,000 Hz and crank up the resonance, but the input waveform has no overtones above 500 Hz, you won't hear the resonance at all.

FILTER MODULATION

The filter cutoff frequency is such an important parameter that most synths offer several ways of modulating it. Just about all filters have their own envelope generators, as already noted. You'll also find an LFO input, which allows the LFO (low-frequency oscillator) to open and close the filter to create a rhythmic wah-wah effect.

The filter can usually be controlled by key velocity: This typically causes the filter to open up more as you play harder. When a lowpass filter opens up, more of the overtones are allowed through, so the sound gets brighter. This type of modulation mimics the effect of plucking a string or striking a drum harder: The sound of an acoustic instrument tends to get brighter as well as louder when it's played with more force.

Another important filter modulation source is the keyboard tracking amount. To explain why this is important, let's take a slightly artificial example, which is illustrated in Figure 3.

(see figure #3)

On the keyboard you're playing a waveform that has a fundamental and four rather prominent overtones. The waveform itself tracks the keyboard in the normal way. Perhaps when you play the low C, the fundamental is at 60 Hz, and the overtones are at 120, 180, 240, and 300 Hz. The cutoff frequency of the lowpass filter is set to, let's say, 600 Hz, so when you play the low C all of the overtones are below the cutoff frequency of the filter, and pass through the filter without being attenuated.

But what happens as you play up the keyboard? By the time you're playing Middle C, which is three octaves above the low C, the fundamental is at 480 Hz. The first overtone is at 960 Hz, the second at 1,440 Hz, and so on. But the cutoff frequency is still at 600 Hz. So all of the overtones will be filtered out: You'll only hear the fundamental. The tone color will be perceived as much less bright than before. Play clear up to the top of the keyboard, and you won't hear the fundamental either!

This may or may not be what you want. By setting the filter cutoff to track the keyboard at a 1:1 ratio, you can cause it to move up and down depending on which note you play on the keyboard. If the cutoff is at 600 Hz when you play low C, it will be at 4,800 Hz when you play Middle C (because each octave doubles the frequency), and all of the overtones of our example wave will still be heard.

MULTIMODE FILTERS

So far I've mostly been assuming you're using a lowpass filter. A highpass filter, as we discussed earlier, behaves in the opposite way: It removes low frequencies from the sound while allowing high frequencies to pass. A bandpass filter removes both the low and high frequencies from the input sound, allowing only a narrow band of frequencies right around the cutoff to pass through. A band-reject (notch) filter does just the opposite: It allows both the highs and the lows to pass through while removing a band of frequencies in the middle. These days, a synthesizer voice often features a single filter that can be switched from lowpass to bandpass or highpass mode as needed.

All of these filter modes have their uses, but lowpass filtering is the most important, because it most closely emulates what happens in an acoustic instrument.

This article presented courtesy of Keyboard Magazine.

Senior editor Jim Aikin has been programming synthesizers for more than 20 years, and he still thinks it's fun.