Equalization

By Scott Lehman

Part of the series of articles Effects Explained

Recovered from archive.org

Introduction

Equalization (EQ) is the process of boosting or cutting certain frequency components in a signal. The name originates from the application of trying to obtain a flat frequency response - no coloration. For example, when transmitting (analog) voice signals over long distances of wire, the high frequencies would be attenuated. By applying some equalization filters, this loss could be 'undone' so that the voice would sound more natural on the receiving end. Equalization is a very important tool in recording for bringing out an instrument's sound.

Tone Controls

The most common equalization system is probably the tone controls that can be found on most stereo systems. They provide a quick and easy way to adjust the sound to suit your tastes and partially compensate for the room. You will often find the controls labeled 'bass' and 'treble.' Each of those knobs controls a special type of filter called a shelving filter, or more precisely, a lowpass shelving filter and a highpass shelving filter respectively. The frequency responses for these two filters are shown in Figure 1. (Most filters have a gain that changes with frequency. The plots are of the frequency response magnitude, which shows you the gain at each frequency component. A gain greater than one will boost the signal and, if the gain is less than one, it cuts the sound.)

Figure 1: Frequency response of a lowpass and highpass shelving filter.

In most applications, lowpass and highpass filters try to totally remove a portion of the spectrum. For example, a lowpass filter tries to eliminate all the high frequencies. But with the shelving filters, we are not always trying to remove anything - we are just boosting or cutting one portion while leaving the rest unaffected.

The frequency where the frequency response makes the transition between the two levels of gain (even though it may be very gradual) is called the cutoff frequency. You could design a tone control that let you change this cutoff frequency in addition to the level of cut or boost, but this is usually fixed at the design stage and cannot be adjusted by the user.

In addition to bass and treble controls, you may find 'mid' controls, such as the 3-band equalizers commonly found on mixers. As you may guess, this affects frequencies 'in between' the highs and lows. This is often referred to as a peaking or bandpass filter. Again, it generally does not attempt to isolate certain frequencies, but rather boost or cut a small portion of the audio spectrum without affecting the other frequency bands. This type of filter generally does not have a defined cutoff frequency, but is instead defined by two other characteristics. The frequency at which the peaking filter is at its maximum gain (or when cutting the signal, the minimum gain) is called the center frequency. The other important characteristic is the bandwidth which basically means how wide the peaking filter is (how wide of a frequency range it affects). Generally you are only able to adjust the boost or cut and the center frequency and bandwidth are fixed.

Figure 2: The frequency response magnitude of a peaking filter.

Tone controls are a very simple equalization system since they only have two, or occasionally three filters. Because of this simplicity, the filters are typically connected together in series.

Graphic Equalizers

Graphic equalizers are a step up from tone controls in terms of flexibility and control and the operation is still quite simple. A graphic equalizer is simply a set of filters, each with a fixed center frequency that cannot be changed. The only control you have is the amount of boost or in each frequency band. This boost or cut is most often controlled with sliders. This interface is pretty intuitive because the frequency response of the equalizer resembles the positions of the sliders themselves. The sliders are a graphic representation of the frequency response, hence the name 'graphic' equalizer.

Some hi-fi systems incorporate graphic equalization, but their primary use is in sound reinforcement and 'tuning' rooms. For example, when performing in a venue, it is desirable to achieve a flat frequency response (or reasonably flat over a certain range) for the sound system. The resonances of a room and the loudspeakers can color the sound. With a graphic equalizer that covers most of the audio spectrum, you can counteract some of that coloration so that, even if you're playing in a different room every night, the sound of the performers and instruments is consistent. At the instrument level, simple stomp-box equalizers can be very useful for providing both a volume boost and tone change for soloing.

The actual implementation of a graphic equalizer is different from common tone controls. The bass and treble tone knobs on your stereo boost or attenuate only certain frequency bands while letting everything else pass unaffected, so we can chain them in series. A graphic equalizer uses a set of bandpass filters that are designed to completely isolate certain frequency bands. Figure 3 shows the frequency response of an ideal bandpass filter. In order to have control over the total audio spectrum, the filters need to be arranged in parallel, as shown in Figure 4. Each filter in the graphic equalizer has the same input. Their job is to allow only a small band of frequencies through.

Figure 3: The ideal bandpass filter completely blocks all frequencies outside of the passband. All practical filters have some ripple in the frequency response.

Figure 4: A diagram of a graphic equalizer with N bands of control.

Once the signal passes through the bandpass filters, you can now manipulate each of those frequency bands independently by inserting some kind of gain control. All those sliders on the front of the equalizer are the gain controls in each band.

The parallel arrangement of the filters, compared to the series connection with the tone controls, is used to reduce the more harmful effects of the filters. The magnitude frequency responses shown above do not tell us everything about the filter. The filter has a phase response as well. While phase distortion is desirable in some cases (such as using a phaser), in most sound reinforcement applications we want to ensure that the sound isn't colored at all if possible. For each filter you add in series, its phase response is added to the phase response of the other filters. The phase response also reveals how the filter actually delays the signal. If you have two or three filters in your tone control, chaining them in series might be fine but, with a 15 or 31 band graphic equalizer, distortion begins to add up and make a difference.

The center frequencies on graphics EQs are usually 'equally' spaced in octaves and not in linear frequency. For example, you can purchase graphic equalizers with one-third or one-sixth octave spacing. An octave is a factor of two (or 2^1), so a one octave spacing starting at 100 Hz would have center frequencies at 200 Hz, 400 Hz, 800 Hz and so on. An EQ with one-third octave spacing is based on a factor of 2^1/3, which is about 1.26. So with the first band at 100 Hz, our one-third octave equalizer would then have filters centered at 126 Hz, 159 Hz, 200 Hz, etc. There is an ISO standard for the preferred frequencies to use.

Parametric Equalizers

The parametric equalizer is the ultimate as far as flexibility goes but requires a little more care to use effectively. A single parametric EQ allows you to set not only the amount of boost or cut, but also the center frequency and the bandwidth. With experience, you can learn where to apply some boost to help an instrument cut through the mix or achieve a fuller sound. For feedback cancellation, a parametric EQ with a lot of cut (also called a notch filter) can be positioned right at the frequency where the feedback is occurring. To minimize the filter's effect on the rest of the sound, you can use a small bandwidth. You might be able to control the feedback with a graphic EQ as well but, if its bands are quite wide, you will be cutting more of the sounds that you do want to be heard. A similar application would be removing the 60 Hz hum in a recording (but you have to notch out the harmonics as well). The shelving and peaking filters are essentially specific types of parametric equalizers, at least mathematically, but most commercial products do have limits on parameters available.

Figure 5: A parametric equalizer allows you to specify the center frequency for the boost/cut and the bandwidth - how wide a frequency range it affects.

Other Notes

Presence

Many amplifiers have 'presence' knob as part of the tone control system. This is simply a boost in the mid to high frequencies, say from 2 to 6 kHz. This control is said to alter an instrument's sound on a recording to give the impression that it is actually in the room with the listener. It can also help an instrument stand out more in a mix.

Speaker Crossovers

Although speaker crossovers are not really a type of equalizer, we've pretty much covered the necessary concepts here. It's very difficult to design a speaker and cabinet that has a nice flat frequency response over most of the range of audible frequencies. If you narrow the frequency range a bit, the design process gets easier but, to get the entire audio range, you then need more than one speaker. For this reason, most hi-fi speakers contain more than one speaker, usually two or three. The biggest is for the low frequencies, called the woofer. The smallest, the tweeter, is designed to project high frequencies. The occasional third speaker is for mid-range. You can damage a speaker if you force it to produce the frequencies that it wasn't designed for, so speaker cabinets have a crossover built in.

A speaker crossover is a filter network that takes the incoming audio signal and splits it up into components that each of the speakers can handle. If you have a woofer/tweeter combination, then the crossover will need a lowpass and highpass filter (but not the shelving type of filters we talked about earlier. In a crossover, you want to completely isolate a band of frequencies). If the enclosure also has a midrange speaker, then you can add a bandpass filter that fits between the woofer and tweeter ranges.

Figure 6: A speaker crossover separates the signal into different frequency bands that the various speakers can handle.

To Learn More

For a technical look at various methods for computing parametric EQ coefficients, check out The Equivalence of Various Methods of Computing Biquad Coefficients for Audio Parametric Equalizers (PDF). Mathematica users can also download a Parametric EQ Notebook which walks you through some theory and design.

References

Handbook of Recording Engineering Eargle, John. New York: Van Nostrand Reinhold, 1992. (ISBN 0442222904)
The Technique of the Sound Studio Nisbett. New York: Hastings House. 1962. (ISBN 024051100X)
Introduction to Signal Processing Orfanidis, Sophocles. New Jersy, Prentice Hall. 1996. (ISBN 0132091720)