Equalization (audio)
Encyclopedia
Equalization is the process commonly used in sound recording and reproduction
to alter the frequency response
of an audio system using linear filter
s. Most hi-fi (stereo) equipment uses relatively simple filters to make bass and treble
adjustments. Graphic and parametric equalizers have much more flexibility in tailoring the frequency content of an audio signal. An equalizer is the circuit or equipment used to achieve equalization.
Equalizers are used in recording studio
s, broadcast studios, and live sound reinforcement to correct the response of microphone
s, instrument pick-ups
, loudspeakers, and hall acoustics
. Equalization may also be used to eliminate unwanted sounds, make certain instruments or voices more prominent, enhance particular aspects of an instrument's tone, or combat feedback
(howling) in a public address
system.
Graphic equalizers are often included in consumer audio equipment and software which plays music on home computers. Parametric equalizers require more expertise than graphic equalizers, and they can provide more specific compensation or alteration around a chosen frequency. This may be used in order to remove (or to create) a resonance, for instance.
The concept of equalization was first applied in correcting the frequency response
of telephone lines using passive networks; this was prior to the invention of electronic amplification. Initially equalization was used to "compensate for" (i.e. correct) the uneven frequency response of an electric system by applying a filter having the opposite response, thus restoring the fidelity
of the transmission
. A plot of the system's net frequency response would be flat, as its response to all frequencies would literally be equal. Hence the term "equalization."
Much later the concept was applied in audio engineering
to adjust the frequency response in recording, reproduction, and live sound reinforcement system
s. Sound engineers correct the frequency response of a sound system so that the frequency balance of the music as heard through speakers better matches the original performance picked up by a microphone
. Audio amplifiers
have long had filters or controls to modify their frequency response. These are most often in the form of variable bass and treble controls (shelving filters), and switches to apply low-cut or high-cut filters for elimination of low frequency "rumble" and high frequency "hiss" respectively.
Graphic equalizers and other equipment developed for improving fidelity have since been used by recording engineers to modify frequency responses for aesthetic reasons. Hence in the field of audio electronics the term "equalization" is now broadly used to describe the application of such filters regardless of intent. This broad definition therefore includes all linear filter
s at the disposal of a listener or engineer.
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The responses of linear filter
s are mathematically described in terms of their transfer function
or, in layman's terms, frequency response
. A transfer function can be decomposed as a combination of first order responses and second order responses (implemented as so-called biquad sections). These can be described according to their so-called pole
and zero
frequencies, which are complex numbers in the case of second-order responses.
A first order filter can alter the response of frequencies above and below a point. In the transition region the filter response will have a slope of up to 6 dB
per octave
. The bass and treble controls in a hi-fi system are each a first order filter in which the balance of frequencies above and below a point are varied using a single knob. A special case of first order filters is a first order high-pass or low-pass filter in which the 6 dB per octave cut of low or high frequencies extends indefinitely. These are the simplest of all filters to implement individually, requiring only a capacitor and resistor.
Second order filters are capable of resonance
(or anti-resonance) around a particular frequency. The response of a second order filter is specified not only by its frequency but its Q
; a higher Q corresponds to a sharper response (smaller bandwidth) around a particular center frequency. For instance, the red response in the accompanying image cuts frequencies around 100 Hz with a higher Q than the blue response which boosts frequencies around 1000 Hz. Higher Q's correspond to resonant behaviour in which the half-power or -3 dB bandwidth, BW, is given by:
where F0 is the resonant frequency of the second order filter. BW is the bandwidth expressed in the same frequency unit that F0 is. Low Q filter responses (where Q < ) are not said to be resonant and the above formula for bandwidth does not apply.
It is also possible to define the Q of a band-pass function as:
,
where B is the bandwidth in octaves.
It should be noted that a second-order filter response with Q of less than 1/2 can be decomposed into two first-order filter functions, a low-cut and a high-cut (or boost). Of more interest are resonant filter functions which can boost (or cut) a narrow range of frequencies. In addition to specifying the center frequency F0 and the Q, the specification of the filter's zeros
determines how much that frequency band will be boosted (or cut). Thus a parametric equalizer section will have three controls for its center frequency F0, bandwidth or Q, and the amount of boost or cut.
The range of second-order filter functions is important because any analog filter function can be decomposed into a (usually small) number of these (plus, perhaps, simpler first order responses). These are implemented directly by each section of a parametric equalizer where they are explicitly adjusted. And each element of a graphic equalizer based on a filter bank
includes one such element whose Q is not adjustable by the user.
is a filter that passes higher frequencies
well but attenuates
lower frequency components. A low-pass filter
passes low-frequency components of signals while attenuating higher frequencies. In audio applications these are frequently termed "low cut" and "high cut" respectively, to emphasize their effect on the original signal. For instance, sometimes audio equipment will include a switch labeled "high cut" or described as a "hiss filter" (hiss being high frequency noise). In the times of phonograph
s many stereos would include a switch to introduce a high-pass (low cut) filter, often called a "rumble filter," to eliminated infrasonic frequencies.
A high shelf or "treble control" will have a frequency response |H(f)| whose square is given by:
where fp and fz are called the pole and zero frequencies, respectively. Turning down the treble control increases fz so that frequences higher than fp are attenuated. Turning up the treble control increases fp so that frequences higher than fz are boosted. Setting the treble control at the center sets fz = fp so that |H(f)|2=1 and the circuit has no effect. At most, the slope of the filter response in the transition region will be 6 dB per octave (thus a doubling of signal voltage and a consequent quadrupling of signal power for every doubling of frequency).
Similarly the response of a low shelf or "bass control" can be represented as
In this case the inclusion of the leading factor simply indicates that the response at frequencies much higher than fz or fp is unity and that only bass frequencies are affected. Note that a high shelve in which fz is set to infinity or a low shelve response in which fz is set to zero implements a first order low-pass or high-pass filter respectively. However usual tone controls have a more limited range, since the purpose isn't to eliminate any frequencies but only to achieve a greater balance when, for instance, the treble is lacking and the sound isn't crisp. Since the range of possible responses from shelving filters is so limited, they are considered quite inadequate for equalization tasks among audio engineers.
In the graphic equalizer, the input signal is sent to a bank of filters
. Each filter passes the portion of the signal present in its own frequency range or band. The amplitude passed by each filter is adjusted using a slide control to boost or cut frequency components passed by that filter. The vertical position of each slider thus indicates the gain applied at that frequency band, so that the knobs resemble a graph of the equalizer's response plotted versus frequency.
The number of frequency channels (and therefore each one's bandwidth) affects the cost of production and may be matched to the requirements of the intended application. A car audio
equalizer might have one
set of controls applying the same gain to both stereo channels for convenience, with a total of five to ten frequency bands. On the other hand, an equalizer for professional live sound reinforcement typically has some 25 to 31 bands, for more precise control of feedback problems and equalization of room modes. Such an equalizer (as shown above) is called a 1/3-octave equalizer (spoken informally as "third-octave EQ") because the center frequency of its filters are spaced one third of an octave
apart, three filters to an octave. Equalizers with half as many filters per octave are common where less precise control is required—this design is called a 2/3-octave equalizer.
Graphic equalizers are sometimes used by stereo owners to obtain a smiley face curve
(also known as "mid scoop") in which the lower and higher frequency channels are boosted relative to the midrange frequencies. This results in a graphical pattern resembling a cartoon "smile."
Parametric equalizers are multi-band variable equalizers which allow users to control the three primary parameters: amplitude
, center frequency
and bandwidth. The amplitude of each band can be controlled, and the center frequency can be shifted, and bandwidth ("Q
") can be widened or narrowed. Parametric equalizers are capable of making much more precise adjustments to sound than other equalizers, and are commonly used in sound recording and live sound reinforcement
.
Parametric equalizers are also sold as standalone outboard gear
units.
A variant of the parametric equalizer is the semi-parametric equalizer, also known as a sweepable filter. It allows users to control the amplitude and frequency, but uses a pre-set bandwidth of the center frequency. In some cases, semi-parametric equalizers allow the user to select between a wide and a narrow preset bandwidth.
Equalizers can correct problems posed by a room's acoustics
, as an auditorium will generally have an uneven frequency response especially due to standing waves and acoustic dampening. The frequency response
of a room may be analyzed using a spectrum analyzer
and a pink noise
generator for instance. Then a graphic equalizer can be easily adjusted to compensate for the room's acoustics. Such compensation can also be applied to tweak the sound quality of a recording studio
in addition to its use in live sound reinforcement system
s and even home hi-fi systems.
During live events where signals from microphones are amplified and sent to speaker
systems, equalization is not only used to "flatten" the frequency response but may also be useful in eliminating feedback
. When the sound produced by the speakers is picked up by a microphone, it is further reamplified; this recirculation of sound can lead to "howling" requiring the sound technician to reduce the gain
for that microphone, perhaps sacrificing the contribution of a singer's voice for instance. Even at a slightly reduced gain, the feedback will still cause an unpleasant resonant sound around the frequency at which it would howl. But because the feedback is troublesome at a particular frequency, it is possible to cut the gain only around that frequency while preserving the gain at most other frequencies. This can best be done using a parametric equalizer tuned to that very frequency with its amplitude control sharply reduced. By adjusting the equalizer for a narrow bandwidth (high Q), most other frequency components will not be affected. The extreme case when the signal at the channel's center frequency is completely eliminated is known as a notch filter.
An equalizer can be used to correct or "flatten" the frequency response of speakers rather than designing the speaker itself to be equalized. For instance, the highly regarded Bose 901 speaker system doesn't use separate woofers and tweeters to cover the bass and treble frequencies, but includes 9 full-range
drivers more akin to what one would find in a table radio. However this speaker system is sold with an active equalizer designed to correct the poor frequency balance of those drivers. That equalizer must be inserted into the amplifier system so that the amplified signal that is finally sent to the speakers has its response increased at the frequencies where the response of these drivers falls off, producing a high fidelity reproduction regardless.
Tone controls (usually designated "bass" and "treble") are simple shelving filters included in most hi-fi equipment for gross adjustment of the frequency balance. The bass control may be used, for instance, to increase the drum and bass parts at a dance party, or to reduce annoying bass sounds when listening to a person speaking. The treble control might be used to give the percussion a sharper or more "brilliant" sound, or can be used to cut such high frequencies when they have been overemphasized in the program material or simply to accommodate a listener's preference.
A "rumble filter" is a high pass (low cut) filter with a cutoff typically in the 20 to 40 Hz range; this is the low frequency end of human hearing. This prevents the wasteful amplification of very low frequencies which aren't going to be effectively reproduced by typical speakers, and which moreover can cause damage to speakers when they "bottom out."
A crossover network
is a system of filters designed to direct electrical energy separately to the woofer
and tweeter
of a 2-way speaker system (and also to the mid-range speaker
of a 3-way system). This is most often built into the speaker enclosure and hidden from the user. However in bi-amplification, these filters operate on the low level audio signals, sending the low and high frequency components to separate amplifiers which connect to the woofers and tweeters respectively.
Equalization is used in a reciprocal manner in certain communication channels and recording technologies. The original music is passed through a particular filter to alter its frequency balance, followed by the channel or recording process. At the end of the channel or when the recording is played, a complementary filter is inserted which precisely compensates for the original filter and recovers the original waveform. For instance, FM broadcast uses a pre-emphasis filter to boost the high frequencies before transmission, and every receiver includes a matching de-emphasis filter to restore it. The white noise
that is introduced by the radio is then also de-emphasized at the higher frequencies (where it is most noticeable) along with the pre-emphasized program, making the noise less audible. Tape recorder
s used the same trick to reduce "tape hiss" while maintaining fidelity. On the other hand, in the production of vinyl records
, a filter is used to reduce the amplitude of low frequencies which otherwise produce large amplitudes on the tracks of a record. Then the groove can take up less physical space, fitting more music on the record. The preamp attached to the phono cartridge has a complementary filter boosting those low frequencies following the standard RIAA equalization
curve.
allow users to make broad, overall adjustments to the sound. With the science of audio engineering
came the demand for more flexible tools such as graphic equalizers, although these were still limited in terms of their flexibility due to the width of the channels supplied.
The Langevin Model EQ-251A was the first equalizer to use slide controls. It featured two passive equalization sections, a bass shelving filter, and a pass band filter. Each filter had switchable frequencies and used a 15-position slide switch to adjust cut or boost. The first true graphic equalizer was the type 7080 developed by Art Davis's Cinema Engineering. It featured 6 bands with a boost or cut range of 8 dB
. It used a slide switch to adjust each band in 1 dB steps. Davis's second graphic equalizer was the Altec Lansing
Model 9062A EQ. In 1967 Davis developed the first 1/3 octave variable notch filter set, the Altec-Lansing "Acousta-Voice" system.
With the development of active R-C filters
using op-amps in the 1960s, it became possible to create equalizers capable of adjusting critical frequency as well as bandwidth (or Q) and amplitude coefficient. In 1972 George Massenburg
introduced parametric filtering based on such technology. Most channel equalization on mixing console
s made thereafter were either semi or fully parametric equalizers.
In the late 1990s and in the 2000s, parametric equalizers became increasingly available as Digital Signal Processing
(DSP) equipment, usually in the form of plug-ins for various digital audio workstations. Standalone outboard gear
versions of DSP parametric equalizers were also quickly introduced after the software versions and are typically called Digital Parametric Equalizers.
Sound recording and reproduction
Sound recording and reproduction is an electrical or mechanical inscription and re-creation of sound waves, such as spoken voice, singing, instrumental music, or sound effects. The two main classes of sound recording technology are analog recording and digital recording...
to alter the frequency response
Frequency response
Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input...
of an audio system using linear filter
Linear filter
Linear filters in the time domain process time-varying input signals to produce output signals, subject to the constraint of linearity.This results from systems composed solely of components classified as having a linear response....
s. Most hi-fi (stereo) equipment uses relatively simple filters to make bass and treble
Treble (sound)
Treble refers to tones of high frequency or range. In music this corresponds to high notes, and for this reason the treble clef is often used for instruments with higher pitch. Examples of treble sounds are guitar tones, female voice , young boy voice, etc. They have frequencies above 9 KHz. Treble...
adjustments. Graphic and parametric equalizers have much more flexibility in tailoring the frequency content of an audio signal. An equalizer is the circuit or equipment used to achieve equalization.
Equalizers are used in recording studio
Recording studio
A recording studio is a facility for sound recording and mixing. Ideally both the recording and monitoring spaces are specially designed by an acoustician to achieve optimum acoustic properties...
s, broadcast studios, and live sound reinforcement to correct the response of microphone
Microphone
A microphone is an acoustic-to-electric transducer or sensor that converts sound into an electrical signal. In 1877, Emile Berliner invented the first microphone used as a telephone voice transmitter...
s, instrument pick-ups
Pickup (music technology)
A pickup device is a transducer that captures mechanical vibrations, usually from suitably equipped stringed instruments such as the electric guitar, electric bass guitar, Chapman Stick, or electric violin, and converts them to an electrical signal that is amplified, recorded, or broadcast.-...
, loudspeakers, and hall acoustics
Room acoustics
Room acoustics describes how sound behaves in an enclosed space.The way that sound behaves in a room can be broken up into roughly four different frequency zones:...
. Equalization may also be used to eliminate unwanted sounds, make certain instruments or voices more prominent, enhance particular aspects of an instrument's tone, or combat feedback
Audio feedback
Audio feedback is a special kind of positive feedback which occurs when a sound loop exists between an audio input and an audio output...
(howling) in a public address
Public address
A public address system is an electronic amplification system with a mixer, amplifier and loudspeakers, used to reinforce a sound source, e.g., a person giving a speech, a DJ playing prerecorded music, and distributing the sound throughout a venue or building.Simple PA systems are often used in...
system.
Graphic equalizers are often included in consumer audio equipment and software which plays music on home computers. Parametric equalizers require more expertise than graphic equalizers, and they can provide more specific compensation or alteration around a chosen frequency. This may be used in order to remove (or to create) a resonance, for instance.
Terminology
Frequency response
Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input...
of telephone lines using passive networks; this was prior to the invention of electronic amplification. Initially equalization was used to "compensate for" (i.e. correct) the uneven frequency response of an electric system by applying a filter having the opposite response, thus restoring the fidelity
High fidelity
High fidelity—or hi-fi—reproduction is a term used by home stereo listeners and home audio enthusiasts to refer to high-quality reproduction of sound or images, to distinguish it from the poorer quality sound produced by inexpensive audio equipment...
of the transmission
Transmission (telecommunications)
Transmission, in telecommunications, is the process of sending, propagating and receiving an analogue or digital information signal over a physical point-to-point or point-to-multipoint transmission medium, either wired, optical fiber or wireless...
. A plot of the system's net frequency response would be flat, as its response to all frequencies would literally be equal. Hence the term "equalization."
Much later the concept was applied in audio engineering
Audio engineering
An audio engineer, also called audio technician, audio technologist or sound technician, is a specialist in a skilled trade that deals with the use of machinery and equipment for the recording, mixing and reproduction of sounds. The field draws on many artistic and vocational areas, including...
to adjust the frequency response in recording, reproduction, and live sound reinforcement system
Sound reinforcement system
A sound reinforcement system is the combination of microphones, signal processors, amplifiers, and loudspeakers that makes live or pre-recorded sounds louder and may also distribute those sounds to a larger or more distant audience...
s. Sound engineers correct the frequency response of a sound system so that the frequency balance of the music as heard through speakers better matches the original performance picked up by a microphone
Microphone
A microphone is an acoustic-to-electric transducer or sensor that converts sound into an electrical signal. In 1877, Emile Berliner invented the first microphone used as a telephone voice transmitter...
. Audio amplifiers
Amplifier
Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...
have long had filters or controls to modify their frequency response. These are most often in the form of variable bass and treble controls (shelving filters), and switches to apply low-cut or high-cut filters for elimination of low frequency "rumble" and high frequency "hiss" respectively.
Graphic equalizers and other equipment developed for improving fidelity have since been used by recording engineers to modify frequency responses for aesthetic reasons. Hence in the field of audio electronics the term "equalization" is now broadly used to describe the application of such filters regardless of intent. This broad definition therefore includes all linear filter
Linear filter
Linear filters in the time domain process time-varying input signals to produce output signals, subject to the constraint of linearity.This results from systems composed solely of components classified as having a linear response....
s at the disposal of a listener or engineer.
Filter functions
Linear filter
Linear filters in the time domain process time-varying input signals to produce output signals, subject to the constraint of linearity.This results from systems composed solely of components classified as having a linear response....
s are mathematically described in terms of their transfer function
Transfer function
A transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant system. With optical imaging devices, for example, it is the Fourier transform of the point spread function i.e...
or, in layman's terms, frequency response
Frequency response
Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input...
. A transfer function can be decomposed as a combination of first order responses and second order responses (implemented as so-called biquad sections). These can be described according to their so-called pole
Pole-zero plot
In mathematics, signal processing and control theory, a pole–zero plot is a graphical representation of a rational transfer function in the complex plane which helps to convey certain properties of the system such as:* Stability...
and zero
Pole-zero plot
In mathematics, signal processing and control theory, a pole–zero plot is a graphical representation of a rational transfer function in the complex plane which helps to convey certain properties of the system such as:* Stability...
frequencies, which are complex numbers in the case of second-order responses.
First order filters
DB
DB may refer to:In science and technology:*Decibel , a logarithmic unit of measurement in acoustics and electronics*Dubnium , a chemical element*DB connector, a size of D-subminiature electrical connector...
per octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
. The bass and treble controls in a hi-fi system are each a first order filter in which the balance of frequencies above and below a point are varied using a single knob. A special case of first order filters is a first order high-pass or low-pass filter in which the 6 dB per octave cut of low or high frequencies extends indefinitely. These are the simplest of all filters to implement individually, requiring only a capacitor and resistor.
Second order filters
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
(or anti-resonance) around a particular frequency. The response of a second order filter is specified not only by its frequency but its Q
Q factor
In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, or equivalently, characterizes a resonator's bandwidth relative to its center frequency....
; a higher Q corresponds to a sharper response (smaller bandwidth) around a particular center frequency. For instance, the red response in the accompanying image cuts frequencies around 100 Hz with a higher Q than the blue response which boosts frequencies around 1000 Hz. Higher Q's correspond to resonant behaviour in which the half-power or -3 dB bandwidth, BW, is given by:
where F0 is the resonant frequency of the second order filter. BW is the bandwidth expressed in the same frequency unit that F0 is. Low Q filter responses (where Q < ) are not said to be resonant and the above formula for bandwidth does not apply.
It is also possible to define the Q of a band-pass function as:
,where B is the bandwidth in octaves.
It should be noted that a second-order filter response with Q of less than 1/2 can be decomposed into two first-order filter functions, a low-cut and a high-cut (or boost). Of more interest are resonant filter functions which can boost (or cut) a narrow range of frequencies. In addition to specifying the center frequency F0 and the Q, the specification of the filter's zeros
Pole-zero plot
In mathematics, signal processing and control theory, a pole–zero plot is a graphical representation of a rational transfer function in the complex plane which helps to convey certain properties of the system such as:* Stability...
determines how much that frequency band will be boosted (or cut). Thus a parametric equalizer section will have three controls for its center frequency F0, bandwidth or Q, and the amount of boost or cut.
The range of second-order filter functions is important because any analog filter function can be decomposed into a (usually small) number of these (plus, perhaps, simpler first order responses). These are implemented directly by each section of a parametric equalizer where they are explicitly adjusted. And each element of a graphic equalizer based on a filter bank
Filter bank
In signal processing, a filter bank is an array of band-pass filters that separates the input signal into multiple components, each one carrying a single frequency subband of the original signal. One application of a filter bank is a graphic equalizer, which can attenuate the components...
includes one such element whose Q is not adjustable by the user.
High and low pass filters
A high-pass filterHigh-pass filter
A high-pass filter is a device that passes high frequencies and attenuates frequencies lower than its cutoff frequency. A high-pass filter is usually modeled as a linear time-invariant system...
is a filter that passes higher frequencies
Audio frequency
An audio frequency or audible frequency is characterized as a periodic vibration whose frequency is audible to the average human...
well but attenuates
Attenuation
In physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, X-rays are attenuated by lead, and light and sound are attenuated by water.In electrical engineering and telecommunications, attenuation affects the...
lower frequency components. A low-pass filter
Low-pass filter
A low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...
passes low-frequency components of signals while attenuating higher frequencies. In audio applications these are frequently termed "low cut" and "high cut" respectively, to emphasize their effect on the original signal. For instance, sometimes audio equipment will include a switch labeled "high cut" or described as a "hiss filter" (hiss being high frequency noise). In the times of phonograph
Phonograph
The phonograph record player, or gramophone is a device introduced in 1877 that has had continued common use for reproducing sound recordings, although when first developed, the phonograph was used to both record and reproduce sounds...
s many stereos would include a switch to introduce a high-pass (low cut) filter, often called a "rumble filter," to eliminated infrasonic frequencies.
Shelving filter
Common tone controls (bass and treble) found in consumer audio equipment are examples of variable shelving filters. These implement a first order response, as discussed above and provide an adjustable boost or cut to frequencies above or lower than a certain point.A high shelf or "treble control" will have a frequency response |H(f)| whose square is given by:
where fp and fz are called the pole and zero frequencies, respectively. Turning down the treble control increases fz so that frequences higher than fp are attenuated. Turning up the treble control increases fp so that frequences higher than fz are boosted. Setting the treble control at the center sets fz = fp so that |H(f)|2=1 and the circuit has no effect. At most, the slope of the filter response in the transition region will be 6 dB per octave (thus a doubling of signal voltage and a consequent quadrupling of signal power for every doubling of frequency).
Similarly the response of a low shelf or "bass control" can be represented as
-
.
In this case the inclusion of the leading factor simply indicates that the response at frequencies much higher than fz or fp is unity and that only bass frequencies are affected. Note that a high shelve in which fz is set to infinity or a low shelve response in which fz is set to zero implements a first order low-pass or high-pass filter respectively. However usual tone controls have a more limited range, since the purpose isn't to eliminate any frequencies but only to achieve a greater balance when, for instance, the treble is lacking and the sound isn't crisp. Since the range of possible responses from shelving filters is so limited, they are considered quite inadequate for equalization tasks among audio engineers.
Graphic equalizer
Filter bank
In signal processing, a filter bank is an array of band-pass filters that separates the input signal into multiple components, each one carrying a single frequency subband of the original signal. One application of a filter bank is a graphic equalizer, which can attenuate the components...
. Each filter passes the portion of the signal present in its own frequency range or band. The amplitude passed by each filter is adjusted using a slide control to boost or cut frequency components passed by that filter. The vertical position of each slider thus indicates the gain applied at that frequency band, so that the knobs resemble a graph of the equalizer's response plotted versus frequency.
The number of frequency channels (and therefore each one's bandwidth) affects the cost of production and may be matched to the requirements of the intended application. A car audio
Car audio
Car audio/video , auto radio, mobile audio, 12-volt and other terms are used to describe the sound or video system fitted in an automobile. While 12-volt audio and video systems are also used, marketed, or manufactured for marine, aviation, and buses, this article focuses on cars as the most common...
equalizer might have one
set of controls applying the same gain to both stereo channels for convenience, with a total of five to ten frequency bands. On the other hand, an equalizer for professional live sound reinforcement typically has some 25 to 31 bands, for more precise control of feedback problems and equalization of room modes. Such an equalizer (as shown above) is called a 1/3-octave equalizer (spoken informally as "third-octave EQ") because the center frequency of its filters are spaced one third of an octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
apart, three filters to an octave. Equalizers with half as many filters per octave are common where less precise control is required—this design is called a 2/3-octave equalizer.
Graphic equalizers are sometimes used by stereo owners to obtain a smiley face curve
Smiley face curve
A smiley face curve in audio signal processing, is a target frequency response curve characterized by boosted low and high frequencies coupled with reduced midrange frequency power...
(also known as "mid scoop") in which the lower and higher frequency channels are boosted relative to the midrange frequencies. This results in a graphical pattern resembling a cartoon "smile."
Parametric equalizer
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
, center frequency
Center frequency
In electrical engineering and telecommunications, the center frequency of a filter or channel is a measure of a central frequency between the upper and lower cutoff frequencies...
and bandwidth. The amplitude of each band can be controlled, and the center frequency can be shifted, and bandwidth ("Q
Q factor
In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, or equivalently, characterizes a resonator's bandwidth relative to its center frequency....
") can be widened or narrowed. Parametric equalizers are capable of making much more precise adjustments to sound than other equalizers, and are commonly used in sound recording and live sound reinforcement
Sound reinforcement system
A sound reinforcement system is the combination of microphones, signal processors, amplifiers, and loudspeakers that makes live or pre-recorded sounds louder and may also distribute those sounds to a larger or more distant audience...
.
Parametric equalizers are also sold as standalone outboard gear
Outboard gear
Musical "outboard equipment" or "gear" alter how an musical instrument sounds. Outboard, can be used either during a live performance or in the recording studio. These are separate from the effects that may be applied by using a mixing console or a digital audio workstation...
units.
A variant of the parametric equalizer is the semi-parametric equalizer, also known as a sweepable filter. It allows users to control the amplitude and frequency, but uses a pre-set bandwidth of the center frequency. In some cases, semi-parametric equalizers allow the user to select between a wide and a narrow preset bandwidth.
Uses
In sound recording, equalization is used to improve an instrument's sound or make certain instruments and sounds more prominent. For example, a recording engineer may use an equalizer to make some high-pitches in a vocal part louder while making low-pitches in a drum part quieter.Equalizers can correct problems posed by a room's acoustics
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
, as an auditorium will generally have an uneven frequency response especially due to standing waves and acoustic dampening. The frequency response
Frequency response
Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input...
of a room may be analyzed using a spectrum analyzer
Spectrum analyzer
A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals...
and a pink noise
Pink noise
Pink noise or 1/ƒ noise is a signal or process with a frequency spectrum such that the power spectral density is inversely proportional to the frequency. In pink noise, each octave carries an equal amount of noise power...
generator for instance. Then a graphic equalizer can be easily adjusted to compensate for the room's acoustics. Such compensation can also be applied to tweak the sound quality of a recording studio
Recording studio
A recording studio is a facility for sound recording and mixing. Ideally both the recording and monitoring spaces are specially designed by an acoustician to achieve optimum acoustic properties...
in addition to its use in live sound reinforcement system
Sound reinforcement system
A sound reinforcement system is the combination of microphones, signal processors, amplifiers, and loudspeakers that makes live or pre-recorded sounds louder and may also distribute those sounds to a larger or more distant audience...
s and even home hi-fi systems.
During live events where signals from microphones are amplified and sent to speaker
Loudspeaker
A loudspeaker is an electroacoustic transducer that produces sound in response to an electrical audio signal input. Non-electrical loudspeakers were developed as accessories to telephone systems, but electronic amplification by vacuum tube made loudspeakers more generally useful...
systems, equalization is not only used to "flatten" the frequency response but may also be useful in eliminating feedback
Audio feedback
Audio feedback is a special kind of positive feedback which occurs when a sound loop exists between an audio input and an audio output...
. When the sound produced by the speakers is picked up by a microphone, it is further reamplified; this recirculation of sound can lead to "howling" requiring the sound technician to reduce the gain
Gain
In electronics, gain is a measure of the ability of a circuit to increase the power or amplitude of a signal from the input to the output. It is usually defined as the mean ratio of the signal output of a system to the signal input of the same system. It may also be defined on a logarithmic scale,...
for that microphone, perhaps sacrificing the contribution of a singer's voice for instance. Even at a slightly reduced gain, the feedback will still cause an unpleasant resonant sound around the frequency at which it would howl. But because the feedback is troublesome at a particular frequency, it is possible to cut the gain only around that frequency while preserving the gain at most other frequencies. This can best be done using a parametric equalizer tuned to that very frequency with its amplitude control sharply reduced. By adjusting the equalizer for a narrow bandwidth (high Q), most other frequency components will not be affected. The extreme case when the signal at the channel's center frequency is completely eliminated is known as a notch filter.
An equalizer can be used to correct or "flatten" the frequency response of speakers rather than designing the speaker itself to be equalized. For instance, the highly regarded Bose 901 speaker system doesn't use separate woofers and tweeters to cover the bass and treble frequencies, but includes 9 full-range
Full-range
A full-range loudspeaker drive unit is defined as a driver which reproduces as much of the audible frequency range as possible, within the limitations imposed by the physical constraints of a specific design. Frequency range is of these drives is maximized through the use of a whizzer cone and...
drivers more akin to what one would find in a table radio. However this speaker system is sold with an active equalizer designed to correct the poor frequency balance of those drivers. That equalizer must be inserted into the amplifier system so that the amplified signal that is finally sent to the speakers has its response increased at the frequencies where the response of these drivers falls off, producing a high fidelity reproduction regardless.
Tone controls (usually designated "bass" and "treble") are simple shelving filters included in most hi-fi equipment for gross adjustment of the frequency balance. The bass control may be used, for instance, to increase the drum and bass parts at a dance party, or to reduce annoying bass sounds when listening to a person speaking. The treble control might be used to give the percussion a sharper or more "brilliant" sound, or can be used to cut such high frequencies when they have been overemphasized in the program material or simply to accommodate a listener's preference.
A "rumble filter" is a high pass (low cut) filter with a cutoff typically in the 20 to 40 Hz range; this is the low frequency end of human hearing. This prevents the wasteful amplification of very low frequencies which aren't going to be effectively reproduced by typical speakers, and which moreover can cause damage to speakers when they "bottom out."
A crossover network
Audio crossover
Audio crossovers are a class of electronic filter used in audio applications. Most individual loudspeaker drivers are incapable of covering the entire audio spectrum from low frequencies to high frequencies with acceptable relative volume and lack of distortion so most hi-fi speaker systems use a...
is a system of filters designed to direct electrical energy separately to the woofer
Woofer
Woofer is the term commonly used for a loudspeaker driver designed to produce low frequency sounds, typically from around 40 hertz up to about a kilohertz or higher. The name is from the onomatopoeic English word for a dog's bark, "woof"...
and tweeter
Tweeter
A tweeter is a loudspeaker designed to produce high audio frequencies, typically from around 2,000 Hz to 20,000 Hz . Some tweeters can manage response up to 65 kHz...
of a 2-way speaker system (and also to the mid-range speaker
Mid-range speaker
A loudspeaker driver that produces the frequency range from approximately 300–5000 hertz is known as a mid-range.Midrange drivers are usually cone types or, less commonly, dome types, or compression horn drivers...
of a 3-way system). This is most often built into the speaker enclosure and hidden from the user. However in bi-amplification, these filters operate on the low level audio signals, sending the low and high frequency components to separate amplifiers which connect to the woofers and tweeters respectively.
Equalization is used in a reciprocal manner in certain communication channels and recording technologies. The original music is passed through a particular filter to alter its frequency balance, followed by the channel or recording process. At the end of the channel or when the recording is played, a complementary filter is inserted which precisely compensates for the original filter and recovers the original waveform. For instance, FM broadcast uses a pre-emphasis filter to boost the high frequencies before transmission, and every receiver includes a matching de-emphasis filter to restore it. The white noise
White noise
White noise is a random signal with a flat power spectral density. In other words, the signal contains equal power within a fixed bandwidth at any center frequency...
that is introduced by the radio is then also de-emphasized at the higher frequencies (where it is most noticeable) along with the pre-emphasized program, making the noise less audible. Tape recorder
Tape recorder
An audio tape recorder, tape deck, reel-to-reel tape deck, cassette deck or tape machine is an audio storage device that records and plays back sounds, including articulated voices, usually using magnetic tape, either wound on a reel or in a cassette, for storage...
s used the same trick to reduce "tape hiss" while maintaining fidelity. On the other hand, in the production of vinyl records
Phonograph
The phonograph record player, or gramophone is a device introduced in 1877 that has had continued common use for reproducing sound recordings, although when first developed, the phonograph was used to both record and reproduce sounds...
, a filter is used to reduce the amplitude of low frequencies which otherwise produce large amplitudes on the tracks of a record. Then the groove can take up less physical space, fitting more music on the record. The preamp attached to the phono cartridge has a complementary filter boosting those low frequencies following the standard RIAA equalization
RIAA equalization
RIAA equalization is a specification for the correct recording of gramophone records, established by the Recording Industry Association of America...
curve.
History
Audio electronic equipment has always included filter elements and adjustments for tonal balance such as bass and treble controls. These are simple shelving filters thatallow users to make broad, overall adjustments to the sound. With the science of audio engineering
Audio engineering
An audio engineer, also called audio technician, audio technologist or sound technician, is a specialist in a skilled trade that deals with the use of machinery and equipment for the recording, mixing and reproduction of sounds. The field draws on many artistic and vocational areas, including...
came the demand for more flexible tools such as graphic equalizers, although these were still limited in terms of their flexibility due to the width of the channels supplied.
The Langevin Model EQ-251A was the first equalizer to use slide controls. It featured two passive equalization sections, a bass shelving filter, and a pass band filter. Each filter had switchable frequencies and used a 15-position slide switch to adjust cut or boost. The first true graphic equalizer was the type 7080 developed by Art Davis's Cinema Engineering. It featured 6 bands with a boost or cut range of 8 dB
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
. It used a slide switch to adjust each band in 1 dB steps. Davis's second graphic equalizer was the Altec Lansing
Altec Lansing
Altec Lansing is a line of professional, home, automotive, computer, and multimedia audio products first developed in 1936. They were used in many studios as monitor speakers...
Model 9062A EQ. In 1967 Davis developed the first 1/3 octave variable notch filter set, the Altec-Lansing "Acousta-Voice" system.
With the development of active R-C filters
Active filter
An active filter is a type of analog electronic filter that uses an amplifier stage. Amplifiers included in a filter design can be used to improve the performance, stability and predictability of a filter. An amplifier prevents the impedance of source or load stages from affecting the...
using op-amps in the 1960s, it became possible to create equalizers capable of adjusting critical frequency as well as bandwidth (or Q) and amplitude coefficient. In 1972 George Massenburg
George Massenburg
George Y. Massenburg is a recording engineer and inventor. Working principally in Baltimore, Los Angeles, Nashville, and Macon, Georgia, Massenburg is widely known for his 1972 paper on the parametric equalizer.-Background:...
introduced parametric filtering based on such technology. Most channel equalization on mixing console
Mixing console
In professional audio, a mixing console, or audio mixer, also called a sound board, mixing desk, or mixer is an electronic device for combining , routing, and changing the level, timbre and/or dynamics of audio signals. A mixer can mix analog or digital signals, depending on the type of mixer...
s made thereafter were either semi or fully parametric equalizers.
In the late 1990s and in the 2000s, parametric equalizers became increasingly available as Digital Signal Processing
Digital signal processing
Digital signal processing is concerned with the representation of discrete time signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing...
(DSP) equipment, usually in the form of plug-ins for various digital audio workstations. Standalone outboard gear
Outboard gear
Musical "outboard equipment" or "gear" alter how an musical instrument sounds. Outboard, can be used either during a live performance or in the recording studio. These are separate from the effects that may be applied by using a mixing console or a digital audio workstation...
versions of DSP parametric equalizers were also quickly introduced after the software versions and are typically called Digital Parametric Equalizers.
to quality factor 
and back