Equalizer
Description
An equalizer can vary the
gain of the different frequencies that compose an audio signal. The most basic
and common form of an equalizer is the treble/bass control. The treble level
determines the gain of higher frequencies while the bass level controls the
lower frequencies. Amplifiers often have gain controls for low range, mid
range, and high range frequencies. The graphic below shows a more advanced
equalizer, which gives the user level control over specific frequency ranges:
An equalizer is built using
filters to isolate specific frequencies ranges. Individual gains are applied to each of the frequency ranges
before they are added together and output.
Graphical Depiction
This graphic depicts a
treble/bass equalizer. The input signal
is split into two separate frequency ranges – above the cut off frequency
(treble) and below the cut off frequency (bass). The high and low frequency signals are then multiplied by their
respective gain levels, combined, and output.
If more than two frequency ranges are desired, additional filters are
necessary. The cut off frequency, high
frequency gain, and low frequency gain are independent variables selected by
the user.
Effect Formula
|
y[n] = g1 *
x_f1[n] + g2 * x_f2[n] + … + gm * x_fm[n] |
|
y[n] = output
signal |
|
g1 = gain of first
frequency range |
|
g2 = gain of
second frequency range |
|
gm = gain of
frequency range m |
|
x_f1[n] = first
frequency range of input signal |
|
x_f2[n] = second
frequency range of input signal |
|
x_fm[n] =
frequency range m of input signal |
|
m = total number
of frequency bands |
This general equalizer
formula divides an input signal x[n] into m different frequency ranges,
multiplies them by their respective gains, and combines them into the output
signal y[n].
Source Code
(.csd files can be viewed with Notepad or any text
editor)
Example
Audio Clips
|
Original unprocessed
signal |
|
|
Low frequencies passed,
high frequencies attenuated |
|
|
High frequencies passed,
low frequencies attenuated |
|
|
Low and high frequencies
passed, mid level frequencies attenuated |
There is static ‘hiss’
audible in the original unprocessed signal.
This hiss has a mid-range frequency that is attenuated by the equalizer
in the last example.
References
Lehman, Scott
(1996). Effects Explained. Harmony Central. Retrieved 6/04 from
http://www.harmony-central.com/Effects/effects-explained.html
Mikelson, Hans
(2000). Modeling a multieffects processor in Csound. In Boulanger,
Richard (2000), The Csound book (pp 575-594). Cambridge, MA: MIT Press.
Schindler,
Allan. (1998). Eastman Csound tutorial.
Eastman School of Music. Retrieved 6/04 from
http://www.esm.rochester.edu/onlinedocs/allan.cs/
Vercoe, Barry.
(1992). The public Csound reference manual, version 4.16. MIT
Press. Retrieved 6/04 from http://www.lakewoodsound.com/csound/hypertext/manual.htm
Zolzer, Udo.
(2002). Digital audio effects. West Sussex, England: Baffins Lane.