Final Project: Digital Equalizer
Class: ECE  3551
Submitted on: December, 12, 2011
Submitted by: John Ernsberger
GSA: Jacob Zurasky
Purpose:
The purpose of this project is to design a fixed and user controlled digital equalizer,
where the user can increase the amplitude of individual frequency ranges or choose a
predetermined setting.
Theory:
Digital Equalizer:
A Digital equalizer works by running an audio input through several band pass filters.
These filters are designed to only allow a certain frequency range to pass through them. Thus,
when that range is multiplied by a scalar It augments the frequencies only within that filter.
Because of the specific frequencies needed for the filtering second order IIR Filters are
necessary. If you use FIR filters, although easier to implement, the coefficient level is far too
high to be practical for the CPU to handle. Thus a much lower order
is needed making IIR filters
a prime selection. These filters have a low coefficient count and are extremely precise.
Below is a visual representation of how the equalizer works. First the input is passed
through several Band Pass filters. The output of those filters is multiplied by an individual gain
and summed. The summed augmented outputs of the filters are then multiplied by a master gain,
which is 1/( the number of filters ).
To discover the individual gains for your filters you can use a db calculator. The
maximum increase is around 12 db or multiplying your filter by four. This is because anymore
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View Full Documentamplification will result in too much energy in the system and the quality of the music will
decrease.
Second Order IIR Filters:
Second Order IIR filters are very useful as they are precise and have a very low
coefficient count. However, the implementation of the code is more complex than FIR filters.
The equation used to calculate second order IIR filters is :
This equation can be implemented as code using the following two equations:
wn = ( input )  ( a1 * wn1 )  ( a2 * wn2 ) ;
yn = ( b1 * wn ) + ( b2 * wn1 ) + ( b3 * wn2 ) ;
where the wn is the current modified input value and wn1 and wn2 are the past modified
inputs. To complete the filtering operations you must pass the wn1 to wn2 and wn to wn1 thus
allowing the past two modified inputs to be recalled for later use within the filter.
Method:
1.
Generate second order IIR pass band filters using MATLAB for the following
frequencies.
a.
100  200 Hz
b.
200  400 Hz
c.
400  800 Hz
d.
800  1,500 Hz
e.
1,500  3,000 Hz
f.
3,000  5,000 Hz
g.
5,000  7,000 Hz
h.
7,000  10,000 Hz
i.
10,000  15,000 Hz
2.
For the second fixed equalizer create second order IIR filters for the following frequency
ranges.
a.
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 Spring '11
 Staff
 Multiplication, Bandpass filter, Finite impulse response, IIR Filters, order iir filters

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