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MATLAB 3-Band Digital Audio Equalizer
创建日期：2024-08-14 17:27:08
所属分类：数学mathematics
标签： MATLAB
3-Band Digital Audio Equalizer

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MATLAB Application Project

3-Band Digital Audio Equalizer

The goal of this project is to build and test a digital audio equalization network in which you will be able to

boost or attenuate the low, mid and high frequency range of music sounds. Audible sounds cover a frequency

range from 20 Hz – 20 kHz (for human hearing). In many listening scenarios sounds are distorted by the audio

system (e.g., the speaker transfer function) or the acoustic environment (room transfer function). One can

correct for the magnitude of such distortions with an audio equalizer. High end audio equalizers typically have

~30 selectable bands that allow you to adjust the sound gain in 1/3 octave frequency steps for frequencies

between 20Hz – 20 kHz. For the purpose of this project, we will consider a simpler equalization network that

allows you to adjust the bass, midrange and treble bands.

In this project, you will design and build a three-band equalizer where you will be able to separately adjust the

bass, midrange and treble using MATLAB. The schematic for this design is illustrated below:

The input sound waveform, x(t), is decomposed by three filters and these outputs are routed a gain term for

each of the three bands (Gb=bass, Gm=mid, and Gt

=treble). The signals are then added together to generate the

corrected output.

The lowpass (LP) filter encompasses frequencies below 100 Hz (bass range). The midrange is selected with a

bandpass (BP) filter covering frequencies in the range 100Hz-5 kHz. The trebles is selected with a highpass

filter (HP) that encompasses the remainder of the audible range (5-22.05 kHz).

You are allowed to work in groups of two or three. However, each student is required to hand in their own

independent report and is required to implement his/her own code. Reports using copied code or text will

be returned without a grade. (Yes, we will check for this! Code needs to be uploaded onto HUSKYCT). Group

members who worked on the project should be identified in the writeup.

Filter Design

HP

BP

LP

x(t)

GB

GM

GT

Treble

Midrange

Bass

+ y(t)

Each of the above filters is implemented using a Kaiser window FIR (Finite Impulse Response) filter

(see chapter 4.9 & 12.8-1 for windowing and FIR filter design). In general, windowed FIR filters are

implemented as the product of an ideal filter impulse response ( hideal [k], for a lowpass, bandpass or highpass)

and a window function (w[k] ) that is used to smoothly truncate the ideal filter impulse response to a total of

2N+1 samples

h[k] = hideal [k]?w[k]

Here N is a filter parameter referred to as the filter order where the total number of coefficients in the discrete

time impulse response of the filter is 2N+1. Conceptually, note that any “ideal” filter requires an infinite amount

of time and therefore an infinite amount of coefficients to implement. As we have discussed in class, this is not

practically feasibleand the ideal filters cannot be implemented in practice. To overcome this, the window

function is used to truncate the filter in a smooth fashion in order to 1) require only finite number of time

samples (2N+1) and 2) minimize filter distortions (or errors) in the passband and stopband.r design.

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