Analisis Del Espectro de Audio en Matlab

7/31/2019 Analisis Del Espectro de Audio en Matlab

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Analysis Frequency Spectra an Audio Signal

Subject: Signals and Systems

Students:Gerardo Hernandez code. 809027

Luis Mendoza code.209045

Orlando Delgado code.809018

Teacher: Oscar Marino

Universidad Nacional de Colombia, Manizales

Abstract With the help computational tool,

Matlab, we want apply some of the concepts dis-

cussed in the signals and systems course.

Well make a software at Matlab that permit usobtain a audio signal in a given format and process

it at different ways for comparing their spectra. The

audio signal can be taken from a sound file existing

in the computer or upload trough direct recording

using P.C microphone. Well implement the object-

oriented programming in the GUIDE for achieve a

nice graphical interface and easy manipulation for

user, according their needs.

Index Terms Fourier transform, signals, sound,

discrete ,sampling, filter, spectrum, frequency.

I. INTRODUCTION

This text discloses a specific application on

Fourier Transform, taking into account the filters

(low pass filters and high pass filters), developed

based on the collection of sounds from outside or

exporting files WAV to then get the transformed

and it filtrated in this manner, you can find the best

way to listen to a recording for which you use the

graphical interface Matlab (Guide), for facilitating

user interaction with application development.

II. GENERAL OBJECTIVE

Develop a practical application of some of

the concepts covered in the course of signals

and systems

III. SPECIFIC OBJECTIVES

Apply the Fourier transform in audio signal

processing using Matlab.

Analyze audio signals from their spectra

in the time domain and frequency, in thediscrete time.

IV. THEORETICAL FRAMEWORK

IV-A. File Wav

Waveform Audio File Format (WAVE, or morecommonly known as WAV due to its filename

extension),[3][6][7][8] (also, but rarely, named,

Audio for Windows[9]) is a Microsoft and IBM

audio file format standard for storing an audio

bitstream on PCs. It is an application of the

RIFF bitstream format method for storing data in

chunks, and thus is also close to the 8SVX and

the AIFF format used on Amiga and Macintosh

computers, respectively. It is the main format

used on Windows systems for raw and typically

uncompressed audio. The usual bitstream encod-

ing is the linear pulse-code modulation (LPCM)

format.

IV-B. Fourier Transform

The Fourier transform is a mathematical

operation that decomposes a signal into its

constituent frequencies. Thus the Fourier

transform of a musical chord is a mathematical

representation of the amplitudes of the individual

notes that make it up. The original signal depends

on time, and therefore is called the time domainrepresentation of the signal, whereas the Fourier

transform depends on frequency and is called the

frequency domain representation of the signal.

The term Fourier transform refers both to the

frequency domain representation of the signal

and the process that transforms the signal to its

frequency domain representation.

In mathematical terms, the Fourier transform

transforms one complex-valued function of

a real variable into another. In effect, theFourier transform decomposes a function into


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oscillatory functions. The Fourier transform and

its generalizations are the subject of Fourier

analysis. In this specific case, both the time

and frequency domains are unbounded linear

continua. It is possible to define the Fouriertransform of a function of several variables,

which is important for instance in the physical

study of wave motion and optics. It is also

possible to generalize the Fourier transform on

discrete structures such as finite groups. The

efficient computation of such structures, by fast

Fourier transform, is essential for high-speed

computing.

There are several common conventions for

defining the Fourier transform of an integrablefunction f : R C. This report will use thedefinition:

F() =

f(x) e2ixdx

For every real number .

When the independent variable x representstime (with SI unit of seconds), the transform

variable represents frequency (in hertz). Undersuitable conditions, f can be reconstructed fromf by the inverse transform:

f(x) =

F() e2ixd

For every real number x.

For other common conventions and notations,

including using the angular frequency instead

of the frequency , see Other conventions andOther notations below. The Fourier transform on

Euclidean space is treated separately, in which

the variable x often represents position and momentum.

IV-C. Filters

Filters are electronic circuits which perform

signal processing functions, specifically to

remove unwanted frequency components from

the signal, to enhance one wanted it, or both.

Filters can be:

IV-C.1. Low Pass Filters: An ideal low-pass

Filters transfer function is shown. The frequency

between pass and stop bands is called the

cut-off frequency (wc). All of the signals with

frequencies below !c are transmitted and allother signals are stopped.

In practical Filters, pass and stop bands are

not clearly defined, |H(jw)| varies continuouslyfrom its maximum toward zero. The cut-off

frequency is, therefore, defined as the frequency

at which |H(jw)| is reduced to 1/2 = 0,7 ofits maximum value. This corresponds to signal

power being reduced by 1/2 as P V2.

IV-C.2. High Pass Filter: A high-pass filter,or HPF, is an LTI filter that passes high fre-

quencies well but attenuates (i.e., reduces the

amplitude of) frequencies lower than the filters

cutoff frequency. The actual amount of attenuation

for each frequency is a design parameter of the

filter. It is sometimes called a low-cut filter or

bass-cut filter.

V. METHODOLOGY

Program development is done as follows:

The program basically allows us to represent an

audio signal at the time domain and transform

it to frequency domain, using Fast Fourier

Transform (FFT) Analysis.

Once represented in frequency terminus, becomes

a high pass filter or low pass filter to desired

frequencies for then compare the changes in the

spectrum and sound reproduction.

For obtain audio signal, we using some commands

in Matlab, which can upload in memory a sound

file with .WAV format (default), or record sincemicrophone an audio signal during a specific

time, that will be able save with the format same,

for after be used. The files have to be in the

same folder where the program run.

Once you enter the signal is possible to see

their representation in the time domain, in this

case graphically shows the evolution of the

amplitude (of the magnitude that we measure:

intensity and volume of sound) versus time.

Later, will be able to observe and characterizethe spectrum of the analog audio signal, through


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Fourier transform, through Fourier transform,

which not only contains information about the

intensity to certain frequency, but also about

phase, this information can be represented as a

two-dimensional vector or as a complex number.Frequency representation capture the spectral

characteristics of the audio signal, which the

signal spectrum shows the energy distribution

within the frequency range. Addition the

fundamental frequency, there are many

frequencies present in a waveform. A spectral

representation shows the frequency content

sound. The individual frequency components

of the spectrum can be called harmonics or

partial. Harmonic frequencies are simple integer

of fundamental frequency.

Fourier analysis will be able to represent

any waveform through a set of harmonically

related components of appropriate amplitude

and phase. As FT is an intensive computational

process, then use a technique called Fast Fourier

Transform (FFT) analysis, available in Matlab,

which provide conversion to the frequency

domain of the auditory signal, allowing spectrum

analysis. The FFT uses mathematical shortcuts

to minimize processing time, but this puts atrisk the itself analysis. The resulting analysis

file known as the FFT size, indicates the

number of original signal samples used in the

analysis and determines the number of discrete

frequency bands. When using many frequency

bands, the bands have less bandwidth, allowing

more accurate frequency readings.

FFT takes N consecutive samples of signal and

performs a mathematical operation to produce N

samples of the signal spectrum. The N samples

are complex values with real and imaginary partwhich can calculate the absolute value, which is

spectrum magnitude. Sampling and quantization

of the analog signal will have a sampling rate of

44100 Hz and will yield a corresponding digital

signal.

Finally, for achieve adequate sampled signal

we use low pass filters or high pass, as needed.

In the end, the program can compare each

spectra of the input signal and used it according

to convenience.

VI. USE R MANUAL

VI-A. Open the Program

For run the program, you must have installed

Matlab on your computer. Then go to the folder

where is the application, select it and double click

or intro and the program will run automatically.

Once executed, the following window opens:

Fig. 1. Main window program.

Here you can see that program contains a space

for the acquisition and audio signal processing

and a graphical interface where it shows thebehavior of signal and their spectra, as explained

in the following points.

VI-B. Upload the Audio Signal to the Program

When is required process an audio signal,

whether the recording of an interview, a sound

of some natural event, a music file, etc, often

the user already has the file which it want to dothe respective analysis, but sometimes, occurrence

of imminent events makes it necessary obtain an

immediate recording and high quality. For this, the

program has two ways to load the audio signal:

VI-B.1. Direct Recording From Microphone:

One way to process the audio signal may be

recorded from outside the computer using the PC

microphone or headset.

For record the signal, connect a microphone to

your computer (if this is not included) and then

position yourself in the position for recording (inthe top left of the program) as shown in figure (2)


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Fig. 2. Recording area.

Later, enter the time in seconds for which to

record and press the record button as shown in

the figure (3).

Fig. 3. Recording made.

Once signal is recorded, can process it im-mediately or save it for later use. To save the

file, simply type the desired name in the place

designated for this (see figure 4). The program

is saved by default in the folder where is the

executable with wav format.

Fig. 4. Save recording.

VI-B.2. Upload Sound File: Another way get

the sound signal, is load an existing file on the

computer, for this, the file must be contained

in the same folder where is the executable ap-

plication. The format of the file must be .wavextension. Once you save the file in the folder,

should be addressed to upload a file.as shown in

Figure (5).

Fig. 5. Upload sound file.

you must Enter the name of the file and sam-pling speed. After click the open button and the

program will load it .

VI-C. Play and Plot the Signal

Play and plot the signal is very simple, once

loaded the audio signal, you must press the play

and graph button (see figure 5) and the program

plays the file and show the spectrum of behavior

of the audio signal in time in sound graphic(see

example in Figure 6)

Fig. 6. Graphic example sound in time.

For look the spectrum of the loudness of the

signal in terms of frequency, simply press the

transform button that shown in Figure (5) and

automatically appear in Spectrum of the audiosignal, see figure (7).


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Fig. 7. Sound spectrum for the example given.

VI-D. Filtering Process

Filter the signal, should be located in the Fil-

tering options, then choose the type of filtering

(high pass or low pass), then enter the frequencyvalue that you want to do the filtering, and press

the filter button for observe the spectrum (see

figure 8), the spectrum appear in the section

spectrum of the audio signal filtered(see figure

9). You can play the filtered signal to observe

changes, as well as save them for later use, which

you need to press the respective button, and name

the file (see figure 8)

Fig. 8. Filtering Options.

Fig. 9. Signal with low pass filter of the example.

VI-E. Note:

For a closer view of the spectra, only pressed

click on the desired graph as many times as

needed for the program to make the respectivezooms.

VII. CONCLUSIONS

The Fourier transform facilitates the analysis

of a function, since it is represented in

terms of frequency and not time facilitating

mathematical development in all the required

operations.

The Fourier transform as one of its main

applications in engineering is the observing

efficiency due to the harmonics produced in

circuits applied.

Guide is an important tool that facilitates

interaction with the user applications, taking

into account the delays the execution pro-

cess.

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Analisis Del Espectro de Audio en Matlab