Introduction to Matlab

Introduction to Matlab, Signal Processing & Speech Signal ProcessingDepartment of Electronics & Telecommunication Engineering, MMCT

Outline:What is Matlab?Matlab ScreenVariables, array, matrix, indexing Operators (Arithmetic, relational, logical )Using of M-FileWriting User Defined FunctionsSignal ProcessingSpeech Signal Processing

What is Matlab?Matlab is basically a high level language which has many specialized toolboxes for making things easier for usHow high?

What are we interested in?Matlab is too broad for our purpose.The features we are going to require is

Matlab ScreenCommand Windowtype commands

Current DirectoryView folders and m-files

WorkspaceView program variablesDouble click on a variable to see it in the Array Editor

Command Historyview past commandssave a whole session using diary

VariablesNo need for types. i.e.,

All variables are created with double precision unless specified and they are matrices.

After these statements, the variables are 1x1 matrices with double precision

Example:>>x=5;>>x1=2;

Array, Matrixa vectorx = [1 2 5 1]x = 1 2 5 1

a matrixx = [1 2 3; 5 1 4; 3 2 -1]

x = 1 2 3 5 1 4 3 2 -1

transposey = x y = 12 51

Long Array, Matrix t =1:10 t = 1 2 3 4 5 6 7 8 9 10k =2:-0.5:-1 k = 2 1.5 1 0.5 0 -0.5 -1

B = [1:4; 5:8]

x = 1 2 3 4 5 6 7 8

Matrix IndexThe matrix indices begin from 1 (not 0 (as in C)) The matrix indices must be positive integerGiven:A(-2), A(0)

Error: ??? Subscript indices must either be real positive integers or logicals.

A(4,2)Error: ??? Index exceeds matrix dimensions.

Concatenation of Matricesx = [1 2], y = [4 5], z=[ 0 0]

A = [ x y]

1 2 4 5

B = [x ; y]

1 2 4 5

C = [x y ;z] Error:??? Error using ==> vertcat CAT arguments dimensions are not consistent.

Operators (arithmetic)+addition-subtraction*multiplication/division^powercomplex conjugate transpose

Matrices OperationsGiven A and B:AdditionSubtractionProductTranspose

Operators (Element by Element)

.*element-by-element multiplication./element-by-element division.^element-by-element power

The use of . Element OperationK= x^2Erorr: ??? Error using ==> mpower Matrix must be square.B=x*yErorr:??? Error using ==> mtimes Inner matrix dimensions must agree.A = [1 2 3; 5 1 4; 3 2 -1] A = 1 2 3 5 1 4 3 2 -1y = A(3 ,:)

y= 3 4 -1b = x .* y

b= 3 8 -3 c = x . / y

c= 0.33 0.5 -3 d = x .^2

d= 1 4 9 x = A(1,:)

x= 1 2 3

General Commands On-line helphelp helpwinhelpdeskhelp topiclookfor stringdemoWorkspace informationwhowhoswhatclearclfclchome

Directory Information & TerminationpwdcddirlsPatheditpathcopyfile

General Information & Terminationcomputerclockdatever^cquit or exit

Arithmetic OperationsCompute following Result 51. 2 5 1.0323 (2 - 1)

2 1/32 Area= r take r= - 1 0.6781

3. Sin /60.5

x4. 3 = 17 for x 2.57

Basic Task: Plot the function sin(x) between 0x4 Create an x-array of 100 samples between 0 and 4.

Calculate sin(.) of the x-array

Plot the y-array

>>x=linspace(0,4*pi,100);>>y=sin(x);>>plot(y)

Plot the function e-x/3sin(x) between 0x4 Create an x-array of 100 samples between 0 and 4.

Calculate sin(.) of the x-array

Calculate e-x/3 of the x-array

Multiply the arrays y and y1

>>x=linspace(0,4*pi,100);>>y=sin(x);>>y1=exp(-x/3);>>y2=y*y1;

Plot the function e-x/3sin(x) between 0x4 Multiply the arrays y and y1 correctly

Plot the y2-array

>>y2=y.*y1;>>plot(y2)

Display Facilitiesplot(.)

stem(.)

Example:>>x=linspace(0,4*pi,100);>>y=sin(x);>>plot(y)>>plot(x,y)

Example:>>stem(y)>>stem(x,y)

Display Facilitiestitle(.)

xlabel(.)

ylabel(.)>>title(This is the sinus function)>>xlabel(x (secs))>>ylabel(sin(x))

Operators (relational, logical)== Equal to~= Not equal to< Strictly smaller> Strictly greater= Greater than equal to& And operator | Or operator

Flow Controlif for while break .

Control Structures If Statement Syntax

if (Condition_1)Matlab Commandselseif (Condition_2)Matlab Commandselseif (Condition_3)Matlab CommandselseMatlab Commandsend

Control Structures For loop syntax

for i=Index_ArrayMatlab Commandsend

Control StructuresWhile Loop Syntax

while (condition)Matlab Commandsend

Dummy Example

while ((a>3) & (b==5)) Some Matlab Commands;end

Use of M-FileClick to create a new M-File Extension .m A text file containing script or function or program to run

Use of M-FileIf you include ; at the end of each statement,result will not be shown immediately

Save file as Denem430.m

Writing User Defined Functions Functions are m-files which can be executed by specifying some inputs and supply some desired outputs. The code telling the Matlab that an m-file is actually a function is

You should write this command at the beginning of the m-file and you should save the m-file with a file name same as the function namefunction out1=functionname(in1)function out1=functionname(in1,in2,in3)function [out1,out2]=functionname(in1,in2)

Writing User Defined Functions Another function which takes an input array and returns the sum and product of its elements as outputs

The function sumprod(.) can be called from command window or an m-file as

Useful CommandsThe two commands used most by Matlabusers are

>>help functionname

>>lookfor keyword

Signal Processing Examples To generate a cosine signal.clc;t=0:.01: pi;y=cos (2*pi*t);subplot (2,1,1);plot (t,y);subplot(2,1,2);stem(t,y);display('the resultant is');

Program Output:

To generate the exponential signalclc;n= input('enter the length of exponential signal');t= 0:n;a= input('enter the a value');z= exp(a*t);subplot(2,2,1);stem(z,t);display('the result length of exponential signal');z

Output:Enter the length of exponential signal 4Enter the a value 1The result length of exponential signalz =1.0000 0.3679 0.1353 0.0498 0.0183

Writing User Defined Functions ExamplesWrite a function : out=squarer (A, ind)Which takes the square of the input matrix if the input indicator is equal to 1And takes the element by element square of the input matrix if the input indicator is equal to 2

DFTDiscrete Fourier transform(DFT) converts a finite list of equally spacedsamplesof afunctioninto the list ofcoefficientsof a finite combination ofcomplexsinusoids, ordered by theirfrequencies, that has those same sample values. It can be said to convert the sampled function from its original domain (oftentimeor position along a line) to thefrequency domain.

DFT In digital signal processing, the function is any quantity orsignalthat varies over time, such as the pressure of asound wave, aradiosignal, or dailytemperaturereadings, sampled over a finite time interval (often defined by awindow function). Inimage processing, the samples can be the values ofpixelsalong a row or column of araster image

DFTThesequenceofNcomplex numbersis transformed into anN-periodic sequence of complex numbersaccording to the DFT formula: N-1 -j(2/N)nkF[n]= f[k] e (n=0; N-1) k=0

Computing DiscreteFourierTransformclc; xn=[2,1,3,1];n=50;l=length(xn);x1=[xn,zeros(1,n-l)];for k=0:1:n-1; for g=0:1:n-1; p=exp(-i*2*pi*g*k/n); x2(k+1,g+1)=p; endendxk=x1*x2;subplot(2,2,1);y= abs(xk);stem(y);z=angle(xk);subplot(2,2,2);stem(z);disp('the resultant signal is');y

Output

Matlab Functionality in Speech Signal Processing Basic Functionality read a speech file (i.e., open a .wav speech file and read the speech sample into a MATLAB array) write a speech file (i.e., write a MATLAB array of speech samples into a .wav speech file) play a MATLAB array of speech samples as an audio file plot a speech file (MATLAB array) as a waveform using a strips plot format plot a speech file (MATLAB array) as one or more 4line plot(s) convert the sampling rate associated with a speech file (MATLAB array) to a different sampling rate high pass filter a speech file (MATLAB array) to eliminate hum and low frequency noise plot a frame of speech and its associated spectral log magnitude plot a spectrogram of a speech file (MATLAB array)

Recording of speech signalclc;close all;%please say your names to record it For i = 1:4Fs=22050;file = sprintf('%s%d.wav','g',i);input('You have 2 seconds to say your name. Press enter when ready to record--> '); y = wavrecord(2*Fs,Fs); sound(y,Fs); wavwrite(y,Fs,file);end

Naming the Speech Filefor i = 1:4 strI=int2str(i); wavName='g'; temp=strcat(wavName,strI); %get the speech signal sample [x,fs]=wavread(temp,[1 44100]);

ms1=fs/1000; % maximum speech Fx at 1000Hz ms20=fs/50; % minimum speech Fx at 50Hz

% hamming window

Y=fft(x.*hamming(length(x)));

Waveform Plot% plot waveform

t=(0:length(x)-1)/fs; % times of sampling instants

figure;name1='waveform of 'title1=strcat({name1},{temp});plot(t,x);

Gridtitle(title1);

xlabel('Time (s)');

ylabel('Amplitude');end

Plotting the spectrum % plot spectrum of bottom 5000Hz

hz5000=5000*length(Y)/fs;

f=(0:hz5000)*fs/length(Y);figure;name2=' spectrum of 'title2=strcat({name2},{temp});

plot(f,20*log10(abs(Y(1:length(f)))+eps));grid;title(title2);

xlabel('Frequency (Hz)');

ylabel('Magnitude (dB)');

Cepstral Analysis to find fundamental frequency% cepstrum is DFT of log spectrum

C=fft(log(abs(Y)+eps));% plot between 1ms (=1000Hz) and 20ms (=50Hz)

q=(ms1:ms20)/fs;

figure;name3=' cepstrum of 'title3=strcat({name3},{temp});plot(q,abs(C(ms1:ms20)));grid;title(title3);xlabel('Quefrency (s)');

ylabel('Amplitude');

%search for the index of the peak in the cepstrum between 1 and 20ms, and then convert back to hertz

[c,fx]=max(abs(C(ms1:ms20)));

fprintf('fundamentalfrequency=%gHz\n',fs/(ms1+fx-1));

%fundamental frequency estimation time domain

% get a section of vowel

[x,fs]=wavread(temp,[1 44100]);

ms20=fs/50; % minimum speech Fx at 50Hz

Fundamental Frequency (Speech Feature)%search for the index of the peak in the cepstrum between 1 and 20ms, and then convert back to hertz

[c,fx]=max(abs(C(ms1:ms20)));

fprintf('fundamentalfrequency=%gHz\n',fs/(ms1+fx-1));

Thank You

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