basic matlab operations

8/6/2019 Basic Matlab Operations

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BASIC MATLAB OPERATIONSFOR MULTIPLICATION:*NO.OF COLUMNS = NO.OF ROWS

a=[1 2 3];(3 COLUMNS) b=[1 2 3;4 5 6;7 8 9];(3 ROWS) c=a*b

c =30 36 42

FOR ELEMENTS MULTIPLICATION:*SQUARE MATRIX = SQUARE MATRIX

a=[4 2;2 4];(2 ROWS=2 COLUMNS)

b=[1 2;2 1];(2 ROWS=2 COLUMNS)c=a*bc=

8 1010 8

FOR DIVISION:*NO.OF ROWS = NO.OF COLUMNS

a=[1 2:2 1];

(2 ROWS)b=[1 2];(2 COLUMNS)c= b\ac =

0 0 00.5000 1.0000 0.5000

FOR ELEMENTS DIVISION:

a=[1 2 4 7];b=[2 4 7 5 ];

c=b\ac =

0 0 0 00 0 0 0

0.1429 0.2857 0.5714 1.00000 0 0 0

Prepared by:Hayat WaliIqra University Page 1


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c=a\bc =

0 0 0 00 0 0 0

0 0 0 00.2857 0.5714 1.0000 0.7143

POWER OF ELEMENTS:

a=[1 2 3 4];

b=(a.^2)b=1 4 9 16

c=(a.^3)c=1 8 27 64

d=(a.^4)d=1 16 81 256

& So On

ADDITION , SUBTRACTION, MULTIPLICATION, DIVISION :

a=[1 4 2 5];

a+1ans =2 5 3 6

a-1ans = 0 3 1 4

a*1ans =1 4 2 5

a/1ans =1 4 2 5

a\1ans =

000

0.2000

COLUMNS ADDITION:



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a=[2 4;5 6];sum(a)

ans =

7 10

ROWS ADDITION:

a=[2 4;5 6];sum(a,2)

ans =

611

ALL ELEMENTS ADDITION:

a=[2 4;5 6];sum(sum(a))

ans =

17INVERSE:

a=[2 4;5 6];

inv(a)ans =

-0.7500 0.50000.6250 -0.2500

DETERMINATE:

a=[2 4;5 6];

det(a)ans =

-8

MEAN:

a=[2 4;5 6];

mean(a)



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ans =

3.5000 5.0000STD:

a=[2 4;5 6];

std(a)ans =

2.1213 1.4142

VARIATION:

a=[2 4;5 6];

var(a)ans =

4.5000 2.0000

FOR MAXIMUM ROW :

a=[1 2 3 4;4 5 6 7;7 8 9 7];

max(a)ans =

7 8 9 7

FOR MINIMUM ROW :

a=[1 2 3 4;4 5 6 7;7 8 9 7];min(a)ans =

1 2 3 4

FOR MAXIMUM ELEMENT:

a=[1 2 3 4;4 5 6 7;7 8 9 7];

max(max(a))ans =

9



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FOR MINIMUM ELEMENT:

a=[1 2 3 4;4 5 6 7;7 8 9 7];

min(min(a))

ans =

1

FOR SPECIFIC ROW:

a=[1 4 7;2 5 8;1 4 7];

a(2,:)ans =

2 5 8

FOR SPECIFIC COLUMN:

a=[1 4 7;2 5 8;1 4 7];

a(:,3)ans =

787

FOR SPECIFIC ELEMENT:

a=[1 4 7;2 5 8;1 4 7];

a(2,3)ans =

8

SIZE OF MATRIX:

a=[1 2 4 7;4 5 8 7;4 1 4 4];

size(a)ans =

3 4

SIZE OF ROWS:



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a=[1 2 4 7;4 5 8 7;4 1 4 4];

size(a,1)ans =

3

SIZE OF COLUMNS:

a=[1 2 4 7;4 5 8 7;4 1 4 4];size(a,2)ans =

4ALL ZEROS WITH REFERENCE OF ANY MATRIX:

a=[1 2 4 7;4 5 8 7;4 1 4 4];

zeros(size(a))ans =

0 0 0 00 0 0 00 0 0 0

REFRENCE ELEMENTS:

a=[1 2 4 7;4 5 8 7;4 1 4 4];a(2:3,3:4)ans =

8 74 4

PLOTING IN MATLAB

Asin(wt+ ) (w=2f)A=Amplitude (f=w/2)w=Angular frequencyt=Time=Phase Differences

x=[1 2 4 5 7];



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y=[4 7 8 5 8];plot(x,y)

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X-axis

Y-Axis

x=[1 2 4 5 7];y=[4 7 8 5 8];plot(y,x)

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Y=Axis

X-Axis

t=[pi*(0:0.02:2)];y=sin(t);plot(y)



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t=[pi*(0:0.02:2)];y=sin(t+pi/2);plot(y)

t=[pi*(0:0.02:2)];plot(t,sin(t))

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t=[pi*(0:0.02:2)];plot(t,cos(t))


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t=[pi*(0:0.02:2)];y=3*sin(3*t+0);plot(y)

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t=[pi*(0:0.02:2)];y=2*sin(6*t+pi);plot(y)

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t=[pi*(0:0.02:2)];



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y=2*cos(2*t+0);plot(y)

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t=[pi*(0:0.02:2)];

plot(t,sin(t))

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t=[pi*(0:0.02:2)];plot(t,cos(t))

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t=[pi*(0:0.02:2)];plot(t,sinc(t))

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t=[pi*(0:0.02:2)];plot(t,exp(t))

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t=[pi*(0:0.02:10)];plot(t,sawtooth(t))



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x=[-5:0.0001:5];y=x.^2;plot(y)

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x=[-5:0.0001:5];y=x.^3;plot(y)

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x=linspace(-5,5);y=sinc(x);



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plot(x,y)

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PLOTINGWITH COLOURS

t=[0:0.0001:2*pi];

plot(t,sin(t),'k')

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With Black

plot(t,sin(t),'g')



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With Green

plot(t,sin(t),'b')

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With Blue

plot(t,cos(t),'r')



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With Red

PLOTINGWITH DESIGNS & COLOURS

x=[0:0.1:2*pi];

plot(x,sin(x),'o-')

plot(x,sin(x),'g+')


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plot(x,sin(x),'kO')

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plot(x,cos(x),'R^')



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plot(x,cos(x),'kd')

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plot(x,cos(x),'r+')



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DIFFERENT TYPES OF PLOTING

t=[0:0.001:1];plot([t t.^2 t.^3])

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t=[0:0.001:1]';



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plot([t,sin(t),cos(t)])

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t=[0:0.001:1];plot(t,[sin(t) cos(t)])

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x=0:0.001:2*pi;fill(x,sin(x),'g')



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fs=10000;t=0:1/fs:1/5;y=sawtooth(2*pi*5*t);plot(t,y)

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t=0:0.00001:10;



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y=sawtooth(2*pi*3*t*3);plot(t,y)

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t=0:0.00001:10;y=sawtooth(t,.5);plot(t,y)

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t=0:0.0001:100;rectpuls(t);plot(t,rectpuls(t))

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t=0:0.0001:100;plot(t,square(t))

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t=0:0.0001:100;y=square(t,80);

fill(t,y,'r')



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t=0:0.0001:100;y=square(t,100);fill(t,y,'g')y=square(t,40);fill(t,y,'r')

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PLOTING WITH (Sine & Exponential)

t=[0:0.01:2*pi];y=exp(sin(t));plotyy(t,y,t,y,'plot','stem')



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t=[0:0.1:2*pi];y=exp(sin(t));plotyy(t,y,t,y,'plot','stem')

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SUBPLOTTING

For plotting many Figures in a single figure



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1

x=linspace(0,2*pi); (linspace is used for equal spacing b/w each number)subplot(2,2,1) (2Rows, 2columns & 1st fig)

x=linspace(0,2*pi);

subplot(3,3,1) (3Rows, 3columns & 1st fig)subplot(3,3,2) (3Rows, 3columns & 2st fig)subplot(3,3,3) (3Rows, 3columns & 3rd fig)subplot(3,3,4) (3Rows, 3columns & 4th fig)subplot(3,3,5) (3Rows, 3columns & 5th fig)

x=linspace(0,2*pi);

subplot(3,3,1) (3Rows, 3columns & 1st fig)subplot(3,3,2) (3Rows, 3columns & 2st fig)subplot(3,3,3) (3Rows, 3columns & 3rd fig)



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subplot(3,3,4) (3Rows, 3columns & 4th fig)subplot(3,3,5) (3Rows, 3columns & 5th fig)

plot(x,sin(x))

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x=[-10:0.01:10];plot(x,exp(x))grid on (grid on is used for lining in graph)hold on (hold on is used for holding a figure for all graphs)plot(x,exp(0.95*x))plot(x,exp(0.85*x))

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PLOTTING WITHCOLOURS, TITLES, & LABELS



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x=[-10:0.01:10];plot(x,sin(x))

hold ongrid onplot(x,sin(2*x),'r--')title('Multi sine plot') (title is used for assigning a Title)ylabel('y-axis') (ylabel is used for assigning Y-Label)xlabel('x-axis') (xlabel is used for assigning X-Label)legend('SinX','Sine2X') (legend is used for assigning

separate notations for graphs)

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1Multi sine plot

y-axis

x-axis

SinX

Sine2X

SEMI-LOG PLOTTING



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x=[1000 10000 100000];y=[2 4 6];semilogx(x,y)

x=[10000,10000];y=[1000,1000];loglog(x,y)

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AXIS DEFINING

axis([0 10 0 10]) (xlim 0 10; ylim 0 10)


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axis([0 4 0 1]) (xlim 0 4; ylim 0 1)

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axis([-10 10 0 10]) (xlim -10 10; ylim -10 10)

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PLOT TOOLS



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UTILITIES OF PLOT TOOLS:

Used for plotting different figures Used for designing graph in many ways Used for Title, X-label, Y-label & Legend as well Giving 2D & 3D views Changing colors

Giving Text & many other tools can be used for plotting graphs

3D PLOTTING



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x=pi*(0:0.05:1);y=2*x;[X,Y]=meshgrid(x,y);plot(X(:),Y(:),'k.')plot(X(:),Y(:),'k.')surf(X,Y,sin(X^2))camlight leftlighting phong

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x=pi*(0:0.05:1);y=2*x;[X,Y]=meshgrid(x,y);plot(X(:),Y(:),'k.')surf(X,Y,sin(X.^2+Y))

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x=pi*(0:0.05:1);y=2*x;[X,Y]=meshgrid(x,y);



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plot(X(:),Y(:),'k.')surf(x,y,sin(X))

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x=pi*(0:0.05:1);y=2*x;[X,Y]=meshgrid(x,y);plot(X(:),Y(:),'k.')surf(x,y,cos(X.^2))

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[X,Y]=meshgrid(-8:0.5:8);R=sqrt(X.^2+Y.^2)+eps;



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Z=sin(R)./R;mesh(X,Y,Z)surf(X,Y,Z)colormap gray

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[X,Y]=meshgrid(-8:0.5:8);R=sqrt(X.^2+Y.^2)+eps;Z=sin(R)./R;mesh(X,Y,Z)surf(X,Y,Z)

colormap hsv

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[X,Y]=meshgrid(-8:0.5:8);



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R=sqrt(X.^2+Y.^2)+eps;Z=sin(R)./R;mesh(X,Y,Z)surf(X,Y,Z)colormap copper

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x=[7 3 9 2 11 15 20 7 5 9];bar([0:length(x)-1],x)th=[0:0.0001:2*pi];rho=2*sin(th).*cos(th);

polar(th,rho)

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x=rand([1 100]);hist(x,10);



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NUMERICAL ANALYSISPrepared by:Hayat WaliIqra University Page 35


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f=@(t,y)2.*y-23;ode45(f,[0,1],1)

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f=@(t,y)2.*y-2;ode45(f,[0,1],1)

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f=@(t,y)2.*y-2;ode45(f,[-1,1],-1)

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f=@(t,y)2.*y-23;ode45(f,[-1,1],1)

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f=@(t,y)2.*y-3;ode45(f,[-1,1],1)



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DIFFERENTIATION

Single Derivative:

syms xg=sin(x);

diff(g) d(g)/dx=d(sinx)/dx=Cosxans =

cos(x)diff(x) d(x)/dx=1

ans =1

Single Derivative:

syms x g=sin(x); g=sin(x)

diff(g,x) d(g)/dx=d(sinx)/dx=Cosx

ans =cos(x)

g=cos(x);diff(g,x)

ans =

-sin(x)

Substitute Values (In Radian) :



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syms xg=sin(x);diff(g,x)

ans =cos(x)subs(ans,x,2.1) cosx=cos(2.1)ans =

-0.5048

Double Derivative:

syms xg=sin(x); g=sin(x)diff(g,x,2) d(g)/dx=d(sinx)/dx

ans =-sin(x)

Higher Order Derivatives :

syms xdiff(sin(x),x,1) (1 Represents for 1st Derivative)

ans =

cos(x)

syms xdiff(sin(x),x,2) (2 Represents for 2nd Derivative)

ans =

-sin(x)

syms xdiff(sin(x),x,3) (3 Represents for 3rd Derivative)

ans =

-cos(x)



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syms xdiff(sin(x),x,4) (4 Represents for 4th Derivative)

ans =

sin(x)

SUBSTITUTING VALUES

This is the shortcut command for substituting values in any function.Subs(diff(f(x)),x,?)

syms x (syms is Short-cut for constructing symbolic objects.)

syms xdiff(tan(x)) (Differentiate Tanx)ans =

1+tan(x)^2subs(ans,x,2) (Putting x=2 in the answer)ans =

5.7744

syms xsubs(diff(tan(x)),x,2) (Putting x=2 after differentiate Tanx)ans =

5.7744

syms xsubs(diff(sin(x)),x,1) (Putting x=1 after differentiate Sinx)ans =

0.5403

syms x

subs(diff(cos(x)),x,36) (Putting x=36 after differentiate Cosx)ans =0.9918

syms xdiff(tan(x^6-3*x+5)) (Differentiate Tan(x^6-3*x+5))ans =

(1+tan(x^6-3*x+5)^2)*(6*x^5-3)



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subs(ans,x,3/2) (Putting x=3/2 in the answer)ans =

69.9149

subs(diff(tan(x^6-3*x+5)),x,3/2) (Putting x=3/2 after differentiating Tan(x^6-3*x+5) )ans =

69.9149

INTEGERATION

syms xint(sin(x),x) (Integrate sin(x) )ans =

-cos(x)

syms xint(x*sin(x),x) (Integrate xsin(x))ans =

sin(x)-x*cos(x)

DOUBLE INTEGERATION:

double(int(sin(x^5+x^3),x,0,pi/2)) (Integratesin(x^5+x^3) ) & (0-/2) is limit

ans =

0.2910

quad8(inline(sin(x^5+x^3)'),0,pi/2) (Integrate sin(x^5+x^3) ) & (0-/2) is limit

ans =

0.2910

quad8(inline(sin(x^5+x^3)'),0,pi/2) (Integrate sin(x^5+x^3) ) & (0-/2) is limit

ans =

0.2910



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RELATIONAL OPERATION

x=[1 2;2 3;5 6]

x =

1 2

2 35 6

x>2 (x>2 shows (1) the areas where x is greater than 2 otherwise 0)ans =

0 00 11 1

x>1 (x>1 shows (1) the areas where x is greater than 1 otherwise 0)ans =

0 11 11 1

3>1ans =

1

3


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ans =

0

32) (Shows all values that are greater than 2)

ans =

536

x(x>1) (Shows all values that are greater than 1)ans =



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25236

POLYNOMIAL EQUATIONS

Polynomial equations are derived from word Poly means many. We are here to find out the slop of the equations. E.g.:( ax^3+bx^2+cx+d )

x=[1:2:20];y=[2:2:20];x=x';y=y';

fit=polyfit(x,y,1)

fit =1.0000 1.0000

plot(x,y,'o',x,fit(1)*x+fit(2))

0 2 4 6 8 10 12 14 16 18 202

4

6

8

10

12

14

16

18

20

22

Finding Polynomial Equation by Roots:

If roots are :x= +3x= -1

We use the command POLY to converts the roots into polynomial.

Manually: In MATLAB



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E.g.: (x-3)(x+1) a=[3;-1]x2 + x - 3x - 3= 0 poly(a)x2 -2x -3 = 0 ans =

1 -2 -3x2 -2x -3 = 0

F inding Roots by Polynomial Equation :

If equation is :

x2 -2x -3 = 0

We use the command ROOTS to find out the roots of the equation:

Manually: In MATLAB

x2-2x-3 = 0 p=[1 -2 -3];x2+x -3x-3 = 0 roots(p)(x-3)(x+1)=0 ans =

x= +3 +3x= -1 -1

OR

roots([1 -2 -3])ans =

+3-1

Evaluate the Polynomial :

If the Polynomial Equation is:

F(x)=x3+6x-3=0F(x)=x3+0x2+6x-3=0

Coefficients are [1 0 6 -3]

Evaluating by x=2

v=[1 0 6 -3];polyval(v,2)ans =

17

Evaluating by x=3

v=[1 0 6 -3];polyval(v,3)ans =

42



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B =

9

3

X =[X1;X2]

X =

X1

X2

AX=B

X=A-1 B

X =

X1= 5.4000

X2= -0.6000

5.4000

-0.6000



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PROGRAM M ING IN MATLAB

Programming is defined as list of instructions. We create M-file for algorithm of any program. F5 is used as a shortcut key to run a program.

Steps for writing & running a program:

1. Click new & go to the M-file.2. Write algorithm of any program,3. Save it using Ctrl-S or by clicking save button after assigning file name.4. Go to the Matlab command window and type the file name.



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Example: Go to M-file & write program.

clcx=0:0.0001:10

save & file name E.g. (Sine1.m) Go to Matlab Command Window & type file name E.g. (Sine1).

Assigning Comments:

Go to M-file & write program. % (Write anything for comments). E.g.: % Hey how are you buddy?

Save it by assigning any file name E.g. (buddy.m). Go to Matlab Command Window & type file name E.g. (help

buddy).

Function [x1, x2] =quadratic (a,b,c) [x1,x2]Output Arguments

(a,b,c) Input Arguments



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Program 1: (Plotting Sine wave):

Go to M-file & write algorithm of program. x=0:0.00001:10;

y=sin(x);plot(x,y)

Save it by assigning file name (a1.m). Go to the Matlab command window and type the file name (a1).

Solution is:

0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Program 2 : (Quadratic Equation Solver) :

x=-bb2-4ac2a

We are going to solve a quadratic equation by quadratic formula algorithm.

Go to M-file & write algorithm of program. function[x1,x2]=quadratic(a,b,c);

a=2;b=3;c=4;d=sqrt(b^2-4*a*c);x1=(-b+d)/(2*a)x2=(-b-d)/(2*a)

Save it by assigning file name (quadratic.m).

Go to the Matlab command window and type the file name (quadratic). Solution is:



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x1 =-0.7500 + 1.1990i

x2 =-0.7500 - 1.1990i

Program 3 : (Displaying a using for - loop ): Go to M-file & write algorithm of program. a=1;

for i=[1:10];a=a+i;disp(a)

end Save it by assigning file name (a3.m). Go to the Matlab command window and type the file name (a3). Solution is:

a1

24711162229374656

Program 4 : (Displaying a using for - loop ):

Go to M-file & write algorithm of program. for i=1:10;

a(i)=i*iend

Save it by assigning file name (a4.m). Go to the Matlab command window and type the file name (a4). Solution is:

a1

a =1a =1 4

a =1 4 9a =1 4 9 16a =1 4 9 16 25a =1 4 9 16 25 36a =



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1 4 9 16 25 36 49a =1 4 9 16 25 36 49 64a =1 4 9 16 25 36 49 64 81a =

1 4 9 16 25 36 49 64 81 100

Program 5 : (Plotting sine wave using No. of cycles & frequency ):

Go to M-file & write algorithm of program. f=input('enter frequency');

n=input('enter n.o of cycles');t=(0:0.0001:n/f);y=sin(2*pi*f*t);plot(t,y)

Save it by assigning file name (a5.m). Go to the Matlab command window and type the file name (a5). Solution is:

a1enter frequency3 (No. of Frequencies are3)enter n.o of cycles3 (No. of Cycles are 3)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Program 6 : (Plotting sine & cosine waves using while-loop ):

Go to M-file & write algorithm of program. x=0:0.1:10;while(1>0)

a=menu('sine cosine',1,2,3,4,5);plot(x,sin(x))if (a==2)

plot(x,cos(x))elseif(a==3)

stem(x,sin(x))



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elseif(a==4)stem(x,cos(x))elseif(a==5)

breakendend

Save it by assigning file name (a6.m). Go to the Matlab command window and type the file name (a6). A table will appear (Sine Cosine) containing numbers from 1-5. Solution is:

By pressing 1:

0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

By pressing 2:

0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

By pressing 3:

By pressing 4:


0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


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0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

By pressing 5: (Program ended)

0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Program 7 : ( Displaying r andom numbers ):

Go to M-file & write algorithm of program. t=rand(1);

if t>0.75;s=0

elseif t


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s=1else

a=1-2*(t-0.25)end


Program 8 : (Displaying Tables of 1,2,3,4,5 ):

Go to M-file & write algorithm of program. clc

while(1>0)

a=menu('table',1,2,3,4,5);if(a==1)for s=1:10z=1*s;disp('1X');disp(s);disp('=');disp(z);endendif(a==2)for s=1:10z=2*s;disp('2x');disp(s);disp('=');disp(z);endendif(a==3)for s=1:10z=3*s;disp('3x');disp(s);disp('=');disp(z);endendif(a==4)for s=1:10z=4*s;disp('4x');disp(s);disp('=');disp(z);endend

if(a==5)breakendend




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SIGNALS & SYSTEMSUSING MATLAB

CREATING SIGNALS (IN DISCREATE TIME) :

Impulse function:

x=[1:11];y=[1 zeros(1,10)];stem(x,y)

1 2 3 4 5 6 7 8 9 10 110

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Unit step function:

x=[1:11];y=[ones(1,11)];stem(x,y)



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1 2 3 4 5 6 7 8 9 1 0 1 10

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6

0 . 7

0 . 8

0 . 9

1

x=[1:10];y=[0,0 ones(1,8)];stem(x,y)

1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Exponential function ( Decaying) :n=1:10;x=0.5.^n;stem(n,x)



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1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Exponential function ( Increasing) :n=0:10;x=2.^n;stem(n,x)

0 1 2 3 4 5 6 7 8 9 100

200

400

600

800

1000

1200

CREATING SIGNALS (IN CONTINUOUS TIME):

Unit step function:t=ones(1,100);plot(t)

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2



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Exponential function (Increasing) :t=1:0.001:10;y=exp(t);plot(t,y)

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5x 10

4

Exponential function (Decaying) :

t=1:0.001:10;y=exp(-t);plot(t,y)

1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

CONVOLUTION

Method #1(On command window)

X[n] =0.5n u[n]

H[n]=1 0n4

Y[n]=?

Input :

n=0:10;x=0.5.^n;stem(n,x)



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Y[n]0246810

1

2

1

4

1

6

1

8

2

0

00

.

2

0

.

4

0

.

6

0

.

8

11

.

2

1

.

4

1

.

6

1

.

8

2

Method #2( By programming )

LAPLACE TRANSFORM

The laplace transform of a signal x(t),



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X(t) X(s)=- xte-st dt

H(s) = T.F =OutputInput

H(s) = T.F =S2-1S2+2S-3 S2-1 = 0

S2=1 S= 1

S2+2S-3=0

S2+3S-S-3 = 0 S (S +3)-1(S +3) = 0

(S -1)( S +3) = 0 S=1;S=-3

IN MATLAB:

For Equation: For Roots:

o=[1 0 -1]; Z1=roots(o)i=[1 2 -3]; Z1 =

1-1

h=tf(o,i) P1=roots(i)Transfer function: P1 =-31

s^2 - 1-------------s^2 + 2 s - 3

For plotting S-plane:

o=[1 0 -1]; Outputi=[1 2 -3]; Inputh=tf(o,i); Transfer functionZ1=roots(o); Zeros



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P1=roots(i); Poles pzmap(Z1,P1) S-plane Map

-3 -2 .5 -2 -1 .5 -1 -0 .5 0 0 .5 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1Pole-Zero Map

Rea l A x is

ImaginaryAxis

For plotting S-plane using Sgrid:



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o=[1 0 -1]; Outputi=[1 2 -3]; Inputh=tf(o,i); Transfer functionZ1=roots(o); ZerosP1=roots(i); Poles

pzmap(Z1,P1) S-plane Mapsgrid

-3 -2 .5 -2 -1 .5 -1 -0 .5 0 0 .5 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

10.350.580.760.860.92

0.96

0.984

0.996

0.350.580.760.860.920.96

0.984

0.996

0.511.522.5

Pole-Zero Map

Rea l A x is

ImaginaryAxis

For viewing samples of audio file:

a=wavread(file location',samples)E.g.: a=wavread('C:\WINDOWS\Media\tada',2000)

MATLAB SOUND:



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t=0:1/8192:1;x=cos(2*pi*400*t);soundsc(x,8198)

For Noise:

t=0:1/8192:1;x=cos(2*pi*400*t);soundsc(x,8000)noise=randn(8192,1);soundsc(noise,8000)

SIMULINKX(t)=Acos(wt+)

A GainCos Trigonometric functionW FrequencyT Time



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Phase difference

dxdy=(-2x+1) dx

dx=-2x+1dx

X=-2x22+x+c

X=-x2+x+c

X(k)=e(k-3)+2.2x(k-1)-1.57x(k-2)+0.3x(k-3)For 0k8



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basic matlab operations

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