hayatwali.weebly.comhayatwali.weebly.com/uploads/5/8/3/5/5835489/basic_m… · web viewbasic...

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*b c= 8 10 10 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 0 0.5000 1.0000 0.5000

FOR ELEMENTS’ DIVISION:

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

0 0 0 0 0 0 0 0 0.1429 0.2857 0.5714 1.0000 0 0 0 0

Prepared by:Hayat WaliIqra University

c=a\bc =

0 0 0 0 0 0 0 0 0 0 0 0 0.2857 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 = 0 0 0 0.2000


COLUMNS ADDITION:

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

ans =

7 10

ROWS ADDITION:

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

ans =

6 11

ALL ELEMENTS ADDITION:

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

ans =

17INVERSE:

a=[2 4;5 6];

inv(a)ans =

-0.7500 0.5000 0.6250 -0.2500

DETERMINATE:

a=[2 4;5 6];

det(a)ans =

-8


MEAN:

a=[2 4;5 6];

mean(a)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

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 =

7 8 7

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:

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 =

4 ALL 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 0 0 0 0 0 0 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 7 4 4


PLOTING IN MATLAB

Asin(wt+ θ) (w=2πf)A=Amplitude (f=w/2π)w=Angular frequencyt=Timeθ=Phase Differences

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

1 2 3 4 5 6 74

4.5

5

5.5

6

6.5

7

7.5

8

X-axis

Y-A

xis

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

4 4.5 5 5.5 6 6.5 7 7.5 81

2

3

4

5

6

7

Y=Axis

X-A

xis


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

0 20 40 60 80 100 120-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

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

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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


0 20 40 60 80 100 120-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

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

0 20 40 60 80 100 120-3

-2

-1

0

1

2

3

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

0 20 40 60 80 100 120-2

-1.5

-1

-0.5

0

0.5

1

1.5

2


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

0 20 40 60 80 100 120-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


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

0 1 2 3 4 5 6 7-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

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

0 1 2 3 4 5 6 70

100

200

300

400

500

600

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

0 5 10 15 20 25 30 35-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


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

0 2 4 6 8 10 12

x 104

0

5

10

15

20

25

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

0 2 4 6 8 10 12

x 104

-150

-100

-50

0

50

100

150

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

-5 -4 -3 -2 -1 0 1 2 3 4 5-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


PLOTINGWITH COLOURS

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

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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1With Black

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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1With Green


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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1With Blue

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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1With Red


PLOTINGWITH DESIGNS & COLOURS

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

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

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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


DIFFERENT TYPES OF PLOTING

t=[0:0.001:1]’;plot([t t.^2 t.^3])

0 200 400 600 800 1000 12000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

t=[0:0.001:1]';plot([t,sin(t),cos(t)])

0 200 400 600 800 1000 12000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


t=[0:0.001:1]’;plot(t,[sin(t) cos(t)])

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

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

0 1 2 3 4 5 6 7-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


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

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

t=0:0.00001:10;y=sawtooth(2*pi*3*t*3);plot(t,y)

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


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

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

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

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


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

0 10 20 30 40 50 60 70 80 90 100-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

t=0:0.0001:100;y=square(t,80);fill(t,y,'r')

0 10 20 30 40 50 60 70 80 90 100-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

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

0 10 20 30 40 50 60 70 80 90 100-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


PLOTING WITH (Sine & Exponential)

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

0 1 2 3 4 5 6 7151

151.5

152

152.5

153

153.5

0 1 2 3 4 5 6 7151

151.5

152

152.5

153

153.5

0 1 2 3 4 5 6 7151

151.5

152

152.5

153

153.5

151 151.5 152 152.5 153 153.50

1

2

3

4

5

6

7

151 151.5 152 152.5 153 153.50

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7151

151.5

152

152.5

153

153.5

0 1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

3

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

0 1 2 3 4 5 6 7151

151.5

152

152.5

153

153.5

0 1 2 3 4 5 6 7151

151.5

152

152.5

153

153.5

0 1 2 3 4 5 6 7151

151.5

152

152.5

153

153.5

151 151.5 152 152.5 153 153.50

1

2

3

4

5

6

7

151 151.5 152 152.5 153 153.50

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7151

151.5

152

152.5

153

153.5

0 1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

3


0 0.5 10

0.2

0.4

0.6

0.8

1

(3,3,3)

0 0.5 10

0.5

1(3,3,1)

0 0.5 10

0.5

1(3,3,2)

0 0.5 10

0.5

1

(3,3,4)

0 0.5 10

0.5

1(3,3,5)

0 0.5 10

0.5

1

SUBPLOTTINGFor plotting many Figures in a single figure

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

plot(x,sin(x))

0 2 4 6 8-1

-0.5

0

0.5

1

0 0.5 10

0.2

0.4

0.6

0.8

1

0 0.5 10

0.2

0.4

0.6

0.8

1

0 0.5 10

0.2

0.4

0.6

0.8

1

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))

-10 -8 -6 -4 -2 0 2 4 6 8 100

0.5

1

1.5

2

2.5x 10

4


PLOTTING WITH COLOURS, TITLES, & LABELS

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)

-10 -8 -6 -4 -2 0 2 4 6 8 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1Multi sine plot

y-ax

is

x-axis

SinXSine2X


SEMI-LOG PLOTTING

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

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

103

104

105

102

103

104


103

104

105

2

2.5

3

3.5

4

4.5

5

5.5

6

AXIS DEFINING

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

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

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

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

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

-10 -8 -6 -4 -2 0 2 4 6 8 100

1

2

3

4

5

6

7

8

9

10


PLOT TOOLS

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

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

01

23

4

0

2

4

6

8-1

-0.5

0

0.5

1

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))

01

23

4

0

2

4

6

8-1

-0.5

0

0.5

1


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

01

23

4

02

4

6

80

0.2

0.4

0.6

0.8

1

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

01

23

4

0

2

4

68

-1

-0.5

0

0.5

1


[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 gray

-10-5

05

10

-10

-5

0

5

10-0.5

0

0.5

1

[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

-10-5

05

10

-10

-5

0

5

10-0.5

0

0.5

1


[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 copper

-10-5

05

10

-10

-5

0

5

10-0.5

0

0.5

1

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)

0.2

0.4

0.6

0.8

1

30

210

60

240

90

270

120

300

150

330

180 0


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

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15


NUMERICAL ANALYSIS

syms t f=@(t,y)2.*y-1

f =

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

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11

1.5

2

2.5

3

3.5

4

4.5

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

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.5

1

1.5

2

2.5x 10

14


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

-1 -0.95 -0.9 -0.85 -0.8 -0.75-14

-12

-10

-8

-6

-4

-2

0x 10

6

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

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-70

-60

-50

-40

-30

-20

-10

0

10

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

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2


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

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-120

-100

-80

-60

-40

-20

0

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

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-600

-500

-400

-300

-200

-100

0

100

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

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-30

-25

-20

-15

-10

-5

0

5


DIFFERENTIATION

Single Derivative:

syms xg=sin(x);

diff(g) d(g)/dx=d(sinx)/dx=Cosx ans = 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):

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 x g=sin(x); g=sin(x) diff(g,x,2) d’’(g)/dx=d”(sinx)/dx

ans = -sin(x)

Higher Order Derivatives:

syms x diff(sin(x),x,1) (1 Represents for 1st Derivative) ans = cos(x)

syms x diff(sin(x),x,2) (2 Represents for 2nd Derivative) ans = -sin(x)

syms x diff(sin(x),x,3) (3 Represents for 3rd Derivative) ans = -cos(x)

syms x diff(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)^2 subs(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 xsubs(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) 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 x int(sin(x),x) (Integrate sin(x) ) ans =

-cos(x)

syms x int(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)) (Integrate sin(x^5+x^3) ) & (0-π/2) is limit ans =

0.2910

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

0.2910

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

0.2910


RELATIONAL OPERATION

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

x =

1 2 2 3 5 6

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

0 0 0 1 1 1

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

0 1 1 1 1 1

3>1 ans =

1

3<1ans =

0

3<=6ans =

1

3==4ans =

0

3<=3ans =

1


POSITION/REFERENCE LOCATORCOLOUMN WISE

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

x = 1 2 2 3 5 6 x([2]) (Locating position at 2 in column)ans =

2 x([2 3 4]) (Locating position at 2,3,4 in column)ans =

2 5 2

x(2) (Locating position at 2 in column)ans =

2

x(3) (Locating position at 3 in column)ans =

5

x(x>2) (Shows all values that are greater than 2)ans =

5 3 6

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

2 5 2 3


6

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

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


Finding 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 +3 x= -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


MATRICES

Manual IN MATLABA =[2 3;1 4]A =

2 3 1 4

Inverse of A:

A-1 ¿ Adj A¿ A∨¿¿

Adj A = 4 -3 -1 2

|A| = (4x2)-(-1x-3)|A| = 8-3|A| = 5

A-1 = 4−3−12

5

A-1 = 0.8000 -0.6000

-0.2000 0.4000

A=[2 3;1 4];A^-1

ans =

0.8000 -0.6000 -0.2000 0.4000


Manual IN MATLAB A=[2 3;1 4]

A =

2 3 1 4

B=[9;3] B =

9 3

X =[X1;X2] X = X1 X2

AX=B X=A-1 B X =

X1= 5.4000 X2= -0.6000

A=[2 3;1 4]; B=[9;3]; X=A^-1*B

X =

5.4000-0.6000


PROGRAMMING 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.


Example: Go to M-file & write program. clc

x=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

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=−b±√b2−4ac2a

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:

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

2 4 7 11 16 22 29 37


46 56

Program 4: (Displaying ‘a’ using “for-loop”):

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

a(i)=i*iend


a1

a =1a =1 4a =1 4 9

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


a1enter frequency3 (No. of Frequencies are 3)


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)) 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

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 random numbers):

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

if t>0.75; s=0elseif t<0.25; s=1


else 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);endendif(a==5)breakendend



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)


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

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)


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

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] =0.5 n u[n] H[n]=1 0≤n≤4Y[n]=?

Input:

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


Input x[n]

0 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

Impulse Response h[n]

1 2 3 4 5 6 7 8 9 10 110

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Impulse Response:

h=ones(1,5);h=[h ones(1,5)];stem(h)

Convolution:

y=conv(x,h);stem(y)


Y[n]

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Method #2 (By programming)

LAPLACE TRANSFORMThe laplace transform of a signal x(t),


X(t) →X(s)=∫−∞

∞

x ( t ) e-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=0S2+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 -1h=tf(o,i) P1=roots(i) Transfer function: P1 = -3 1 s^2 - 1-------------s^2 + 2 s - 3

For plotting S-plane:Prepared by:Hayat WaliIqra University

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

Real Axis

Imag

inar

y Ax

is


For plotting S-plane using Sgrid :

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

0.511.522.53

Pole-Zero Map

Real Axis

Imag

inar

y Ax

is

For viewing samples of audio file:


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

MATLAB SOUND:

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)

SIMULINKPrepared by:Hayat WaliIqra University

X(t)=Acos(wt+θ) A → Gain Cos → Trigonometric function W → Frequency T → Time θ → Phase difference

dxdy

=∫(−2 x+1)dx

∫ dx=∫ (−2 x+1 )dx

X=-2 x2

2+x+c

X=-x2+ x+c

X(k)=e(k-3)+2.2x(k-1)-1.57x(k-2)+0.3x(k-3)For 0≤k≤8


hayatwali.weebly.comhayatwali.weebly.com/uploads/5/8/3/5/5835489/basic_m… · web viewbasic...

Documents