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Introductory Matlab Tutorial

Mohamed Aslan

April 1, 2010

1 Introduction

Variables

To create a variable just use it on the left hand side of an equal sign:

1 x = 1 0 ;2 z = x 0 . 2 5 ;

To print the value of a variable, just type its name without the semi-colon:

1 z

Vectors

A vector is a matrix with either one row or one column. A vector is definedby placing a sequence of numbers within square braces.

1 % H o r i z o nt a l v e c t o r2 h = [3 1 0 ] ;3 % V e r t i c a l v e ct o r

4 v = [4 ; 5 ; 6 ] ;

Matrices

Creating a matrix is the same as a vector, separate the rows of a matrix usingsemicolons:

1 A = [ 1 2 3 ; 2 3 1 ; 1 10 1];

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To transpose a matrix:

1 B = A ;

Matrix multiplication:

1 A = [ 3 2 1 ; 2 0 1 ; 1 1 1 ] ;2 A = [ 1 6 3 ; 4 3 4 ; 1 3 2 ] ;3 C = A B;

Conditional If

Execute statements if condition is true.if expression1statements1elseif expression2statements2elsestatements3end

1 A = 5 ;2 B = 6 ;3 C = 0 ;4 i f A == B5 C = 1 ;6 e l s e i f A < B7 C = 2 ;8 e l s e9 C = 3 ;

10 en d

For Loop

The for loop executes statements for a number of times.for index = start:increment:endstatementsend

1 x = 0 ;2 f o r k = 1 : 103 x = x + k;4 en d

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Math Functions

Trigonometry

sin Sine

sind Sine in Degrees

asin Inverse sine

asind Inverse sine in Degrees

cos Cosine

cosd Cosine in Degrees

acos Inverse cosine

acosd Inverse cosine in Degrees

tan Tangent

tand Tangent in Degrees

atan Inverse tangent

atand Inverse tangent in Degrees

sec Secant

secd Secant in Degrees

asec Inverse secant

asecd Inverse secant in Degrees

csc Cosecant

cscd Cosecant in Degrees

acsc Inverse cosecant

acscd Inverse cosecant in Degrees

cot Cotangent

cotd Cotangent in Degrees

acot Inverse cotangent

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acotd Inverse cotangent in Degrees

1 % Fin d t he s i n e o f a n g le x = 0 . 9 r a di a n2 x = 0 . 9 ;3 y = s i n( x ) ;

Exponential

a n a to the power n

sqrt Square root

log10 Base 10 logarithm

exp Exponential (Natural)

log Natural logarithm (ln)

1 % Fin d th e s qu ar e r o o t o f x = 42 x = 4 ;3 y = s q r t( x ) ;

Rounding

round Round towards nearest integer

floor Round towards minus

ceil Round towards plus

1 x = 4 . 5 ;

2 y = round ( x ) ;

Other Functions

abs Absolute value

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Statistics Functions

Min

1 X = [ 5 5 1 2 4 4 ] ;2 % Find the minimum3 C = min ( X ) ;

Max

1 X = [ 5 5 1 2 4 4 ] ;2 % Find the maximum3 C = max( X ) ;

Mean, Average

1 X = [ 5 5 1 2 4 4 ] ;2 % F in d th e mean o f a v e ct o r3 M = mean ( X ) ;4 % F in d t he mean o f a ma t r ix5 A = [ 1 2 3 ; 3 3 6 ; 4 6 8 ; 4 7 7 ] ;6 Z = mean ( A ) ;

Median

1 X = [ 5 5 1 2 4 4 ] ;2 % F in d t h e m ed ia n3 M = median ( X ) ;

Mode

1 X = [ 5 5 1 2 4 4 ] ;2 % F in d t h e mode3 M = mode ( X ) ;

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Standard Deviation

1 X = [ 5 5 1 2 4 4 ] ;2 % F in d t h e s t an d ar d d e v i a ti o n3 S = s t d( X ) ;

2 Graphs

Plotting

1 X = [1 2 3 4 5 ] ;2 Y = [1 4 9 16 2 5 ];3 % P lo t X a g ai n s t Y f o r f u n ct i o n Y = X24 p l o t( X, Y ) ;5 % Try p l o t (X , Y , ) and p l o t (X , Y , r . )6 % S et t h e gr ap h s t i t l e7 t i t l e( Y=X2 ) ;8 % Se t the l a b el s f o r Xa x i s and Ya x i s9 x l a b e l( X ) ;

10 y l a b e l( Y ) ;

Bar Chart

1 z = [ 1 2 3 4 6 4 3 4 5 ] ;2 ba r ( z ) ;3 x l a b e l( I n d e x ) ;4 y l a b e l( Value ) ;

3 Image Processing

Read Image

1 % L oa d t h e i m ag e2 im = i m r e a d ( f i l e n a m e ) ;

Display Image

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1 % D i s p l ay t h e i ma ge2 i m s h o w ( im ) ;

Get Size of Image

1 % Get h e i g h t and wi dt h o f t h e i ma ge2 [ y, x] = s i z e( im ) ;

Complement Image

1 % Complement the image2 n e w _ i m g = i m c o m p l e m e n t ( im g ) ;

RGB to Grayscale

1 % C o n ve r t RGB i ma g e t o g r a y s c a l e i m ag e2 i m _ g r a y = r g b 2 g r a y ( i m _ r g b ) ;

Grayscale to BW

1 % C on ve rt g r a y s c a l e i m ag e t o b l a c k and w h it e i ma ge w i th t h r e s h o l d o f 0 . 5

2 i m _ b w = i m 2 b w ( im_gray , 0 . 5 ) ;3 % To c a l c u l a t e t he t h r es h o ld a u t om a t ic a ll y a nd t he n c o nv e rt t o b l a ck

a nd w h i t e i ma g e4 th r = g r a y t h r e s h ( i m _ g r a y ) ;5 i m _ b w = i m 2 b w ( im_gray , th r ) ;

Save Image

1 % Save image to a BMP f i l e2 i m w r i t e ( im , f i l e na me .bmp , bmp ) ;3 % Save image t o a JPEG f i l e4 i m w r i t e ( im , f i l e na me . j pg , jpg ) ;

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Crop Image

1 % C r ea t e s an i n t e r a c t i v e C rop Ima ge t o o l a s s o c i a t e d w i th t h e im ag e2 im = i m c r o p3 % Cro ps t he i ma ge and s p e c i f i e s t he s i z e a nd p o s i t i o n o f t he c ro p

r e c t a n g l e4 i m _ c r o p = i m c r o p ( im , [x y w h ] ) ;

Subtract Images

1 % S u b t r a c t s on e i ma ge fr om a no t h e r2 im = i m s u b t r a c t ( im 1, im 2 ) ;

Entropy of Grayscale Images

1 % C a l c u l a t e s t h e e n tr o py o f g r a y s c a l e im ag e2 j = e n t r o p y ( im ) ;

Image Histograms

1 % D i s pl a y s th e hi st o gr a m o f i ma ge2 i m h i s t ( im ) ;

4 Video Processing

Acquire Video

1 % S e l e c t v id eo d e vi c e2 ca m = v i d e o i n p u t ( winvi deo , 3 ) ;3 % D i sp la y t he l i v e v id eo4 p r e v i e w ( ca m ) ;5 % Tak e t h e s n a ps h o t6 im = g e t s n a p s h o t ( ca m ) ;

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5 Audio Processing

Acquire Audio

1 r e c o r d e r = a u d i o r e c o r d e r;2 % R ec or d v o i c e f o r 5 s e co n ds3 r e c o r d b l o c k i n g ( recorder , 5 ) ;4 % P la y t h e r e c o r d i n g5 play ( r e c o r d e r ) ;6 % S t o re so un d d at a in a r r ay7 sn d = g e t a u d i o d a t a ( r e c o r d e r ) ;8 % P l o t a u d i o w av ef or m9 p l o t( sn d ) ;

Load Audio (from Wav file)

1 sn d = wavread ( song .wav ) ;2 % P l o t a u d i o w av ef or m3 p l o t( sn d ) ;

6 2D-Filters

average: Averaging filter

gaussian: Gaussian lowpass filter

laplacian: Approximates the two-dimensional Laplacian operator

motion: Approximates the linear motion of a camera

sobel: Sobel horizontal edge-emphasizing filter

unsharp: Unsharp contrast enhancement filter

Average

1 % C hoos e the f i l t e r2 f = f s p e c i a l ( ave rag e , [ 3 , 3 ] ) ;3 % P a s s t h r o u gh a v e r a g e f i l t e r4 f i l t e r e d _ o b j = i m f i l t e r ( ob j, f ) ;

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Gaussian

1 % Cho ose t he f i l t e r , w it h s ig ma = 0 . 52 f = f s p e c i a l ( g a u s s i a n , [ 3 , 3 ] , 0 . 5 ) ;3 % P a s s t h r o u gh g a u s s i a n f i l t e r4 f i l t e r e d _ o b j = i m f i l t e r ( ob j, f ) ;

Laplacian

1 % Cho ose t he f i l t e r , w it h a lp ha = 0 . 2 ( b et wee n 0 . 0 t o 1 . 0 )2 f = f s p e c i a l ( l a p l a c i a n , 0 . 2 ) ;3 % P a ss t h ro u gh l a p l a c i a n f i l t e r4 f i l t e r e d _ o b j = i m f i l t e r ( ob j, f ) ;

Motion

1 % Cho ose t he f i l t e r , w it h l e n = 2 p i x e l s and t h et a = 02 f = f s p e c i a l ( motion , 2 , 0 ) ;3 % P a s s t h r o u gh m o ti o n f i l t e r4 f i l t e r e d _ o b j = i m f i l t e r ( ob j, f ) ;

Sobel

1 % C hoos e the f i l t e r2 f = f s p e c i a l ( s o b e l ) ;3 % P a ss t h ro u gh s o b e l f i l t e r4 f i l t e r e d _ o b j = i m f i l t e r ( ob j, f ) ;

Unsharp

1 % Cho ose t he f i l t e r , w it h a lp ha = 0 . 2 ( b et wee n 0 . 0 t o 1 . 0 )2 f = f s p e c i a l ( uns harp , 0 . 2 ) ;3 % P a s s t h r o u gh u n sh a r p f i l t e r4 f i l t e r e d _ o b j = i m f i l t e r ( ob j, f ) ;

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7 Fourier Analysis

Discrete Fourier Transform

1 X = [ 1 2 3 4 5 6 ] ;2 % Co mp ut es t h e d i s c r e t e F o u r i e r t r a n s f o r m (DFT) o f v e c t o r X3 Y = f f t( X ) ;

Inverse Discrete Fourier Transform

1 X = [ 1 2 3 4 5 6 ] ;2 % Co mp ut es t h e d i s c r e t e F o u r i e r t r a n s f o r m (DFT) o f v e c t o r X3 Y = f f t( X ) ;4 % Computes t h e i n v e r s e d i s c r e t e F o u r ie r t r a n s fo r m ( IDFT ) o f v e c t o r Y5 X = i f f t( Y ) ;

2-D Discrete Fourier Transform

1 X = [ 1 2 3 ; 4 5 6 ] ;

2 % C ompute s the 2D d i s c r e t e F o u r ie r t r a ns f or m (DFT) o f m at ri x X3 Y = f f t 2( X ) ;

2-D Inverse Discrete Fourier Transform

1 X = [ 1 2 3 4 5 6 ] ;2 % C ompute s the 2D d i s c r e t e F o u r ie r t r a ns f or m (DFT) o f m at ri x X3 Y = f f t 2( X ) ;4 % Co mp ut es t h e i n v e r s e 2D d i s c r e t e F o u r ie r t r a ns f or m ( IDFT ) o f m at ri x

Y5 X = i f f t 2( Y ) ;

Zero Shift

1 % S h i f t z er of r e q u e n c y c o mp on en t t o c e n t e r o f s p ec t ru m2 Z = f f t s h i f t( Y ) ;

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8 Wavelet Analysis

Single-level discrete 1-D wavelet transform

1 % Computes 1 l e v e l d i s c r et e ha ar 1D w a v e l et t r a n s fo r m2 [ A, D] = dw t ( X, h a a r ) ;3 % Computes 1 l e v e l d i s c r et e db1 1D w a v e l et t r a n s f or m4 [ A, D] = dw t ( X, db1 ) ;5 % Computes 1 l e v e l d i s c r et e db2 1D w a v e l et t r a n s f or m6 [ A, D] = dw t ( X, db2 ) ;7 % Computes 1 l e v e l d i s c r et e db4 1D w a v e l et t r a n s f or m8 [ A, D] = dw t ( X, db4 ) ;9 % Computes 1 l e v e l d i s c r e t e c o i f4 1D w a v e l et t r a n s f or m

10 [ A, D] = dw t ( X, c o i f 4 ) ;

Single-level inverse discrete 1-D wavelet transform

1 % Computes 1 l e v e l d i s c r et e ha ar 1D w a v e l et t r a n s fo r m2 [ A, D] = dw t ( X, h a a r ) ;3 % Computes 1 l e v e l i n ve r se d i s c r et e ha ar 1D w a v e l et t r a n s fo r m4 X = idwt ( A, D, h a a r ) ;

Single-level discrete 2-D wavelet transform

1 % Computes 1 l e v e l d i s c r et e ha ar 2D w a v e l et t r a n s fo r m2 [ A, H, V, D] = dwt2 ( X, h a a r ) ;

Single-level inverse discrete 2-D wavelet transform

1 % Computes 1 l e v e l d i s c r et e ha ar 2D w a v e l et t r a n s fo r m2 [ A, H, V, D] = dwt2 ( X, h a a r ) ;3 % Computes 1 l e v e l i n ve r se d i s c r et e ha ar 2D w a v e l et t r a n s fo r m4 X = i d w t 2 ( A, H, V D, h a a r ) ;

9 Artificial Neural Networks

Feed-Forward Neural Networks

Example: XOR gate

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1 % C r e at e f e e df o r w a r d n e tw o r k2 % Parame te rs :3 % 1 Max a nd min o f t h e i n pu t v a l u e s ( 2 i n p u ts )4 % 2 Number o f l a y e r s 2 l a y e r s , 1 s t ( h d id de n ) h as 2 n eu ro ns , 2 nd (

o u tp u t ) h as 1 n e ur o n5 % 3 A ct i va t io n f u n c ti o n s f o r e ac h l a ye r , s ig mo id f u n ct i o n i s u se d6 ne t = n e w f f( [ 0 1 ; 0 1 ] , [ 2 1 ] , { l o g s i g , l o g s i g }) ;78 % I np ut i s i n t he c ol umn s o f th e ma tr ix9 % 1 1 0 0

10 % 1 0 1 011 % The 1 s t i np ut i s 1 1 , t he 2 nd i s 1 0 , t he 3 r d i s 0 1 and t h e 4 th i s

0 012 i n p u t = [ 1 1 0 0 ; 1 0 1 0 ] ;1314 % T a rg e t m at r ix ( e x p e ct e d o u tp u t )

15 t a r g e t = [0 1 1 0 ] ;1617 % T r ai n t h e n et wo r k18 ne t = t r a i n ( ne t, input, t a r g e t ) ;1920 % S i m ul a t e t h e n et wo r k21 % T es t t h e n et wo rk w i th i n pu t a s i n pu t a nd s e e i f o ut pu t i s t h e same

a s t a r g e t22 o u t p u t = si m ( ne t, i n p u t)

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