THEORY:
MATLAB® is a high-performance language
for technical computing. It integrates computation, visualization, and
programming in an easy-to-use environment where problems and solutions are
expressed in familiar mathematical notation. Typical uses include
·
Math
and computation
·
Algorithm
development
·
Data
acquisition
·
Modeling,
simulation, and prototyping
·
Data
analysis, exploration, and visualization
·
Scientific
and engineering graphics
·
Application
development, including graphical user interface building
MATLAB is an interactive system whose
basic data element is an array that does not require dimensioning. This allows
you to solve many technical computing problems, especially those with matrix
and vector formulations, in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or Fortran.
The name MATLAB stands for matrix
laboratory. MATLAB was originally written to provide easy access to matrix
software developed by the LINPACK and EISPACK projects. Today, MATLAB engines
incorporate the LAPACK and BLAS libraries, embedding the state of the art in
software for matrix computation.
FUNCTIONS
USED IN MATLAB:
1) Logarithm:
Syntax: Y = log(X)
Description:
The
log function operates element-wise on arrays. Its domain includes complex and
negative numbers, which may lead to unexpected results if used unintentionally.
Y =
log(X) returns the natural logarithm of the elements of X. For complex or
negative, where, the complex logarithm is returned. log(z) = log(abs(z)) +
i*atan2(y,x).
Example:
(log(-1))
ans
=
3.1416
2) Plot:
Syntax: plot(Y)
plot(X1,Y1,...)
Description:
plot(Y)
plots the columns of Y versus their index if Y is a real number. If Y is
complex, plot(Y) is equivalent to plot(real(Y),imag(Y)). In all other uses of
plot, the imaginary component is ignored.
plot(X1,Y1,...)
plots all lines defined by Xn versus Yn pairs. If only Xn or Yn is a matrix,
the vector is plotted versus the rows or columns of the matrix, depending on
whether the vector's row or column dimension matches the matrix.
Example: x = -pi:pi/10:pi;
y = tan(sin(x)) -
sin(tan(x));
plot(x,y)
Syntax: Y = exp(X)
The
exp function is an elementary function that operates element-wise on arrays.
Its domain includes complex numbers.
Y =
exp(X) returns the exponential for each element of X. For complex , it returns
the complex exponential .
Example:
y = exp(2)
y =
7.3891
4) Grid:
Syntax: grid on
grid off
grid minor
Description:
The grid function turns
the current axes' grid lines on and off.
grid on adds major grid
lines to the current axes.
grid off removes major and
minor grid lines from the current axes.
grid toggles the major
grid visibility state.
Example:
x=-pi:0.01:pi;
plot(x,sin(x)),grid on
Syntax: stem(Y)
stem(X,Y)
Description:
A
two-dimensional stem plot displays data as lines extending from a baseline
along the x-axis. A circle (the default) or other marker whose y-position
represents the data value terminates each stem.
stem(Y)
plots the data sequence Y as stems that extend from equally spaced and
automatically generated values along the x-axis. When Y is a matrix, stem plots
all elements in a row against the same x value.
stem(X,Y)
plots X versus the columns of Y. X and Y must be vectors or matrices of the
same size. Additionally, X can be a row or a column vector and Y a matrix with
length(X) rows.
Example:
x=45;
h=stem(x,sin(x))
h =
152.0028
6) Xlabel,
Ylabel & Title
Syntax: xlabel('string'), ylabel('string'), title('string')
Description:
Each
axes graphics object can have one label for the x-, y-, and z-axis. The label
appears beneath its respective axis in a two-dimensional plot and to the side
or beneath the axis in a three-dimensional plot.
xlabel('string'),
ylabel('string') labels the x-axis, y-axis of the current axes.Each axes
graphics object can have one title. The title is located at the top and in the
center of the axes.
title('string')
outputs the string at the top and in the center of the current axes.
Example: x = [1,2,3];
y=sin(x);
z=stem(y);
xlabel('x')
ylabel('y')
title('Stem
Plot')
7) Maximum:
Syntax: C = max(A)
C =
max(A,B)
Description:
C =
max(A) returns the largest elements along different dimensions of an array.
If A is
a vector, max(A) returns the largest element in A.
If A is
a matrix, max(A) treats the columns of A as vectors, returning a row vector
containing the maximum element from each column.
If A is
a multidimensional array, max(A) treats the values along the first
non-singleton dimension as vectors, returning the maximum value of each vector.
C =
max(A,B) returns an array the same size as A and B with the largest elements
taken from A or B.
Example:
x =
[1,2,3;4,5,6;7,8,9];
max(x)
ans =
7
8 9
8) Minimum:
Syntax: C = min(A)
C = min(A,B)
Description:
C = min(A) returns the smallest elements along
different dimensions of an array.
If A is a vector, min(A) returns the smallest
element in A.
If A is
a matrix, min(A) treats the columns of A as vectors, returning a row vector
containing the minimum element from each column.
If A is a multidimensional array, min operates
along the first nonsingleton dimension.
C =
min(A,B) returns an array the same size as A and B with the smallest elements
taken from A or B.
Example:
x =
[1,2,3;4,5,6;7,8,9];
min(x)
ans =
1
2 3
9) Modulus:
Syntax: M = mod(X,Y)
Description:
M =
mod(X,Y) if Y ~= 0, returns X - n.*Y where n = floor(X./Y) . If Y is not an
integer and the quotient X./Y is within roundoff error of an integer, then n is
that integer. By convention, mod(X,0) is X. The inputs X and Y must be real
arrays of the same size, or real scalars.
Example:
mod(13,5)
ans =
3
10) Transfer
Function:
Syntax: sys = tf(num,den)
sys = tf(num,den,Ts)
sys = tf(M)
sys = tf(num,den,ltisys)
Description:
tf is
used to create real- or complex-valued transfer function models (TF objects) or
to convert state-space or zero-pole-gain models to transfer function form.
Example: h=tf([1,0],[1 2 10])
Transfer function:
s
--------------
s^2 + 2 s + 10
11) Absolute
Syntax: Y = abs(X)
Description:
abs(X)
returns an array Y such that each element of Y is the absolute value of the
corresponding element of X.
If X is
complex, abs(X) returns the complex modulus (magnitude), which is the same as
sqrt(real(X).^2 + imag(X).^2).
Example: abs(-5)
ans =
5
12) Matrix
addition
Syntax: A+B
Description:
MATLAB
has two different types of arithmetic operations. Matrix arithmetic operations
are defined by the rules of linear algebra. Array arithmetic operations are
carried out element by element, and can be used with multidimensional arrays.
The period character (.) distinguishes the array operations from the matrix
operations. However, since the matrix and array operations are the same for
addition and subtraction, the character pairs .+ and .- are not used.
+
Addition or unary plus. A+B adds A and B. A and B must have the same size,
unless one is a scalar. A scalar can be added to a matrix of any size.
Example:
a=[1,2,3;4,5,6];
b=[4,5,6;1,2,3];
a+b
ans =
5
7 9
5
7 9
13) Matrix
Subtraction
Syntax: A-B
Description:
MATLAB
has two different types of arithmetic operations. Matrix arithmetic operations
are defined by the rules of linear algebra. Array arithmetic operations are
carried out element by element, and can be used with multidimensional arrays.
The period character (.) distinguishes the array operations from the matrix
operations. However, since the matrix and array operations are the same for
addition and subtraction, the character pairs .+ and .- are not used.
-
Subtraction or unary minus. A-B subtracts B from A. A and B must have the same
size, unless one is a scalar. A scalar can be subtracted from a matrix of any
size.
Example:
a=[1,2,3;4,5,6];
b=[4,5,6;1,2,3];
a-b
ans =
-3
-3 -3
3
3 3
14) Matrix
Multiplication
Syntax: A*B
A.*B
Description:
MATLAB
has two different types of arithmetic operations. Matrix arithmetic operations
are defined by the rules of linear algebra. Array arithmetic operations are
carried out element by element, and can be used with multidimensional arrays. The
period character (.) distinguishes the array operations from the matrix
operations. However, since the matrix and array operations are the same for
addition and subtraction, the character pairs .+ and .- are not used.
* Matrix
multiplication. C = A*B is the linear algebraic product of the matrices A and
B.
.* Array
multiplication. A.*B is the element-by-element product of the arrays A and B. A
and B must have the same size, unless one of them is a scalar.
Example:
a=[1,2,3;4,5,6];
b=[4,5,6;1,2,3];
a.*b
ans =
4
10 18
4
10 18
15) Matrix
Power
Syntax: A^B
Description:
MATLAB
has two different types of arithmetic operations. Matrix arithmetic operations
are defined by the rules of linear algebra. Array arithmetic operations are
carried out element by element, and can be used with multidimensional arrays.
The period character (.) distinguishes the array operations from the matrix
operations. However, since the matrix and array operations are the same for
addition and subtraction, the character pairs .+ and .- are not used.
^ Matrix
power. X^p is X to the power p, if p is a scalar. If p is an integer, the power
is computed by repeated squaring. If the integer is negative, X is inverted
first.
.^ Array
power. A.^B is the matrix with elements A(i,j) to the B(i,j) power. A and B
must have the same size, unless one of them is a scalar.
Example:
a=[1,2,3;4,5,6;7,8,9];
a.^2
ans =
1
4 9
16
25 36
49
64 81
16) Fourier
Transform
Syntax: F = fourier(f)
Description:
The
Fourier transform is a representation of an image as a sum of complex
exponentials of varying magnitudes, frequencies, and phases. The Fourier
transform plays a critical role in a broad range of image processing
applications, including enhancement, analysis, restoration, and compression.
The
Fourier transform of the expression f = f(x)
with respect to the variable x at the point w is
defined as follows:
Here c and s are
parameters of the Fourier transform. The fourier function uses c = 1, s = –1.
Example:
syms x y
f =
exp(-x^2);
fourier(f,
x, y)
ans =
pi^(1/2)*exp(-y^2/4)
17) Z-Transform
Syntax: F =
ztrans(f)
Description:
The Z-transform of the expression f = f(n) is defined as follows:
Example:
syms k x
f =
sin(k);
ztrans(f,
k, x)
ans =
(x*sin(1))/(x^2 - 2*cos(1)*x
+ 1)
18) Laplace
Transform
Syntax: L
= laplace(F)
Description:
The
Laplace transform is defined as follows:
Example:
syms a t
y
f =
exp(-a*t);
laplace(f,
y)
ans =
1/(a + y)
19) Length
Syntax:
length(X)
Description:
It finds the number of elements along the largest
dimension of an array. array is an array of any MATLAB® data
type and any valid dimensions. numberOfElements is a whole number of
the MATLAB double class.
For nonempty arrays, numberOfElements is
equivalent to max(size(array)). For empty
arrays, numberOfElements is zero.
Example:
X = [5, 3.4, 72, 28/4, 3.61, 17 94 89];
length(X)
ans =
8
20) Size
Syntax:
D = size(X)
Description:
If X is a
scalar, then size(X) returns the vector [1 1]. Scalars are
regarded as a 1-by-1 arrays in
MATLAB®.
If X is a table, size(X) returns
a two-element row vector consisting of the number of rows and the number of variables in the table.
Variables in the table can have multiple columns, but size only
counts the variables and rows.
Example:
v=[1 2
3; 4 5 6]
size(v)
ans =
2
3
21) Display
Syntax: display(X)
Description:
prints the value of X. MATLAB® implicitly
calls display after any variable or expression that is not terminated
by a semicolon.
To customize the display of objects, overload
the disp function instead of
the display function. display calls disp.
Example:
X =
magic(3);
display(X)
X =
8
1 6
3
5 7
4
9 2
22) Figure
Syntax:
figure(H)
Description:
figure
Create figure window.
figure,
by itself, creates a new figure window, and returns
its
handle.
figure(H)
makes H the current figure, forces it to become visible,
and
raises it above all other figures on the screen. If Figure H
does not
exist, and H is an integer, a new figure is created with
handle
H.
Example:
Figure
Opens a figure window
23) whos
Syntax:
whos
Description:
whos
List current variables, long form.
whos is
a long form of WHO. It lists all the
variables in the current
workspace,
together with information about their size, bytes, class,
etc.
In a
nested function, variables are grouped into those in the nested
function
and those in each of the containing functions, each group
separated
by a line of dashes. In nested functions
and in functions
containing
nested functions, even uninitialized variables are listed.
whos
GLOBAL lists the variables in the global workspace.
whos
-FILE FILENAME lists the variables in the specified .MAT file.
whos ...
VAR1 VAR2 restricts the display to the variables specified.
The
wildcard character '*' can be used to display variables that match
a
pattern. For instance, whos A* finds all
variables in the current
workspace
that start with A.
Example:
whos
Name
Size Bytes Class
Attributes
X
3x3 72 double
24) who
Syntax:
who
Description:
who
lists the variables in the current workspace.
In a
nested function, variables are grouped into those in the nested
function and those in each of
the containing functions. who displays
only the variables names, not the function to
which each variable
belongs. For this information, use WHOS. In nested functions and
in
functions containing nested functions, even unassigned variables
are
listed.
Example:
who
Your
variables are:
Area ans
k n s1
s3 theta x
z
a f
m r s2
t v y
25) imread
Syntax:
A = imread(FILENAME,FMT)
Description:
It reads
a grayscale or color image from the file specified by the string filename. If
the file is not in the current folder, or in a folder on the MATLAB® path,
specify the full pathname.
The text
string fmt specifies the format of the file by its standard file extension. For
example, specify 'gif' for Graphics Interchange Format files. To see a list of
supported formats, with their file extensions, use the imformats function. If
imread cannot find a file named filename, it looks for a file named
filename.fmt.
The
return value A is an array containing the image data. If the file contains a grayscale
image, A is an M-by-N array. If the file contains a truecolor image, A is an
M-by-N-by-3 array. For TIFF files containing color images that use the CMYK
color space, A is an M-by-N-by-4 array. See TIFF in the Format-Specific
Information section for more information.
The
class of A depends on the bits-per-sample of the image data, rounded to the
next byte boundary. For example, imread returns 24-bit color data as an array
of uint8 data because the sample size for each color component is 8 bits. See
Tips for a discussion of bitdepths, and see Format-Specific Information for
more detail about supported bit depths and sample sizes for a particular
format.
Example:
A =
imread('ngc6543a.jpg');
imread
returns a 650-by-600-by-3 array, A.
26) Imresize
Snytax:
B = imresize(A, SCALE)
Description:
imresize
Resize image.
B =
imresize(A, SCALE) returns an image that is SCALE times the
size of
A, which is a grayscale, RGB, or binary image.
B =
imresize(A, [NUMROWS NUMCOLS]) resizes the image so that it has
the
specified number of rows and columns.
Either NUMROWS or NUMCOLS
may be
NaN, in which case imresize computes the number of rows or
columns
automatically in order to preserve the image aspect ratio.
Example:
I =
imread('rice.png'); J =
imresize(I, 0.005)
J =
121
114
67
59
27) fliplr
Snytax:
fliplr(X)
Description:
fliplr
Flip matrix in left/right direction.
fliplr(X)
returns X with row preserved and columns flipped
in the
left/right direction.
Example:
X=[1 2
3; 4 5 6];
fliplr(X)
ans
=
3
2 1
6
5 4
28) display
Syntax:
display(X)
Description:
Display
text and numeric expressions
Example:
display(X)
X =
1
2 3
4
5 6
