In the name of Allah
Chapter 1
Before beginning the computer exercises, some of the fundamental tools
Used to construct signals in MATLAB is covered here. You can use the
MATLAB user’s guide as the best help to continue.
Matrix:
>> A = [1, 2; 3, 4];
A =
1
3
2
4
☺ try to see the effect of character ‘; ‘at end of the command.
It is used for preventing echo.
>> A (2, 1)
ans =
3
>> A’
ans =
1
2
3
4
>> det( A )
ans =
-2
☺ see “ inv( A )” .
>> B = zeros (2, 4)
B=
0
0
0
0
☺ see “ones (n, m)”.
0
0
0
0
>> C = [A, B]
C=
1
3
2
4
0
0
0
0
0
0
0
0
-2
-1
0
1
2
3
-1.8
…
1.8
1.9
2
>> C = [-3: 3]
C=
-3
>> C = [-2: 0.1: 2]
C=
-2
-1.9
>> A (: 2)
ans =
2
4
>> A (1, : )
ans =
1
2
>> A * A
ans =
7
15
10
22
>> A .* A
ans =
1
9
4
16
☺ “A * A “ and “A .* A “ are different !!
See ‘Arithmetic Operations’ in index part of HELP.
>> C = [pi / 3, pi]
>> Sin(C)
ans =
0.86603
1.2246e-6 ≈ 0
Some other functions and commands available:
>> clc
use help !
>> clear
>>A = [-10: 10];
>> B = sin (2 * pi / 20 * [1: 21]);
>>stem (A, B)
See result!
>> plot (A, B)
>> title ( ' this is title ' )
>> xlabel( ' this is x label ' )
>> ylabel( ' this is y label ' )
See result !
☺ also see
subplot command.
☺ Note that you can save these Figures.
>> x = sym( 'sin( w * t ) ' )
This is a symbolic expression with two variables.
Many functions exist which are used with symbolic expressions.
x = sin( w * t )
>> x = subs( x, ' w ', 4 )
x = sin( 4 * t )
>> int ( x )
ans =
-1/4 * cos( 4 * x ) this is indefinite integral.
☺ see int and diff functions.
☺ see the useful function : ezplot( x, [ min, max ] ) .
[ min, max] is the domain interval.
ezplot( x, [ 1, 10 ] )
Here we have some other functions, I recommend you to read the primer. PDF file in
homepage.
abs
absolute value or complex magnitude
angle(phase) phase angle
sqrt
square root
real
real part
imag
imaginary part
conj
complex conjugate
gcd
greatest common divisor
lcm
least common multiple
round
round to nearest integer
fix
round toward zero
floor
round toward -∞
ceil
round toward ∞
sign
signum function
rem
remainder
exp
exponential base e
log
natural logarithm
log10
log base 10
sin, asin, sinh, asinh
cos, acos, cosh, acosh
tan, atan, atan2, tanh, atanh
cot, acot, coth, acoth
sec, asec, sech, asech
csc, acsc, csch, acsch
semilogx
semilogy
Polynomial:
residue
roots
poly
polyval
polyvalm
polyfit
conv
plot data as logarithmic scales
Convert between partial fraction expansion and polynomial coefficients
Polynomial roots
Polynomial with specified roots
Polynomial evaluation
Polynomial curve fitting
Convolution and polynomial multiplication
Matrix:
linspace
cumsum
cumprod
diag
length
Cumulative sum
Cumulative production
Computer exercises:
1- Transformation of the Time Index for Discrete-Time Signals.
x[ n ] = 2 n = 0, 1 n = 2, -1 n = 3, 3 n =4, 0 otherwise.
Represent the following discrete signals :
x[ n - 2 ], x[ n + 1 ], x[ - n ] , x[ - n + 1 ].
Use stem command for discrete functions.
2- Properties of Discrete-Time Signals.
Construct a counter-example using MATLAB to demonstrate if the system violate the
properties:
linearity, time invariance , stability, causality, invertibility.
y[ n ] = x ³[ n ]
y[ n ] = n x [ n ]
y[ n ] = x[ 2n ]
3- Transformation of the Time Index for Continuous-Time Signals.
first create an mfile called Heaviside.m in your working directory. The contents of
the file are as follow:
function myf = Heaviside( t )
myf = ( t >= 0 );
now we have
f( t ) = t ( U( t ) - U( t – 2 ) )
use ezplot to plot the following functions:
g1( t ) = f( - t )
g2 ( t ) = f( t + 1 )
g3 ( t ) = f( t – 3 )
g4 ( t ) = f( - t + 1 )
g5 ( t ) = f( -2t + 1 )
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