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Metode Kuantitatif

TUTORIAL SINGKAT
MATLAB

oleh:
Judi Prajetno Sugiono

Sekolah Tinggi Teknik Surabaya
(2005, 2008, 2011)

judi@stts.edu ©2005

p. 1 of 40

MATLAB
Short Tutorial
Reserve word (don’t used it as variable's name)
·
·
·
·
·

ans pi nan inf eps

Special sign
·
·
·
·
·

%
[]
;
'
:

line comment begin - end of matrix row separation, or not echoed command if place in the end of a statement begin - end of string indexing sign

Variable is assume as matrix
% empty matrix
A=[]
A =
[]
% matrix 1x1 or a constant
A=[0]
A =
0
% same with
A=0
A =
0
% complex number: use i or j to express imaginary part z=3+4j z =
3.0000 + 4.0000i

Entry a matrix
% use as column separation and or as row separation
A=[1 2 3; 4 5 6; 7 8 9]
A =
1
4
7

2
5
8

3
6
9

Last saved by jpsugiono 9/23/2011

judi@stts.edu ©2005

p. 2 of 40

How to point element of matrix
% A(row,column)
A(1,3)
ans =
3
% sign use as get all row or column
A(2,:)
ans =
4

5

6

% sign use as get from m to n cell in row or colomn
A(1:2, 2:3) ans =
2
5

3
6

row and column vector
% row vector a=[0 1 2 3 4 5] a =
0

1

2

3

4

5

% column vector b=[0; 1; 3; 4; 5] b =
0
1
3
4
5
% Shortcut to build a vector
% init:step:final a=0:0.2:1 a =
0

0.2000

0.4000

0.6000

String
% begin and end with < ' >, and act like a matrix of character
S='surabaya'

Last saved by jpsugiono 9/23/2011

0.8000

1.0000

judi@stts.edu ©2005

p. 3 of 40

S = surabaya S(1:3) ans = sur Operation
Matrix or constant
+
*
/
\
^
'

Cell by cell operation
(array)
+
.*
./
.\
.^
.'

add substract multiply right division left division power Matrix transpose

Relation
==
~=
>
<
>=
0
Tò
0
T

2 bk = ò f (t )sin( kwt ) dt ® k > 0
T 0

w=

2p
(rad / sec)
T

® a0 =

ak
2

k =0

Last saved by jpsugiono 9/23/2011

judi@stts.edu ©2005

p. 39 of 40

If signal input f(t) is continuos, it must be sample for N data point with DT interval sampling. t=nDT T=NDT ω=2p/T=2p/(NDT) f(t)
Periode (T)=N DT
DT

t
DT 2DT

0

3DT 4DT

T

ak =

2
2
ò f (t ) cos(kwt )dt = N DT
T 0
T

bk =

2
2
ò f (t )sin(kwt )dt = N DT
T 0

n.DT
N

å n =1

N

N.DT

æ k 2p nDT f (nDT ) cos ç è N DT

2 æ k 2p nDT ö
÷ DT =
N DT ø
N

å f (nDT ) sin ç è n =1

2 ö ÷ DT =
N
ø

æ k 2p n ö
÷
N ø

N

å f (n) cos ç è n =1

N

æ k 2p n ö
÷
N ø

å f (n) sin ç è n =1

function [avg, ak, bk]=fsctrig(f,t,K,test)
%FSCTRIG find trigonometric fourier series coefficient
%
using trapezoidal rule
%
%[AVG, AK, BK]=FSCTRIG(F, T, K) compute fourier
%
coefficient AVG, A1, ..., AK and
%
B1, B2, ..., BK from 1 periode signal F
%
with time vector T. The approximation of F
%
will store in vector FS with trapezoidal rule.
%
%[AVG, AK, BK]=FSCTRIG(F, T), will compute fourier
%
series coefficient of signal F over time vector T,
%
for first five components
%
%[AVG, AK, BK]=FSCTRIG(F), will compute fourier
%
series coefficient of sequence F, for first five components
%
%[AVG, AK, BK]=FSCTRIG(F, T, K, 1) will plot the result.
%

Last saved by jpsugiono 9/23/2011

judi@stts.edu ©2005

p. 40 of 40

testplot=0; if nargin==4 testplot=1; elseif nargin==2
K=5;
elseif nargin==1; t=0:length(f); K=5; end N=length(f); w=2*pi/N; for k=0:K
Tak=0; Tbk=0; for n=0:N-1
Tak=Tak+f(n+1)*cos(k*w*n);
Tbk=Tbk+f(n+1)*sin(k*w*n); end ak(k+1)=Tak; bk(k+1)=Tbk; end ak=2/N * ak; bk=2/N * bk; avg=ak(1)/2; ak=ak(1,2:K+1) bk=bk(1,2:K+1) if testplot==1
%calculate the FS approximation using FSTRIG
[fs, fak, fbk]=fstrig(t, avg, ak, bk); subplot(221), plot(t,f), title('original function f(t)') xlabel('t'), ylabel('f(t)'), grid subplot(223), plot(t,fs,'-', t, avg,'--', t,fak,'-.', t,fbk,':'), title('Fourier Series Approximation') xlabel('t'), ylabel('f(t)'), grid
Subplot(222), stem(ak), title('Cosine Coefficient') xlabel('k'), ylabel('Ak(k)'), grid
Subplot(224), stem(ak), title('Sine Coefficient') xlabel('k'), ylabel('Bk(k)'), grid end Last saved by jpsugiono 9/23/2011