Mathlab Transformasi Z, Fourier, dan Laplace
4/07/2014 04:23:00 PM
Transformasi Z,
Transformasi Fourier, dan Transformasi Laplace
1. Transformasi
Z
>> syms a b c x y z t n s f
>>
f=5*((sqrt(x))^3)+2*(sqrt(y))+5
f =
5*x^(3/2)+2*y^(1/2)+5
>> a=ztrans(f,t,s)
a =
(5*x^(3/2)+2*y^(1/2)+5)*s/(s-1)
>> pretty(a)
3/2 1/2
(5 x + 2 y
+ 5) s
-----------------------
s - 1
>> a=ztrans(f,t,z)
a =
(5*x^(3/2)+2*y^(1/2)+5)*z/(z-1)
>> pretty(a)
3/2 1/2
(5 x + 2 y
+ 5) z
-----------------------
z - 1
Transformasi
Fourier
>> syms a b c x y z t n s f w
>> f=5*((sqrt(x))^3)+2*(sqrt(y))+5
f =
5*x^(3/2)+2*y^(1/2)+5
>> b=fourier(f,t,w)
b =
2*(5*x^(3/2)+2*y^(1/2)+5)*pi*Dirac(w)
>> pretty(b)
3/2 1/2
2 (5 x + 2 y
+ 5) pi Dirac(w)
Transformasi
Laplace
>> syms a b c x y z t n s f w
>>
f=5*((sqrt(x))^3)+2*(sqrt(y))+5
f =
5*x^(3/2)+2*y^(1/2)+5
>> c=laplace(f,t,s)
c =
(5*x^(3/2)+2*y^(1/2)+5)/s
>> pretty(c)
3/2 1/2
5 x + 2 y
+ 5
-------------------
s
2. Transformasi
Z
>> syms a b c x y z t n s f
>>
f=x^6-12*x^5+59*x^4-152*x^3+216*x^2-160*x+48
f =
x^6-12*x^5+59*x^4-152*x^3+216*x^2-160*x+48
>> a=ztrans(f,t,s)
a =
(x^6-12*x^5+59*x^4-152*x^3+216*x^2-160*x+48)*s/(s-1)
>> pretty(a)
6 5
4 3 2
(x
- 12 x + 59 x - 152 x
+ 216 x - 160 x + 48) s
-----------------------------------------------------
s - 1
>> a=ztrans(f,t,z)
a =
(x^6-12*x^5+59*x^4-152*x^3+216*x^2-160*x+48)*z/(z-1)
>> pretty(a)
6 5
4 3 2
(x
- 12 x + 59 x - 152 x
+ 216 x - 160 x + 48) z
-----------------------------------------------------
z - 1
Transformasi
Fourier
>> syms a b c x y z t n s f w
>>
f=x^6-12*x^5+59*x^4-152*x^3+216*x^2-160*x+48
f =
x^6-12*x^5+59*x^4-152*x^3+216*x^2-160*x+48
>> b=fourier(f,t,w)
b =
2*(x^6-12*x^5+59*x^4-152*x^3+216*x^2-160*x+48)*pi*Dirac(w)
>> pretty(b)
6 5
4 3 2
2 (x - 12 x + 59 x
- 152 x + 216 x - 160 x + 48) pi Dirac(w)
Transformasi
Laplace
>> syms a b c x y z t n s f w
>>
f=x^6-12*x^5+59*x^4-152*x^3+216*x^2-160*x+48
f =
x^6-12*x^5+59*x^4-152*x^3+216*x^2-160*x+48
>> c=laplace(f,t,s)
c =
(x^6-12*x^5+59*x^4-152*x^3+216*x^2-160*x+48)/s
>> pretty(c)
6 5
4 3 2
x - 12 x
+ 59 x - 152 x + 216 x
- 160 x + 48
-------------------------------------------------
s
3. Transformasi
Z
>> syms a b c x y z t n s f
>> f=sqrt(4*x^2+4*x-1)
f =
(4*x^2+4*x-1)^(1/2)
>> a=ztrans(f,t,s)
a =
(4*x^2+4*x-1)^(1/2)*s/(s-1)
>> pretty(a)
2 1/2
(4 x + 4 x - 1)
s
---------------------
s - 1
>> a=ztrans(f,t,z)
a =
(4*x^2+4*x-1)^(1/2)*z/(z-1)
>> pretty(a)
2 1/2
(4 x + 4 x - 1)
z
---------------------
z - 1
Transformasi
Fourier
>> syms a b c x y z t n s f w
>> f=sqrt(4*x^2+4*x-1)
f =
(4*x^2+4*x-1)^(1/2)
>> b=fourier(f,t,w)
b =
2*(4*x^2+4*x-1)^(1/2)*pi*Dirac(w)
>> pretty(b)
2 1/2
2 (4 x + 4 x - 1)
pi Dirac(w)
Transformasi
Laplace
>> syms a b c x y z t n s f w
>> f=sqrt(4*x^2+4*x-1)
f =
(4*x^2+4*x-1)^(1/2)
>> c=laplace(f,t,s)
c =
(4*x^2+4*x-1)^(1/2)/s
>> pretty(c)
2 1/2
(4 x + 4 x - 1)
-------------------
s
Persamaan Kuadrat
1. >> syms x
g=15*x^2-19*x-132
g =
15*x^2-19*x-132
>> solve(g)
ans =
[ -12/5]
[
11/3]
2. >> syms x y
g=(x+y)/4-(x-y)/3-1
g =
-1/12*x+7/12*y-1
>> solve(g)
ans =
7*y-12
3. >> syms x y
g= 2*((sqrt(x))^3)+sqrt(y)
g =
2*x^(3/2)+y^(1/2)
>> solve(g)
ans =
[1/2*2^(1/3)*y^(1/3)]
[
-1/4*2^(1/3)*y^(1/3)+1/4*i*3^(1/2)*2^(1/3)*y^(1/3)]
[ -1/4*2^(1/3)*y^(1/3)-1/4*i*3^(1/2)*2^(1/3)*y^(1/3)]
Suku Banyak
1. >> f=[5 2 -4 11]
f =
5 2 -4
11
>> g=[3 4]
g =
3 4
>> [h,s]=deconv(f,g)
h =
1.6667 -1.5556 0.7407
s =
0 0
0.0000 8.0370
2. f=[2 5 3 0 12]
f =
2 5 3
0 12
>> g=[2 3]
g =
2 3
>> [h,s]=deconv(f,g)
h =
1 1 0
0
s =
0 0 0
0 12
3. f=[6 8 -15 45 900]
f =
6 8 -15
45 900
>> g=[1 5]
g =
1 5
>> [h,s]=deconv(f,g)
h =
6 -22 95
-430
s =
Columns 1 through 4
0 0 0 0
Column 5
3050
Pembagian dan Penyebut
1. syms x
f=(x/x-2)-(3*(x-2)/x)
f =
-1-(3*x-6)/x
>> [a,b]=numden(f)
a =
-4*x+6
b =
x
2. syms x
f=((x-sqrt(3)/x+sqrt(3))+(x+sqrt(3)/x-sqrt(3)))
f =
2*x
>> [a,b]=numden(f)
a =
2*x
b =
1
3. syms x
f=(2*(3*x+1)/5*(2*x-3))-(x+2)/(x+1)
f =
(6/5*x+2/5)*(2*x-3)-(x+2)/(x+1)
>> [a,b]=numden(f)
a =
12*x^3-2*x^2-25*x-16
b =
5*x+5
JAKARTA
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