1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
|
//Solved_Ex.4.4->Determine the Trigonometric form of Fourier Series of the Full Wave Rectified sine wave
clc;
clear;
T=8;//Defining Time Period
A=2;//Defining Amplitude
t=0:0.01:15;
w0=2*%pi/T;
function x=f(t),x=A.*abs(sin(t.*w0)) ,endfunction //given full wave rectified continuous signal
plot(t,f);
xlabel("time");
ylabel("x(t)");
//Check if Even Signal,if yes,then bn=0
if(f(t)==f(-1*t))
disp('even');
disp('bn=0');
function x=f(t),x=A.*abs(sin(t.*w0)) ,endfunction //given signal
//Evaluation of a0 & an
//Evaluation of a0:
a0=4*intg(0,T/2,f)/T; //definite integral of 'f' from 0 to T/2
disp(a0,'a0');
//Evaluation of an:
disp('due to convergence,for all odd values of n,a=0');
disp('for even values of n,an values are=>');
y0=a0/2+zeros(1,length(t));
for n=2:2:8 //changing the end value of n,we can get more numbers of an
function xn=f1(t),xn=A.*abs(sin(t.*w0)).*cos(n.*w0.*t) ,endfunction
an=4*intg(0,T/2,f1)/T;
disp(n,'a');
disp(an);
y0=y0+an.*cos(n*w0.*t);
xset('window',1);
subplot(2,2,n/2);
plot(t,y0);
xlabel("time");
ylabel("x(t)*cos(n*w0*t) for n=");
end
xset('window',2);
plot(t,y0);
xset('window',2);
plot(t,y0);
else if(f(t)==(-1*f(-1*t)))
disp('odd signal=>a0=an=0');
function x=f(t),x=A.*abs(sin(t.*w0)) ,endfunction //redefining signal
//Evaluation of bn=>
y0=zeros(1,length(t));
for n=1:1:8 //changing the end value of n,we can get more numbers of bn
function xn=f1(t),xn=A.*abs(sin(t.*w0)).*sin(n.*w0.*t) ,endfunction
bn=4*intg(0,T/2,f1)/T;
disp(n,'b');
disp(bn);
y0=y0+bn.*sin(w0.*n.*t);
xset('window',1);
subplot(2,4,n);
plot(t,y0);
xlabel("time");
ylabel("x(t)*sin(n*w0*t) for n=");
end
else
disp('unknown');
function xn=f1(t),xn=A.*abs(sin(t.*w0)).*sin(n.*w0.*t) ,endfunction
//Evaluation of a0,an & bn
//Evaluation of a0:
a0=4*intg(0,T/2,f)/T; //definite integral of 'f' from 0 to T/2
disp(a0,'a0');
//Evaluation of an:
y0=a0/2+zeros(1,length(t));
for n=1:1:8 //changing the end value of n,we can get more numbers of an
function xn=f1(t),xn=A.*abs(sin(t.*w0)).*cos(n.*w0.*t) ,endfunction
an=4*intg(0,T/2,f1)/T;
disp(n,'a');
disp(an);
y0=y0+an.*cos(n*w0.*t);
xset('window',1);
subplot(2,2,n/2);
plot(t,y0);
xlabel("time");
ylabel("x(t)*cos(n*w0*t) for n=");
end
//Evaluation of bn=>
y0=zeros(1,length(t));
for n=1:1:8 //changing the end value of n,we can get more numbers of bn
function xn=f1(t),xn=A.*abs(sin(t.*w0)).*sin(n.*w0.*t) ,endfunction
bn=4*intg(0,T/2,f1)/T;
disp(n,'b');
disp(bn);
y0=y0+bn.*sin(w0.*n.*t);
xset('window',1);
subplot(2,4,n);
plot(t,y0);
xlabel("time");
ylabel("x(t)*sin(n*w0*t) for n=");
end
end
end
xset('window',2);
plot(t,y0);//x(t) signal till 8 harmonics
|
