Dear friends generation of signals in matlab is very simple method once you understand the code you can easily plot any kind of signal for your engineering works etc , here is some code and prepare plot signals along with diagram, read it carefully and try to understand each and every point of it,
PLOTTING A CONTINUOUS TIME COMPLEX EXPONENTIAL SIGNAL
c=10;
f=5;
ph=pi/2;
T=1/f;
t=0:T/40:10*T; %10 cycles
x=c*cos(2*pi*f*t+ph);
a=input('enter 1,0 or -1;a='); %enter either positive, negative, zero
y=exp(a*t);
z=y.*x;
plot(t,z),
xlabel('t'),
ylabel('z'),
title('PLOTTING A CONTINUOUS TIME COMPLEX EXPONENTIAL SIGNAL'),
grid on
TASK-3:
TO PLOT A PIECE-WISE SIGNAL
%for first segment
t0=-2:0.01:0;
x0=t0;
%for second segment
t1=0:0.01:3;
x1=4*ones(size(t1));
%for third segment
t2=3:0.01:4;
x2=-3*t2+4;
x=[x0 x1 x2 ];
t=[t0 t1 t2 ];
plot(t,x,'red','linewidth',3);
xlabel('time');
ylabel('x(t)');
title('PLOTTING PIECEWISE CONTINUOUS TIME SIGNAL');
axis([-3 4 -10 5]);
grid on;
TASK-4:
TIME TRANSFORMATION OFF A PIECE WISE SIGNAL
%for first segment
t0=-2:0.01:0;
x0=t0;
%for second segment
t1=0:0.01:3;
x1=4*ones(size(t1));
%for third segment
t2=3:0.01:4;
x2=-3*t2+4;
x=[x0 x1 x2 ];
t=[t0 t1 t2 ];
subplot(2,1,1),
plot(t,x,'red','linewidth',5),
xlabel('time'),
ylabel('x(t)'),
title('TIME TRANSFORMATION OF CT SIGNAL(ORIGINAL SIGNAL)'),
grid on,
axis([-4 8 -10 5]);
%TIME TRANSFORMATION (Shifting, Scaling, Reversal)
t4=-2*t+4;
subplot(2,1,2),
plot(t4,x,'black','linewidth',5),
xlabel('time'),
ylabel('x(t)'),
title('TIME TRANSFORMATION OF CT SIGNAL(TRANSFORMED SIGNAL)'),
grid on,
axis([-4 8 -10 5]);
TASK-5:
3D PLOT OF CONTINUOUS TIME EXPONENTIAL SIGNAL
t=0:0.0001:10;
x=20*exp(i*5*t);
subplot(2,2,1),
plot(t,real(x)),
xlabel('time'),
ylabel('real part'),
title('PLOTTING REAL PART');
subplot(2,2,2),
plot(t,imag(x)),
xlabel('time'),
ylabel('imag part'),
title('PLOTTING IMAGINARY PART');
subplot(2,2,3),
plot(t,x),
xlabel('time'),
ylabel('x'),
title('PLOTTING(X)');
subplot(2,2,4),
plot3(real(x),imag(x),t),
xlabel('real part'),
ylabel('imag part'),
zlabel('time'),
title('3D PLOT OF A CONTINUOUS TIME SIGNAL');
TASK-6:
A)PLOTTING CONTINUOUS TIME SQUARE WAVE USING FOURIER SERIES
B)PLOTTING CONTINUOUS TIME TRIANGULAR WAVE USING FOURIER SERIES
% Square Wave
t=-10:0.001:10;
dc=1/2;
sum=0;
for k=1:2:200;
sum=sum+(3/(k*pi))*sin(k*t);
end
x=sum+dc;
subplot(2,1,1),
plot(t,x),
xlabel('time'),
ylabel('magnitude'),
title('square wave'),
%Triangular Wave
t=0:0.01:5;
sum=0;
for k=1:2:200;
sum=sum+(-16/(k^2*pi^2))*cos(6*pi*k*t);
end
subplot(2,1,2),
plot(t,sum),
xlabel('time'),
ylabel('magnitude'),
title('triangular wave')
TASK-7:
SOLVING DERIVATIVES, INTEGRALS & DIFFERENTIAL EQUATIONS
% DERIVATIVE
syms x a b c f
f=3*x^3-4*x^2+6*x-3;
a=diff(f,x)
b=diff(a,x)
c=diff(b,x)
RESULT:
%a = 9*x^2 - 8*x + 6
%b = 18*x - 8
%c = 18
% PARTIAL DERIVATIVE
f=x^2*y+x*y^3-x^3+y^2;
a=diff(f,x)
b=diff(f,y)
RESULT:
%a = - 3*x^2 + 2*x*y + y^3
%b = x^2 + 3*x*y^2 + 2*y
%INTEGRALS
PART-A:
f=3*x^3-4*x^2+5*x-3;
a=int(f,x)
b=int(f,x,0,5)
RESULT:
% a = (3*x^4)/4 - (4*x^3)/3 + (5*x^2)/2 - 3*x
% b = 4195/12
PART-B:
f=cos(x)*sin(y);
a=int(f,x,pi/2,pi)
b=int(a,y,0,2*pi)
RESULT:
% a = -sin(y)
% b = 0
%DIFFERENTIAL EQUATION
PART-A:
d=dsolve('D2y+3*Dy+2=sin(t)','t')
RESULT:
% d =C18 - (2*t)/3 - (3*cos(t))/10 - sin(t)/10 + C19/exp(3*t) + 2/9
PART-B:
f=dsolve('3*D2y+4*Dy=sin(t)','t')
RESULT:
%f =C25 - (4*cos(t))/25 - (3*sin(t))/25 + C26/exp((4*t)/3)
PART-C:
g=dsolve('D2y+2*Dy+3=sin(x)','y(0)=0','x')
RESULT:
%g =C30/exp(2*x) - (3*x)/2 - (2*cos(x))/5 - sin(x)/5 - C30 + 2/5
TASK-8:
EVALUATING LAPLACE TRANSFORM AND Z-TRANSFORMS
% LAPLACE TRANSFORM
>> syms f a t F C b
f=exp(-a*t)*heaviside(t);
// heaviside(t), 0 for t<0, 1 for t>0 and 0.5 for t==0
F=laplace(f)
RESULT:
% F = 1/(a + s)
>> syms x h t X H Y y
x=sin(t);
h=10*exp(10*t);
X=laplace(x)
H=laplace(h)
Y=H*X;
y=ilaplace(Y) // inverse laplace
RESULT:
% X = 1/(s^2 + 1)
%H = 10/(s - 10)
%y =(10*exp(10*t))/101 - (10*cos(t))/101 - (100*sin(t))/101
% z-transform
>>syms x h X H Y y a n
x=a^n;
h=b^(-n);
X=ztrans(x)
RESULT:
% X = -z/(a - z)
TASK-9:
DISCRETE TIME SIGNAL
PLOTTING
% DISCRETE TIME SEQUENCE
n=-4:4;
x=[9 1 -2 4 -5 6 -1 7 -8];
stem(n,x);
xlabel('time(sampled)');
ylabel('magnitude');
title('DT Sequence');
axis([-5 5 -10 10]);
% DISCRETE TIME EXPONENTIAL SIGNAL (n>=0)
% case 01(a>1)
c=2;
a=5;
n=0:15;
x=c*a.^n;
subplot(3,2,1);
stem(n,x,'linewidth',2);
xlabel('time(sampled)');
ylabel('magnitude');
title('DT exponential signal when a>1');
grid on;
%case 02(0<a<1)
c=2;
a=0.5;
n=0:15;
x=c*a.^n;
subplot(3,2,3);
stem(n,x,'linewidth',2);
xlabel('time(sampled)');
ylabel('magnitude');
title('DT exponential signal when 0<a<1');
grid on;
%case 03(a=1)
c=2;
a=1;
n=0:15;
x=c*a.^n;
subplot(3,2,5)
stem(n,x,'linewidth',2);
xlabel('time(sampled)');
ylabel('magnitude');
title('DT exponential signal when a=1');
grid on;
%case 04(a<-1)
c=4;
a=-2;
n=0:60;
x=c*a.^n;
subplot(3,2,2);
stem(n,x,'linewidth',2);
xlabel('time(sampled)');
ylabel('magnitude');
title('DT exponential signal when a<-1');
grid on;
%case 05(-1<a<0)
c=2;
a=-0.5;
n=0:30;
x=c*a.^n;
subplot(3,2,4);
stem(n,x,'linewidth',2);
xlabel('time(sampled)');
ylabel('magnitude');
title('DT exponential signal when -1<a<0');
grid on;
%case 06(a=-1)
c=2;
a=-1;
n=0:15;
x=c*a.^n;
subplot(3,2,6)
stem(n,x,'linewidth',2);
xlabel('time(sampled)');
ylabel('magnitude');
title('DT exponential signal when a=-1');
grid on;
% DISCRETE TIME EXPONENTIAL SIGNAL (n<=0)
% case 01(a>1)
c=2;
a=5;
n=-15:0;
x=c*a.^-n;
subplot(3,2,1);
stem(n,x,'linewidth',2);
xlabel('time(sampled)');
ylabel('magnitude');
title('DT exponential signal when a>1');
grid on;
%case 02(0<a<1)
c=2;
a=0.5;
n=-15:0;
x=c*a.^-n;
subplot(3,2,3);
stem(n,x,'linewidth',2);
xlabel('time(sampled)');
ylabel('magnitude');
title('DT exponential signal when 0<a<1');
grid on;
%case 03(a=1)
c=2;
a=1;
n=-15:0;
x=c*a.^-n;
subplot(3,2,5)
stem(n,x,'linewidth',2);
xlabel('time(sampled)');
ylabel('magnitude');
title('DT exponential signal when a=1');
grid on;
%case 04(a<-1)
c=4;
a=-2;
n=-60:0;
x=c*a.^-n;
subplot(3,2,2);
stem(n,x,'linewidth',2);
xlabel('time(sampled)');
ylabel('magnitude');
title('DT exponential signal when a<-1');
grid on;
%case 05(-1<a<0)
c=2;
a=-0.5;
n=-30:0;
x=c*a.^-n;
subplot(3,2,4);
stem(n,x,'linewidth',2);
xlabel('time(sampled)');
ylabel('magnitude');
title('DT exponential signal when -1<a<0');
grid on;
%case 06(a=-1)
c=2;
a=-1;
n=-15:0;
x=c*a.^-n;
subplot(3,2,6)
stem(n,x,'linewidth',2);
xlabel('time(sampled)');
ylabel('magnitude');
title('DT exponential signal when a=-1');
grid on;
TASK-10:
DISCRETE TIME CONVOLUTION
n0=0:20;
x=5*(-0.5).^n0;
n1=-10:5;
h=(2/3).^n;
n2=-20:10;
y1=conv(x,h);
y=y1(1:length(n2));
subplot(3,1,1);
stem(n0,x);
xlabel('time(sampled)');
ylabel('magnitude x(n)');
title('input signal');
grid on;
subplot(3,1,2);
stem(n1,h);
xlabel('time(sampled)');
ylabel('magnitude h(n)');
title('transfer function h(n)');
grid on;
subplot(3,1,3);
stem(n2,y);
xlabel('time(sampled)');
ylabel('magnitude y(n)');
title('output signal');
grid on;
TASK-11:
CONTINUOUS TIME CONVOLUTION
t=0:0.01:10;
x=ones(1,length(t));
h=2*exp(-1*t);
y1=conv(x,h)*0.01; //multiplying with step size
y=y1(1:length(t));
figure(1);
subplot(3,1,1);
plot(t,x);
xlabel('time');
ylabel('x(t)');
title('convolution of continuous time signal');
subplot(3,1,2);
plot(t,h);
xlabel('time');
ylabel('h(t)');
subplot(3,1,3);
plot(t,y);
xlabel('time');
ylabel('y(t)');
title('convolved signal')
grid on;
