Matlab - Week 2

Copy and paste the code below into a *.m file and then run the program.The file name must be saved with *.m extension , without spaces in between and no clashing of already existing functions in MATLAB Library

Example code for sinusoidal signals

%Generate Sine Wave
N=30;%Number of samples
t=-10:0.1:10;
x=sin(2*pi*25*t/N); %this is x(t)
plot(t,x)
title('Sine Wave');
xlabel('time scale');
ylabel('Amplitude');
axis([-70 70 -2 2]);
grid

Example code for square wave
%Square wave generation
A=2;
t = 0:0.0005:1;
x=A*square(2*pi*5*t,25); %5 Hertz wave with duty cycle 25%
plot(t,x);
grid
axis([0 1 -3 3]);

Example code for triangular wave
%Triangular wave generation
A=2;
t = 0:0.0005:1;
x=A*sawtooth(2*pi*5*t,0.25); %5 Hertz wave with duty cycle 25%
plot(t,x);
grid
axis([0 1 -3 3]);

Example code for rectangular pulse
%To generate a rectangular pulse
t=-5:0.01:5;
pulse = rectpuls(t,2); %pulse of width 2 time units
plot(t,pulse)
axis([-5 5 -1 2]);
grid

Example code for exponential signals
%Exponential signal
B=5;
alpha=5;
t=-1:0.1:1;
x=B*exp(-alpha*t);
plot(t,x);

%This part is for discrete signal
r=0.85;
n=-10:10;
y=B*r.^n;
stem(n,y);

Example code for decaying exponential signals
%Exponentially damped signal
A=10;
f=5; %5 Hertz
phi=0; %Phase info
a=6;
t=0:0.01:1;
x=A*sin(2*pi*f*t+phi).*exp(-a*t); %Elemental operation is required
plot(t,x);
grid

Elementary signals
%To generate a step signal
%Completely automatic
t=-2:0.01:2;
A=2;
len = length(t);
len_pos = length(find(t>=0));
u=A*([zeros(1,len-len_pos), ones(1,len_pos)]);
figure
plot(t,u);
axis([-2 4 0 3]);
grid

%Impulse function
%To generate impulse signal
delta = [zeros(1,(len-len_pos)+1), 1, zeros(1,len_pos-2)];
figure
plot(t,delta);

%Ramp function
%To generate ramp using step
u=A*([zeros(1,len-len_pos), ones(1,len_pos)]);
ramp = u.*t;
figure
plot(t,ramp);

Find Even and Odd signal
%Even and Odd signals
%Continuous time signal
t=-1:0.01:1;
len = length(t);
%Generate x(t)
x=sin(2*pi*t);
x_rev = sin(2*pi*(-t));
%Find Even and odd of x(t)
x_even = 0.5*(x + x_rev);
x_odd = 0.5*(x - x_rev);
plot(t,x,'r--',t,x_rev,'g-.',t,x_even,'m-',t,x_odd,'b*');
legend('x','x_rev','x_even', 'x_odd');
grid

Find the energy of the signal

%Find Energy

%To generate a rectangular pulse
t=-5:0.5:5;
pulse = 2*rectpuls(t,2.1); %pulse of width 2 time units
stem(t,pulse)
axis([-5 5 -1 2]);
grid

%Energy
Energy = 0;
t_mod = find(pulse > 0);
for i=t_mod(1):t_mod(length(t_mod))
Energy = Energy+ pulse(i).^2;
end
Energy

Operations that are checked are
1. Amplitude scaling
2. Addition
3. Multiplication
4. differentiation
5. Integration

Time scaling, reflection, time shifting

Example code to show all the operations on a exponentially damped signal
%Exponentially damped signal
A=10;
f=5; %5 Hertz
phi=0; %Phase info
a=6;
t=0:0.01:1;
x=A*sin(2*pi*f*t).*exp(-a*t); %Elemental operation is required
figure
plot(t,x);
grid

%Amplitude scaling
scale = 0.5;
y= scale * x;
figure
plot(t,x,'-',t,y,':');
grid

%Addition
figure
plot(t,x,'-',t,y,':',t,(x+y),'*');

%Multiplication
figure
plot(t,x,'-',t,y,':',t,(x.*y),'.');

%Time scaling
k=0.2;
scaled_time =t/k;
figure
plot(t,x,'g:',scaled_time, x);
grid

%Time Reflection
reflect_time = -t;
figure
plot(t,x,'g:',reflect_time, x);
grid

%Time shifting
shift = 1;
shifted_time = t-(-shift);
figure
plot(t,x,'g:',shifted_time, x);
grid