TITLE: Generation of Different Basic
Signals Using Matlab
clc; %clear command window
close all;% close all opened window
clear all; %clear all the previously stored values
continuous time impulse sequence
N = 50; % the variablel N is given a value to be used for the
size of t and n
t = -N:1:N; % range of t extends from -N to N
x = zeros(1,length(t)); % an array x is taken such that it has
a row of zeroes eqal to the length of t
x(1,51) = 1; % 51st element of the array is taken as 1, that
lies at t =0.
figure(1)
subplot(2,1,1) %
plot(t,x,'r') % the continuous unit step funtion plotted with
red colored line
xlabel('Time'); %labelling of x-axis
xlabel('Amplitude'); % labelling of y-axis
title('continuous time unit impulse sequence'); % giving title
to the graph
% discrete time impulse sequence
n = -N:1:N; % range of N extends from -N to N with a gap of 1
between them
xn = zeros(1,length(n)); % an array is taken such that it has a
row of zeroes equal to the lenght of sample 'n'
xn(1,51) = 1; % 51st sample is taken as 1 which is at n=0
subplot(2,1,2)
stem(n,xn); % discrete stem plot of the impulse sequence
xlabel('discrete samples'); %labelling x-axis
ylabel('Amplitude'); % labelling y-axis
title('discrete time unit impulse sequence'); % title to the
graph
Unit Impulse function is a function which is zero at all
other places except at 0. The function was realized using the matlab for both
the continuous and discrete time domain plot. The graph in both the cases had
same properties except for the fact that one was discrete and the other
continuous.
continuous time unit step sequence
x = ones(1,length(t)); % an array x is taken such that it has a
row of ones eqal to the length of t
x(1,1:51) = 0; % 51st sample is taken as 0 which is at t=0
figure(2)
subplot(2,1,1)
plot(t,x, 'r'); %plotting of the continuous unit step sequence
with red color
xlabel('Time'); % labelling of x-axis
xlabel('Amplitude'); %labelling y-axis
title('continuous time unit step sequence'); % title to the
graph
% continuous time unit step sequence
xn = ones(1,length(t)); % an array is taken such that it has a
row of 0nes equal to the lenght of sample 'n'
xn(1,1:51) = 0; % 51st sample is taken as 0 which is at n=0
subplot(2,1,2)
stem(n,xn); % discrete plot of the unit step sequence
xlabel('discrete samples'); %labelling x-axis
ylabel('Amplitude'); % labelling y-axis
title('discrete time unit step sequence'); % title to the graph
Unit Step function has value 0 for all the negative arument
and one for the positive argument. This function was implemented successfully
using the matlab code for both the continuous time and discrete time domain.
continuous time ramp function
t = 0:0.1:N; % time interval for the ramp function choosen from
0 to N with a interval of 0.1
m = 1; %slope of the ramp function
x = m*t; % equation depicting ramp function
figure(3)
subplot(2,1,1)
plot(t,x); % continuous plotting of ramp function
xlabel('time'); %labelling x-axis
ylabel('Amplitude'); % labelling y-axis
title('continuous time ramp function') % title to the graph
% discrete time ramp function
n =0:1:N; % samples for the discrete time ramp function from 0
to N.
xn = m*n; % equation depicting discrete time ramp function
subplot(2,1,2)
stem(n,xn); % discrete plot
xlabel('discrete samples'); % labelling x-axis
ylabel('Amplitude'); % labelling y-axis
title('Discrete time ramp function') % title of the graph
Ramp funtion can be represented by a simple linear equation
passing through the origin. Its value is always zero in negative x-axis. The
equation was successfully represented and plotted in the matlab in both
continuous time and discrete time domain.
continuous time sinusoidal function
t = 0:0.01:1; % time range for the sinusoidal function
x = sin(2*pi*5*t); % equation depicting sinusoidal signal
figure(4)
subplot(2,1,1)
plot(t,x); % continuous plot of signal x with respect to t.
xlabel('time');% labelling x-axis
ylabel('Amplitude'); %labelling y-axis
title('continuous time sinusoidal function') % title of the
graph
% discrete time sinusoidal function
n = 0:0.01:1; % number of samples for the sinusoidal wave
figure(4)
xn = sin(2*pi*5*n); % equation depicting discrete sinusoidal
equation
subplot(2,1,2);
stem(n,xn); % discrete plot of the sine wave
xlabel('discrete samples'); % labelling x-axis
ylabel('amplitude'); % labelling y-axis
title('discrete time sinusoidal function'); %title to the graph
Sinusoidal sine waves
were also successfully coded in continuous and discrete time domain using
matlab and the graphs were obtained. The behaviour of the graph was as expected
continuous time exponential function
a = 2; %coeffficient of exponential function
t = 0:0.01:2; % time range for exponential funtion
x =exp(a*t); % equation depicting exponential function
figure(5)
subplot(2,1,1)
plot(t,x) % continuous plot of exponential funtion
xlabel('time'); % labelling x-axis
ylabel('amplitude') % labelling y-axis
title('continuous exponential function'); % title to the graph
% discrete time exponential function
a = 2; %coeffficient of exponential function
x =exp(a*t);% equation depicting exponential function
figure(5)
subplot(2,1,2)
stem(t,x) % discrete plot of the exponential function
xlabel('time'); % labelling x-axis
ylabel('amplitude') % labelling y-axis
title('discrete time exponential function'); % title to the
graph
Exponential signals were also represented in discrete and
continuous time domain using matlab code. The behavior of the graphs obtained
was as expected.The above graph was obtained for positive exponential functiom
and the same code can generate the negative exponential function by simply changing
the coefficient of exponential funtion to some negative value.
continuous triangular wave generation
y = 0:0.1:1; % the amplitude of the triangular wave limited
between 0 and 1.
figure(6)
subplot(2,1,1)
for i = 0:3 % for loop
implemented for the first half of the ramp signal in triangular wave
x = y +(2*i); %
generalized equation found using two point formula for the positive ramp of the
triangular wave
plot(x,y) % plotting
the graph for the above generalized equation
hold on % the plotted
value of x and y is kept on hold
end % end of for loop
for i = 1:3 % for loop implemented for the second half of the
ramp signal in triangular wave
x = (2*i)-y; % generalized equation found using two point
formula for the negative ramp of the triangular wave
plot(x,y) %plotting
the graph for the above generalized equation
hold on; % the
plotted value of x and y is kept on hold
end % end of for loop
xlabel('time'); % labelling x-axis
ylabel('amplitude'); % labelling y-axis
title('Continuous triangular wave signal') % title of the graph
hold off; % the hold is removed.
% discrete triangular wave generation
y = 0:0.1:1; % the amplitude of the triangular wave limited
between 0 and 1.
figure(6)
subplot(2,1,2)
for i = 0:3 % for loop
implemented for the first half of the ramp signal in triangular wave
x = y +(2*i); %
generalized equation found using two point formula for the positive ramp of the
triangular wave
stem(x,y) % discrete
plotting the graph for the above generalized equation
hold on % the plotted
value of x and y is kept on hold
end % end of for loop
for i = 1:3 % for loop implemented for the second half of the
ramp signal in triangular wave
x = (2*i)-y; % generalized equation found using two point
formula for the negative ramp of the triangular wave
stem(x,y) %discrete
plotting the graph for the above generalized equation
hold on; % the
plotted value of x and y is kept on hold
end % end of for loop
xlabel('time'); % labelling x-axis
ylabel('amplitude'); % labelling y-axis
title('Discrete triangular wave signal') % title of the graph
hold off; % the hold is removed.
Triangular wave was also obtained using the matlab code. To
obtain the graph for triangular wave, for loop was extensively used. The
behaviour of the graph was as expected. Discrete plot was also obtained using
the stem function.
sawtooth wave generation
figure(7)
subplot(2,1,1)
y = 0:1; % the amplitude of the sawtooth wave limited between 0
and 1
for i = 0:5 % for loop
implemented for the first half of the ramp signal in sawtooth wave
x = y -i; %
generalized equation for the positive ramp of the sawtooth wave.
plot(x,y) % plotting
of the above generalized equation
hold on; % the values
of x and y and the plot is kept on hold
end % end of for loop
x = -4:1:1; % value of x-axis limited between -4 and 1
for j = 0:0.001:1; % for loop implemented for the other half of
the sawtooth wave
y = j; % all the
value of j between 0 and 1 is assigned as y with a small interval of 0.001
plot(x,y); % plotting
of the graph of x and y to obtain a straight line connecting the ramp to the
x-axis
hold on; % the
plotted values ar kept on hold
end % end of for loop
xlabel('time'); %labelling x-axis
ylabel('amplitude'); % labelling y-axis
title('Continuous sawtooth wave signal'); % title of the graph
hold off; % the hold is removed
figure(7)
subplot(2,1,2)
y = 0:0.1:1; % the amplitude of the sawtooth wave limited
between 0 and 1
for i = 0:5 % for loop
implemented for the first half of the ramp signal in sawtooth wave
x = y -i; %
generalized equation for the positive ramp of the sawtooth wave.
stem(x,y) % discrete
plotting of the above generalized equation
hold on; % the values
of x and y and the plot is kept on hold
end % end of for loop
x = -4:1:1; % value of x-axis limited between -4 and 1
for j = ones(length(x)); % for loop implemented for the other
half of the sawtooth wave
y = j; % all the
value of j between 0 and 1 is assigned as y with a small interval of 0.001
stem(x,y); % discrete
plotting of the graph of x and y to obtain a straight line connecting the ramp
to the x-axis
hold on; % the
plotted values ar kept on hold
end % end of for loop
xlabel('time'); %labelling x-axis
ylabel('amplitude'); % labelling y-axis
title(' Discrete sawtooth wave signal'); % title of the graph
hold off; % the hold is removed
Sawttooth wave obtained using the matlab coding was as
expected. Limiting of the value of amplitude to calculate the time period was
used here as in the triangualr wave above.
continuous square wave
m = 0:0.001:1; % variable m assigned value from 0 to 1 with a
intrval of 0.001
figure(8)
subplot(2,1,1)
for i = 0:1:10; % for loop implemented to assign the value of
the square wave funtion at x = 0 to 10 with a interval of 1
x = i;
y = m; % amplitude
assigned with a value increasing from 0 to 1.
plot(x,y); %
continous plot of x and y
hold on; % the plotted
value is kept on hold
end % end of foor loop
for j = 0:2:10; %
another for loop implemented to assign the maximum value to the square wave at
fixed time intervals
x = j + m; % the
square wave function from 0 to 1, 2 to 3, 4 to 5 and so on taken into
consideration
y = 1; % functional
value at those points assigned as one
plot(x,y) % obtained
value of y and x is plotted
hold on; % value kept
on hold for further use
end % end of for loop
for k = 1:2:10; %for loop implemented to assign the minimum
value to the sqare wave at fixed time intervals
x = k + m; %the
square wave function from 1 to 2, 3 to 4, 5 to 6 and so on taken into
consideration
a = 0; % functional
value at those point assigned as zero
plot(x,a) %plot of x
and y is done
hold on; % obtained
plot is kept on hold
end % end of for loop
hold off; % hold is called off
xlabel('time'); % labelling of x-axis
ylabel('amplitude'); % labelling of y-axis
title('Continuous square wave signal') % title to the graph
axis ([-5 15 -0.5 1.5]); % axis of the plot is fixed
% Discrete Square Wave
m = 0:0.2:1; % variable m assigned value from 0 to 1 with a
intrval of 0.001
figure(8)
subplot(2,1,2)
for j = 0:2:10; %
another for loop implemented to assign the maximum value to the square wave at
fixed time intervals
x = j + m; % the
square wave function from 0 to 1, 2 to 3, 4 to 5 and so on taken into
consideration
y = ones(length(x));
% functional value at those points assigned as one
stem(x,y) % obtained
value of y and x is discrete plotted
hold on; % value kept
on hold for further use
end % end of for loop
for k = 1:2:10; %for loop implemented to assign the minimum
value to the sqare wave at fixed time intervals
x = k + m; %the
square wave function from 1 to 2, 3 to 4, 5 to 6 and so on taken into
consideration
a = zeros(length(x));
% functional value at those point assigned as zero
stem(x,a) % discrete
plot of x and y is done
hold on; % obtained
plot is kept on hold
end % end of for loop
hold off; % hold is called off
xlabel('time'); % labelling of x-axis
ylabel('amplitude'); % labelling of y-axis
title('Discrete square wave signal') % title to the graph
axis ([-5 15 -0.5 1.5]); % axis of the plot is fixed
square waves are periodic in nature whose amplitude varies
between two fixed values and the time period in each value is equal. Sqaure
wave was obtained just as explained by the defination using the matlab code.
For loop was used to achieve the wave.Similarly Square wave was also obtained in
discrete time, using the stem function.
