Question

Using matlab, create and plot the following signals for time t = -10 to t=10.

40(t) = cos(0.5πt) × rect 2 [t-40

Answer 1

********************MATLAB Code*************************

t = -10:0.05:10; % defining the time limits and time precision for simulation
x10 = cos(0.5*pi*t).*rectangularPulse(t/2); % declaring the function.
% rectangularPulse is the matlab function for generating 'rect' signal.
plot(t,x10);        % To plot the function x10
ylim([-0.1 1.1]);   % to declare the y-axis limits
grid on;            % to add grid to the plot

********************** End of Code *********************

The plot for the function x₁₀(t) as obtained from the above matlab code is as follows:

The value value of rect(t) is 0 when |t| > 0.5. For rect(t/2) the limits will be |t/2| > 0.5 i.e, |t| > 1. So the entire function is '0' for t > 1 and t < -1, as rect(t/2) becomes '0'. The function values between -1 < t < 1 is given by cos(0.5*pi*t). At values t = +1 and t = -1, the value of rect(t/2) is '0.5' but the function becomes '0' as the term cos(0.5*pi*t) becomes '0' at these instants.