Question

(A.) Use MATLAB to generate a pulsed sine wave signal having a frequency F-10KHZ and a pulse width of T-.5ms. The pulse repetition time is 1ms (pulse repetition rate is 1000 pulses/sec), i.e., the signal is zero between pulses. Model the signal to start at time t-0 and to end at a time t=Tstop. Use a sample time of .001ms to approximate an analog environment. Display the signal in MATLAB appropriate for an analog signal, first for Tstop 1ms and then for Tstop 5ms (B.) In the MATLAB part (A) simulation sample the analog pulsed sine wave signal with sample times of.01ms. Display these sampled pulse sine waves in MATLAB appropriate for a discrete signal (C.) In MATLAB compute and display the magnitude of the DTFT of the pulse sin wave signals for w between 0 and pi. Do this for each of the Tstop times given above. Determine the physical frequency associated with the largest peak in the magnitude spectrum. Estimate the frequency spacing of significant minor peaks away from the major peak. What comment can you make when comparing the DTFT's of the two signals?

Answer 1

(A) MATLAB CODE:

clc
clear all
close all

F = 10;            % Frequency in KHz
T = 1/F;
Ts = 0.001;         % Sample time in ms
Tstop = input('Enter Tstop in ms:');
t = 0:Ts:Tstop;     % Time t in ms

% Sinusoidal with frequency F
x = sin(2*pi*F.*t);

Tp = 1;
Wp = 0.5;

% Generating Pulse with width Wp and Pulse Repetition Tp
y = [];
for n = 1:Tstop
    if n == 1
        for i = 1:length(t)
            if t(i) >= 0 & t(i) < Wp
                y = horzcat(y,1);
            elseif t(i) >= Wp & t(i) <= Tp
                y = horzcat(y,0);
            end
        end
    elseif n > 1
        for i = 1:length(t)
            if t(i) >= 0 & t(i) < Wp
                y = horzcat(y,1);
            elseif t(i) >= Wp & t(i) < Tp
                y = horzcat(y,0);
            end
        end
    end
end

z = x.*y; % Pulsed Sine Wave Signal

plot(t,z,'r')
xlabel('t in ms')
title('Pulsed Sinewave Signal')
grid on

OUTPUT:

Tstop = 1 ms

Pulsed Sinewave Signal 0.8 0.6 0.4 0.2 0 -0.2 -0.4 0.6 -0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0,9 1 t in ms
Tstop = 5 ms

Pulsed Sinewave Signal 0.8 0.6 0.4 0.2 -0.2 -0.4 -0.6 -0.8 0.5 1 1.5 2 2.5 tin ms 3 3.5 4 4,5 5
(B) MATLAB CODE:

clc
clear all
close all

F = 10;            % Frequency in KHz
T = 1/F;
Ts = 0.001;         % Sample time in ms
Tstop = input('Enter Tstop in ms:');

ts = 0.01; % Sampling time interval

t = 0:Ts:Tstop;     % Time t in ms

% Sinusoidal with frequency F
x = sin(2*pi*F.*t);

Tp = 1;
Wp = 0.5;

% Generating Pulse with width Wp and Pulse Repetition Tp
y = [];
for n = 1:Tstop
    if n == 1
        for i = 1:length(t)
            if t(i) >= 0 & t(i) < Wp
                y = horzcat(y,1);
            elseif t(i) >= Wp & t(i) <= Tp
                y = horzcat(y,0);
            end
        end
    elseif n > 1
        for i = 1:length(t)
            if t(i) >= 0 & t(i) < Wp
                y = horzcat(y,1);
            elseif t(i) >= Wp & t(i) < Tp
                y = horzcat(y,0);
            end
        end
    end
end

z = x.*y; % Pulsed Sine Wave Signal

stem(t*ts,z,'r')
xlabel('n')
title('Sampled Pulsed Sinewave Signal')

OUTPUT:

Tstop = 1 ms

Sampled Pulsed Sinewave Signal 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 0.004 0,005 0.007 0.01 0.001 0.002 0.003 0.006 0.008 0.009
Tstop = 5 ms

Sampled Pulsed Sinewave Signal S pas 0.8 0.6 0,4 0.2 0 -0.2 -0.4 -0.6 0.8 0.005 0.03 0.035 0.05 0.01 0.015 0.02 0.025 0.04 0.045