# How to integrate LFM signal into pulse

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tinkyminky93 on 13 Jan 2022
Commented: Chunru on 14 Jan 2022
I am trying to generate a Linear Frequency Modulated (LFM) Pulse waveform like below.
I generated periodic chirp signals but the problem is i can not put inside these chirps into pulse boundaries. I mean outside of the duty cycle is not zero. How can I solve this problem? By the way, I am not using a toolbox. Thank you for your help.

Chunru on 14 Jan 2022
Edited: Chunru on 14 Jan 2022
fl = 100; % Hz
fu = 200;
fs = 1000;
pw = 0.1; % sec
pri = 1; % sec
% LFM
t = (0:1/fs:pw)';
x = cos(2*pi*(fl*t + .5*(fu-fl)/pw*t.^2));
% One pulse
x(end+1:round(pri*fs)) = 0;
% Npulses
Npulses = 3;
y = repmat(x, [3 1]);
t = (0:length(y)-1)'/fs;
plot(t, y)
Chunru on 14 Jan 2022
You can try the following (but you need to know why your need to have that kind of amplitude):
fl = 100; % Hz
fu = 200;
fs = 1000;
pw = 0.1; % sec
pri = 1; % sec
% LFM
t = (0:1/fs:pw)';
x = 0.5*(1+cos(2*pi*(fl*t + .5*(fu-fl)/pw*t.^2)));
plot(t, x)

R2021b

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