linear chirp signal generation ?

hello i don't want to use chirp inbuilt function and i have written a code for chirp. could any one tell me is the code is correct ? i have simulate it and getting plot but at instantaneous time t1, I am not getting frequency change.

i have written a code according to equation of chirp signal generation.

please tell me this is correct ?

*****************************************

f1 =10;

f2 = 50 ;

t =0:0.001:20;

t1 = 10;

alpha = (f2-f1)/t1;

f= (alpha)*t + f1;

xx =1*cos(f);

plot (t,xx);

**********************************************

[Neal Bambha]

This is not the correct expression for a linear chirped signal. See the wikipedia page for "Chirp" There is a t-squared term in the sine. Otherwise you will not have the correct spectrum

chirp_slope = (f2 - f1)/t(end);

chirp_signal = sin(2*pi*(0.5*chirp_slope*t.^2 + f1*t));

Answer 1

[Youssef Khmou]

hi, try this :

 Fs=1000; % sample rate 
tf=2; % 2 seconds
t=0:1/Fs:tf-1/Fs;
f1=100;
f2=400; % start @ 100 Hz, go up to 400Hz
semi_t=0:1/Fs:(tf/2-1/Fs);
sl=2*(f2-f1/2);
f1=f1*semi_t+(sl.*semi_t/2);
f2=f1(end)+f2*semi_t-sl.*semi_t/2;
f=[f1 f2];
y=1.33*cos(2*pi*f.*t);
plot(t,y)

To check the Amplitude spectrum (100Hz,400Hz), try my submission : http://www.mathworks.com/matlabcentral/fileexchange/40002-psd-power-spectral-density-and-amplitude-spectrum-with-adjusted-fft

[Aniket]

Hello Youssef, i have used your code and got some results. but i am not getting what is going in the following step

f1=f1*semi_t+(sl.*semi_t/2);

f2=f1(end)+f2*semi_t-sl.*semi_t/2;

could you please explain

[Youssef Khmou]

hi, consider the slope as :

 K=f2-f1/2 ;
then :

 f1=f1*semi_t+(K*semi_t);

 f2=f1(end)+f2*semi_t-(K*semi_t);

We added "f(end)" to have continuity in the frequency , to test do this :

f1=f1*semi_t+(K*semi_t);

f2=f2*semi_t-(K*semi_t); 

f=[f1 f2]; plot(t,f)

[vamsi]

hi youssef i execuded the code but the output is not comming for fs=500e6,f1=160e6 ,f2=170e6 ,t=5e-6 could u please explain that...

[Youssef Khmou]

hi vamsi,

Your parameters do not fit the last example because of scaling problem; the frequency continues to increase or cant reach the final value f2 . To overcome this issue, consider the frequency as function F=at+constant that when time ends F=f2 and when time starts F=f1 :

Fs=500e6; 
f=5e-6; 
t=0:1/Fs:tf-1/Fs;
f1=160e6 ;
f2=170e6; 
SLOPE=(f2-f1)./t(end);
F=f1+SLOPE*t;
y=1.33*cos(2*pi*F.*t);
plot(t,y)
fy=fft(y);
Freq=(0:length(t)-1)*Fs/length(t);
figure, plot(Freq(1:end/2),abs(fy(1:end/2)))

Have you ever used the function chirp(t,f0,t1,f1) ?

[Atilla Golan]

Hi Youssef, Can we try up-going and down going chirp together? (without using chirp function on Matlab). In a time range of [1.2s 2.7s] (for example) my function should go up 0.6s (since 1.2s to 1.8s) and go down for the rest (since 1.8s to the end:2.7s). I mean in a constant frequency range, function goes up and down during time like quadratic chirp function but without using chirp.

[Dhananjay Singh]

hi youssef,

the code you last sent doesn't work when i set the values of f1, f2 in Khz. can you help?

Answer 2

[Honglei Chen]

It should be

cos(2*pi*f.*t)

instead of

cos(f)

Answer 3

[REEM ALI]

please i want to generate triangular modulation sweep of fmcw of rx and tx

Answer 4

[farouk behar]

f = 150; a =5; w =2*pi*f; t =0:0.1:20; theta = pi/2; X = a*cos((w*t)+theta); y0 = X + 2*rand(size(t));

plot(t,y0)