Square wave Chirp

How can we generate a chirp sequence using square wave as oposed to sine?

Answer 1

[Dr. Seis]

Here is an example:

signal_length = 20; % length of signal in seconds
wave_length = 2*pi; % wavelength of rectangle pulse in seconds
amplitude = 0.75; % amplitude of wave
dt = 1/(2*pi); % time increment in seconds
time = 0:dt:signal_length; % time samples in seconds

% Define the sine and rectangle signal timeseries
sinesignal = sin(2*pi*time/wave_length)*amplitude;
rectsignal = sign(sin(2*pi*time/wave_length)).*amplitude;

% Plot the timeseries
plot(time,rectsignal,'r-',time,sinesignal,'b-');

If you can generate a sinusoidal chip, then you can turn it into a square wave using the above. It basically takes a sinusoidal wave and throws everything away but the sign of the number (+/- 1) or 0. Then you would just multiply the square wave with you desired amplitude. Just make sure you have a large enough sample rate that your high frequency waves are not under-sampled.

EDIT

I didn't realize Matlab had something to generate a chirp signal, example modified above:

signal_length = 100; % length of signal in seconds
dt = 1/10; % time increment in seconds
time = 0:dt:signal_length; % time samples in seconds
amplitude = 0.75; % amplitude of wave
f0 = 0.01; % Frequency of wave at t0
f1 = 0.1; % Frequency of wave at time(end)

% Define the rectangle signal timeseries
chirpsignal = chirp(time,f0,time(end),f1)*amplitude;
squarechirpsignal = sign(chirpsignal)*amplitude;

% Plot the timeseries
plot(time,squarechirpsignal,'r-',time,chirpsignal,'b-');

[Walter Roberson]

The sites I glanced at were pretty dismissive of that approach, and said things like "You could _call_ it a chirp signal but it will not have any of the desirable properties of a real chirp signal".

[Dr. Seis]

Is this because it losses its shape in the frequency domain, or...?

Answer 2

[Walter Roberson]

The closest I can find to that topic is this paper, http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=308500