Chirp generation

I would like to creat a customized chirp sequence where frequency is changing every half cycle and I do not know how to go about it.

[Walter Roberson]

I do not see how the result could have the necessary properties to be called a "chirp" ?

Answer 1

[Dr. Seis]

As Walter says, this will not give you a true chirp signal. If you are aware of this and would still like to have a pseudo-chirp then you can take a look at the example below. I show the difference between trying to generate the type of chirp you are after and a real chirp signal. I also plot the derivative of the resulting signals, so I can highlight that between half cycles you will have a sometimes subtle (sometimes not so subtle) jump in gradient.

df = 0.1; % define frequency increment
f = 0.1 : df : 1; % define frequencies for "chip" signal

dt = 0.1; % define a dt for final timeseries

% Generate 1Hz cosine wave
nt = 0 : 1/360 : 1-1/360;
a = 1;
s = a*cosd(0 : 1 : 359);

% Initialize x & y
x = zeros(1,179*numel(f)+1);
y = a*ones(1,179*numel(f)+1);

end_time = 0;
for i = 1 : numel(f)
  x((1:179) + (i-1)*179 + 1) = nt(2:180)/f(i) + end_time;
  if mod(i,2) ~= 0       
      y((1:179) + (i-1)*179 + 1) = s(2:180);
  else
      y((1:179) + (i-1)*179 + 1) = s(182:360);
  end
  end_time = nt(180)/f(i) + end_time;
end

% x is irregular spacing
% we need to interpolate to a regular spacing
x_new = 0 : dt : x(end);
y_new = interp1(x,y,x_new,'spline')
y_chirp = chirp(x_new,f(1),x_new(end),f(end));

% Determine derivative/differential info
x_diff = x_new(2:end-1);
y_diff = arrayfun(@(n)(y_new(n+1)-y_new(n-1))/(2*dt),2:numel(x_new)-1);
y_cdiff = arrayfun(@(n)(y_chirp(n+1)-y_chirp(n-1))/(2*dt),2:numel(x_new)-1);

% plot results
figure;
subplot(2,1,1)
plot(x_new,y_new); hold on;
plot(x_new,y_chirp,'r-'); hold off;
legend('pseudo-chirp','real chirp');
subplot(2,1,2);
plot(x_diff,y_diff); hold on;
plot(x_diff,y_cdiff,'r-'); hold off;
legend('pseudo-chirp','real chirp');