# How do I extrapolate a 1D chirped signal?

Following a past question, I'd like to extrapolate a signal like the one below: (red is signal, blue is the the extrapolated )

t1 = 0:0.1:30;
t2 = 0:0.1:40;
s = @(t) sin(0.2*t)+sin(0.5*t+0.05*t.^2);
figure;
plot(t2,s(t2)); hold on
plot(t1,s(t1));


Linear predictive coding, or AR Burg's method are not successful here. How can you extrapolate that?

• Only commenting as I only have my guess as to what I might do (which I am sure is not optimum). I would low pass filter to estimate and fit the low frequency sinusoidal component, and high pass filter to estimate the high frequency sinusoidal component including it's chirp rate. From this I would then extrapolate the result based on those estimates. – Dan Boschen Sep 13 '18 at 1:19
• Think of what Burg is doing: it’s an autoregressive method, so it’s assuming that there is a linear phase relationship between samples. If you have an LFM that you’re trying to approximate, what you have is actually quadratic phase information; therefore, Burg isn’t really the right tool here (no auto regressive method is for that matter). Have you looked at any other methods that aren’t AR based? Singular spectrum analysis extrapolation comes to mind – matthewjpollard Sep 13 '18 at 1:55
• yes I'm aware that LPC or Burg's are not appropriate. Can you give more details on the option you mentioned? – bla Sep 13 '18 at 7:52
• I’ve worked with SSA quite a lot but never for extrapolation, though I’m aware economists use it there (I’ve never had a need). There’s a nice write up on Wikipedia you could/should check out if you’re interested. – matthewjpollard Sep 15 '18 at 0:16