Extrapolation using fft in octave

Using GNU octave, I'm computing a fft over a piece of signal, then eliminating some frequencies, and finally reconstructing the signal. This give me a nice approximation of the signal ; but it doesn't give me a way to extrapolate the data.

Suppose basically that I have plotted three periods and a half of

f: x -> sin(x) + 0.5*sin(3*x) + 1.2*sin(5*x)

and then added a piece of low amplitude, zero-centered random noise. With fft/ifft, I can easily remove most of the noise ; but then how do I extrapolate 3 more periods of my signal data? (other of course that duplicating the signal).

The math way is easy : you have a decomposition of your function as an infinite sum of sines/cosines, an开发者_StackOverflow社区d you just need to extract a partial sum and apply it anywhere. But I don't quite get the programmatic way...

Thanks!

The Discrete Fourier Transform relies on the assumption that your time domain data is periodic, so you can just repeat your time domain data ad nauseam - no explicit extrapolation is necessary. Of course this may not give you what you expect if your individual component periods are not exact sub-multiples of the DFT input window duration. This is one reason why we typically apply window functions such as the Hanning Window prior to the transform.