interpolation with FFT?


KZoli
04-06-2005, 10:27 AM
Hy all!

I have got a theoretical question. Consider that I have sampled a function f(x) -> g(k) = f(k*dx) ; k=0,1,2,...,N ; dx = L/N
Than I fourier transform it, G = FFT(g). With the inverse DFT I can obtain the original series g(k). If I would like to use the IDFT for function interpollation(with some modification: k -> x*N/L )

N-1
---
\
f_int(x) = 1/N / G(n) exp( -i*2*pi*n*x/L) ,
---
n=0

than the values of f_int(x) only equal with f(x) at the original sample point, despite I 'am sampling f(x) = x^2 (for checking) with N=1024 and L = 1. Between the original sample points f_int(x) is badly oscillating and provides function results that are different from f(x) with sever ten percents. I have a feeling that there is something that I don't know.
I would like to interpolate a very badly oscillating function with nearly constant frequency, that is why I am trying to use some fourier method.

Can anybody help me?

tushar.swamy
11-18-2008, 07:37 PM
Hey, Im facing the exact same problem. If you know the answer now, please do let me know. thanks.

davekw7x
11-20-2008, 08:59 AM
...facing the exact same problem...

What problem? I can't understand what the Original Poster was trying to say in the first part of the post.

I wasn't hanging around this forum way back then (three and a half years ago), anyhow, and apparently no one else could help.

As for the last part:

I would like to interpolate a very badly oscillating function with nearly constant frequency,

That's called a bandpass filter.

I personally can't see trying to teach Digital Signal Processing fundamentals on a forum like this, which was created to help people with Numerical Recipes books and code, but...

If you have any specific questions maybe someone can help.

Regards,

Dave