aatish, since you seem interested, I'll throw another fun-fact at you that I found very interesting even after years of working with Fourier transforms:

You can view the Fourier transform as a fitting problem. Yes, you fit the data to a function. Ie you take the data points and fit it to a sum of exponential functions. There is actually a much more general approach called "Prony method" that extends the concept and adds a dampening factor into the function to fit:

http://www.engr.uconn.edu/~sas03013/docs/PronyAnalysis.pdf

You can take it further and use matrix pencil methods and eventually you'll see connections to ESPRIT algorithm and even least squares algorithm. It's really interesting how they're all actually connected.

Cheers