Fourier transform of text How could I/is it possible to take a fourier transform of text? i.e. What domain would/does text exist in? Any help would be great.
NOTE: I do not mean text as an image. I understand it's value, but I'm wondering if it is possible to map text to some domain and transform text on the basis of letters. This is in hopes of performing frequency filtering on said text.
 A: You could take the text as a 2-D image and use a 2-D Fourier transform. This could be useful e.g. to find the orientation of the text and subsequently - if necessary - apply an appropriate rotation, which makes it easier for text recognition methods to give satisfactory results.
A: I had a similar idea last night when I was trying to explain the concept of FFTs for fundamental analysis and synthesis of sounds to someone, and  the analogy that popped into my head was of the prevalence of lowercase letters, uppercase letters, and punctuation in a page of text corresponding to signals that occur with high, medium and low frequency.
I haven't tried this yet, but I was thinking of converting the symbols to numbers (using their ASCII values might be enough) and feeding the resulting sequence into an FFT analysis to see if a paragraph of text could be decomposed into the sum of a reasonably finite series of sine waves such that the list of coefficients would be smaller than the original text.
I don't think it would have any meaning as such; it certainly wouldn't be useful to count word frequencies or to synthesize texts, but it's a very interesting question!
A: Not quite in the frequency domain, but there is a way to look for periodic structures in text -- the Index of Coincidence. For normal text the IoC will be pretty much flat. But for text encrypted with, say, an 8-letter key and the Vigenère cipher, the IoC will show a pattern of 7 low values and a spike every 8th.
That tells you to take every 8th character and look for a key for that position, then try the next position. This also works with XOR and other ciphers.
