well well good try infact i must say U HAV visualized the fourier series /transform to all readers ,u r absolutly right in what u r saying
BUT
brother my problem is some what different i want certain basis other then sine/cosine to represent my signal in signal space, WHAT i asked in the post was a curious question that is there any basis like natural basis in finite domain ,but now i am thinking that the best possible basis is infact of fourier domain basis,CAN ANY BODY HAV ANY IDEA OF OTHER BASIS WE CAN CALL NATURAL BASIS OF CONTINOUS DOMAIN