I am fond of Fourier Transform. I have some queries about Fourier Transform
In most of the cases,the Fourier transform of a signal is symmetric about positive and negative axis.I think the computational complexity increases because only half part of symmetric spectrum (i.e. spectrum except on negative axis) is of use. Also,while calculating in frequency domain we could get wrong value of energy /power due to the spectrum on negative axis .
In the Fourier transform formula the limits of integration are from -infinity to +infinity .But for a signal which is continuously or exponentially increasing with time,one can't compute it's Fourier transform.
After computation of Fourier transform of a signal, we get Phase and Frequency spectrum of the whole signal which is localised in frequency domain only . But from both these spectrums,we don't get any spatial component features like which frequency component is present at which time (and same with the phase value ).
If we think practically ,concept of negative frequency doesn't exists. But after computation of Fourier transform of signal,with dc and positive frequencies we also get unnecessary negative frequency components. I think concept of negative frequency doestn't exists practically.
So can anybody give explanation on any of the above doubts?