I have some queries about the Fourier transform
In most of the cases, the Fourier transform of a signal is symmetric with respect to positive and negative frequency. I think the computational complexity increases because only half of the symmetric spectrum (i.e. spectrum for only positive frequencies) is useful. Also, while working in the frequency domain we could get wrong value of energy or power due to the spectrum on negative axis.
In the Fourier transform formula the limits of integration are from $-\infty$ to $\infty$. However, 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 localized in frequency domain only. But from both of these spectrum, we don't get any spatial component features like which frequency component is present at which time (and same with the phase value).
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 doesn't exists practically.
I feel that these are the "shortcomings" of Fourier transform but don't know whether they really are or not.
So can anybody give explanation on any of above doubts?