I'm new in digital signal processing and having hard time understanding this. By Fourier Transform I mean Discrete Fourier Transform as it's the only one I'm learning.
As far as I know Fourier Transform transforms a signal into an equivalent set of signals in sinusoid form, which when summed gives the original signal back.
If I got it right, a signal could also be represented by other things instead of sinusoids but because sinusoids are easy to process this is preferred and FT is used.
I also understand that with DFT I get amplitude and phase of the sinusoid at given frequency. But why should I care about these properties(amplitude, phase and frequency) of equivalent sinusoids? What's so special about it and does it really have a "natural" meaning?