You can take a general function and break it into its 'component' polynomial terms, this is called the taylor series.
You can also take a periodic function and break it into its 'component' sines and cosines. This is called the fourier series.
Fourier transform is essentially similar to the fourier series except you're allowed to have non-integer frequency multiples.
You can see how FT and FS are useful for analyzing all sorts of things that are periodic. MP3s, for example use a similar system to encode music (it's called the discrete cosine transform) and compression is enabled by deleting information that your ear will fill in - but this information is most easily selected and deleted by looking at the MP3 in terms of frequency and amplitude over time.
You can also take a periodic function and break it into its 'component' sines and cosines. This is called the fourier series.
Fourier transform is essentially similar to the fourier series except you're allowed to have non-integer frequency multiples.
You can see how FT and FS are useful for analyzing all sorts of things that are periodic. MP3s, for example use a similar system to encode music (it's called the discrete cosine transform) and compression is enabled by deleting information that your ear will fill in - but this information is most easily selected and deleted by looking at the MP3 in terms of frequency and amplitude over time.