Complex sentence: The most widely accepted analytic tool for such problems is the Fourier transform; this decomposes a signal into basis functions of different frequencies, known as frequency components, and gives us the amplitude of each frequency component in the signal.
Split into simpler sentences: The most widely accepted analytic tool for such problems is the Fourier transform. The Fourier transform decomposes a signal into basis functions of different frequencies, known as frequency components, and gives us the amplitude of each frequency component in the signal.