Fourier Transform

The Fourier transform named after Joseph Fourier, is a mathematical transformation employed to transform signals between time (or spatial) domain and frequency domain, which has many applications in physics and engineering. It is reversible, being able to transform from either domain to the other. The term itself refers to both the transform operation and to the function it produces.

The Fourier Transform is a tool that breaks a waveform (a function or signal) into an alternate representation, characterized by sine and co-sines. The Fourier Transform shows that any waveform can be re-written in the sum of sine wave functions.The sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation.

Virtually everything in the world can be described via a waveform - a function of time, space or some other variable. For instance, sound waves, electromagnetic fields, the elevation of a hill versus location, a plot of VSWR versus frequency, the price of your favorite stock versus time, etc. The Fourier Transform gives us a unique and powerful way of viewing these waveforms.

Reference
Wikipedia [Fourier Transform]