In many disciplines, signals and systems problems in N-dimensions are solved either in the time or frequency domains. In the time-domain, these problems are solved using classical methods for solving differential/difference equations. In the frequency-domain, problems are solved by addressing algebraic equations. Where is the advantage? If integration and differentiation can be transformed into algebraic equations then we have facilitated the problem solving process.
In general, signals and system problems, can either be solved using differential/difference or albebraic equations. The tools that allow us to go back and forth from one domain to the other are known as transforms. Two widely used transforms are the Laplace Transform and the Fourier Transform, and both are related. Here we will look at the Discrete Fourier Transform (DFT).