The Fourier Transform is an important image processing tool which is used to decompose an image into its sine and cosine components. The output of the transformation represents the image in the Fourier or frequency domain, while the input image is the spatial domain equivalent.

The Fast Fourier Transform (FFT) is an important measurement method in the science of audio and acoustics measurement. It converts a signal into individual spectral components and thereby provides frequency information about the signal.

One of the advantages of using the Laplace Transform to solve differential equations is that all initial conditions are automatically included during the process of transformation, so one does not have to find the homogeneous solutions and the particular solution separately.

The different properties are: Linearity, Differentiation, integration, multiplication, frequency shifting, time scaling, time shifting, convolution, conjugation, periodic function. There are two very important theorems associated with control systems.