It is convenient to represent common signal operations and transformation as operators. In the context of signal processing, an operator can be seen as a signal-valued function.
In a sense, an operator is similar to systems as both transform input signals to output signals, though operators are usually predefined and are used as building blocks of systems.
One great property of the operator notation is that we can perform algebraic manipulation on them. This way, we can identify and analyze equivalent systems.
Examples of Operators
Differentiation
See: D-notation
We often write differential equations with the “D-notation” like
Convolution
See: convolution
The convolution of two signals
Fourier-related Transforms
We often write Fourier transform and other related transforms as operators.
- Fourier Transform:
- Laplace transform: