2: Signals and Systems
- Page ID
- 1605
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- 2.1: Complex Numbers
- While the fundamental signal used in electrical engineering is the sinusoid, it can be expressed mathematically in terms of an even more fundamental signal: the complex exponential. Representing sinusoids in terms of complex exponentials is not a mathematical oddity. Fluency with complex numbers and rational functions of complex variables is a critical skill all engineers master.
- 2.2: Elemental Signals
- Elemental signals are the building blocks with which we build complicated signals. By definition, elemental signals have a simple structure. Exactly what we mean by the "structure of a signal" will unfold in this section of the course. Signals are nothing more than functions defined with respect to some independent variable, which we take to be time for the most part.
- 2.3: Signal Decomposition
- A given signal can often be decomposed into a sum of simpler signals, which we term the "signal decomposition." Though we will never compute a signal's complexity, it essentially equals the number of terms in its decomposition.
- 2.4: Discrete-Time Signals
- Analog signals are functions having continuous quantities as their independent variables, such as space and time. Discrete-time signals are functions defined on the integers; they are sequences. One of the fundamental results of signal theory will detail conditions under which an analog signal can be converted into a discrete-time one and retrieved without error. This result is important because discrete-time signals can be manipulated by systems instantiated as computer programs.
- 2.5: Introduction to Systems
- Signals are manipulated by systems. A system's input is analogous to an independent variable and its output the dependent variable. For the mathematically inclined, a system is a functional: a function of a function (signals are functions). Simple systems can be connected together--one system's output becomes another's input--to accomplish some overall design. Interconnection topologies can be quite complicated, but usually consist of weaves of three basic interconnection forms.