13.1:
Signal and System
Signals are sets of data or information.
One-dimensional signals include single-variable functions, such as the variations in air pressure over time in human speech.
Multi-dimensional signals are those that function based on two or more variables. An example is a monochromatic image that measures light intensity according to the horizontal and vertical positioning.
Systems are collections of devices that process input signals into one or more output signals.
Systems can be classified as single-input, single-output, or multi-input or multi-output.
Systems can vary widely, encompassing things like electrical systems, mechanical systems, computer programs, and the human body.
The resistor-capacitor network is a simple system with a source voltage as the input and the capacitor voltage as the output.
The human body, a complex system, responds to heat exposure on a fingertip by sending signals from the nerve ending the finger to the central nervous system. This system then produces multiple output signals instructing various muscles in the arm to retract the finger.
Mathematical modeling of signals and systems facilitates the development of systems to execute specific operations.
13.1:
Signal and System
A signal x(t) is a set of data or a time function representing a variable of interest. Signals typically convey information about a phenomenon, such as atmospheric temperature, humidity, human voice, television images, a dog's bark, or birdsongs. More generally, a signal can be a function of more than one independent variable. For instance, images depend on horizontal and vertical positions and can be regarded as two-dimensional signals. However, this text will focus on one-dimensional signals with time as the independent variable.
A system is a collection of devices that operate on an input signal x(t) (or excitation) to produce an output signal y(t) (or response). A system can also be considered a mathematical model of a physical process that relates the input signal to the output signal. Examples of systems include electric circuits, computer programs, the stock market, weather patterns, and the human body.
A system may have several mathematical models or representations. The variables in these models are described as signals, which may represent current, voltage, or displacement. In electrical systems, signals are often currents and voltages. In mechanical systems, signals are typically temperatures, forces, and velocities. In hydraulic systems, signals may be displacements and pressures.
We classify the signals that enter the system as input signals, while the signals produced by the system are output signals. For example, in an electric circuit, voltages and currents as functions of time are considered signals, while the circuit itself is regarded as a system. In engineering systems, both input and output signals may carry energy or information.
This framework of signals and systems is fundamental for analyzing and designing systems capable of specific operations in various engineering fields.