This document is a compilation of my notes for ELE 532: Signals and Systems I at TMU. All information comes from my professor’s lectures, as well as the course textbook Linear Systems and Signals by B.P. Lathi.
Adam Szava - 2tor.ca
F2022
This lecture begins with the definition of a signal and a system:
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Definition 1.1 (Signal)
A signal is any time-varying physical phenomenon intended to convey information.
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Examples of signals include temperature, sound, light (as in fiber optics cables, or traffic lights on the road), and stock prices.
Technically, a signal does not need to be a function of time, but it is the typical independent variable. For example, when considering electric charge distributed over a body, the signal is the charge density and is a function of space rather than time. We will continue to make reference to time as the independent variable, but the techniques developed in this course can be applied other contexts.
<aside> ➡️ Definition 1.2 (System)
A system is any entity which is designed to process one or more signals. The system takes in a set of signals as input, and yields another set of signals as output.
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For example, a circuit is a system. Take the following example… A sinusoid is used as input, and the output is the same sinusoid but the negatives are cut off.
This circuit processed a signal, and output another signal. By definition, the circuit is a system. Electronics are the building blocks to make systems. This course, however, is not exactly a circuit course, it is a course about the higher-level theory which determines how systems interact with the signals they process, and with other systems.
Other examples of systems include mechanical systems, hydraulic systems, or algorithms.
The size of signals indicates its “largeness” or strength. We want to measure the size of the time-varying signal with a single number. This is difficult because the amplitude of signals vary with time. Whatever measure of size we devise must account for all the amplitudes of the signal, as well as the duration that the signal has that amplitude.
Signal energy of a signal $x(t)$ is defined as the area under the curve, as in:
$$ E_x=\int_{-\infty}^{\infty}|x(t)|^2\, dt \tag{1.1} $$