Introduction to Signals and Systems

The lecture series on signals and systems begins with an introduction to the syllabus, divided into ten parts. It starts with basic definitions and classifications of signals and systems, followed by operations like scaling, shifting, integration, differentiation. System properties such as static or dynamic behavior are explored next. Time-domain analysis for both continuous-time (CTS) and discrete-time signals (DTS), Fourier series/transform analyses for CTS/DTS come afterward along with Laplace transform applications. The course concludes covering Z-transform techniques, sampling theorem principles, random signal behaviors.

A signal is defined as a dependent variable or function that relies on one or more independent variables, such as x1 to xn. A quantity qualifies as a signal if it varies with its independent variable; for instance, alternating current (AC) is considered a signal because it changes over time. In contrast, direct current (DC), which remains constant over time, does not qualify as a signal since no variation occurs. Signals are categorized into single-variable signals and multi-variable signals based on the number of independent variables they depend upon. Single-variable signals rely solely on one variable—examples include functions like f(x) or g(t). Multi-variable signals depend on multiple variables—for example, f(x1,x2) depends on two variables while g(p1,t2,t3) depends on three.

A system is defined as a meaningful interconnection of physical devices and components, which alone cannot achieve tasks without being linked to signals. For example, a pump (system) requires electricity (input signal) to produce mechanical work (output signal), enabling it to fill an overhead tank with water. The desirability of input or output signals depends on the task; in this case, mechanical work is more desirable than electricity for pumping water. Problems involving systems are categorized into analysis problems—where the response/output signal from given inputs and systems must be determined—and synthesis problems—where the system itself needs identification based on known input-output relationships.

Continuous-time signals are defined for every moment in time, representing a smooth and uninterrupted flow of information. These signals can be described mathematically as functions that exist over an infinite range of time values. In contrast, discrete-time signals only exist at specific intervals or moments in time, often derived by sampling continuous-time counterparts. They represent data points rather than a seamless curve.