Signals and Systems Lecture Review

This flashcard set covers the vocabulary and fundamental concepts of Signals and Systems based on the introductory lecture notes, including signal operations, system classifications, and elementary signals.

System

A meaningful interconnection of components that act as a total system or subsystem when properly arranged.

Signal

A function of an independent variable, typically time ($t$) or index ($n$), that is not a constant and can be single-variable or multi-variable.

Analysis Problem

An engineering problem where the input and system are known, and the goal is to determine the output.

Synthesis/Design Problem

A problem where the input and the desired output are known, and the goal is to design or find the system components.

Folding (Reflection)

A signal operation represented as $x(-t)$, which reflects the signal across the vertical axis.

Compression

A time-scaling operation where the signal is speeded up, such as $x(2t)$.

Expansion

A time-scaling operation where the signal is slowed down, such as $x(t/2)$.

Continuous Time (CT) Signal

A signal defined for a continuum of values of the independent variable $t$.

Discrete Time (DT) Signal

A signal defined only at discrete values of the independent variable, often represented as $x(n)$ where $n$ is an integer.

Sampling Interval ($T$)

The time interval between samples in a discrete-time signal, often expressed by the relationship $t = nT$.

Even Signal

A signal that satisfies the mathematical condition $x(-t) = x(t)$, showing symmetry about the vertical axis.

Odd Signal

A signal that satisfies the mathematical condition $x(-t) = -x(t)$, showing anti-symmetry.

Periodic Signal

A signal for which there exists a positive value $T$ such that $x(t) = x(t + T)$ for all $t$. ($T$ is the period).

Fundamental Period

The smallest positive value of $T$ that satisfies the periodicity condition $x(t) = x(t + T)$ for continuous signals or $x(n) = x(n + N)$ for discrete signals.

Unit Impulse ($\delta(t)$)

Also called the Dirac delta function, it exists only at $t = 0$ and is defined such that the area under the curve is $1$.

Unit Step ($u(t)$)

A signal defined as $u(t) = 1$ for $t > 0$ and $u(t) = 0$ for $t < 0$; the value at $t = 0$ is not mathematically defined.

Static System

A memoryless system where the output at any instant depends only on the input at that same instant.

Dynamic System

A system with memory where the output depends on past or future values of the input; often involves components like integrators or capacitors.

Causal System

A system whose output at any time depends only on present and/or past values of the input, making it physically realizable in real-time.

Invertible System

A system where the input can be uniquely recovered from the output using an inverse system.

BIBO Stability

A property where a Bounded Input results in a Bounded Output ($B I B O$).

Time-Invariant System

A system where a time shift in the input signal results in an identical time shift in the output signal without changing the shape of the output.

Linear System

A system that satisfies the principles of superposition and homogeneity.

SISO System

A system classified as Single-Input Single-Output.

MIMO System

A system classified as Multi-Input Multi-Output.