Classification of Signals and Systems

Flashcards covering key concepts from the lecture on the classification of signals and systems, including definitions and properties of various signal types and system functionalities.

What defines a continuous-time signal in terms of the variable t?

A continuous-time signal is defined for every real value of t, represented mathematically as x = x(t), t ∈ R.

How is a discrete-time signal defined in terms of the variable k?

A discrete-time signal is defined for certain (mostly whole) values of k, represented mathematically as x = x[k], k ∈ Z.

What are the four classes of signals based on continuity of the domain and range?

1. Continuous-time and continuous-value signals 2. Discrete-time and continuous-value signals 3. Continuous-time and discrete-value signals 4. Discrete-time and discrete-value signals.

What is the characteristic of a deterministic signal?

A deterministic signal has known values at each time instant and is reproducible, such as a sine signal generated by a function generator.

What defines a stochastic signal?

A stochastic signal has values that change randomly at each time instant and is not reproducible, typically represented by electric noise.

What is an entering signal?

An entering signal is one that has values identically zero in the negative time domain, meaning it is valid only starting from the t = 0 time instant.

What characterizes an even signal?

An even signal satisfies the condition x(−t) = x(t) for all t, indicating symmetry to the vertical axis of the coordinate system.

What characterizes an odd signal?

An odd signal satisfies the condition x(−t) = −x(t) for all t, indicating symmetry to the origin of the coordinate system.

What does it mean for a signal to be bounded?

A bounded signal satisfies |x(t)| < M for some finite M, meaning the signal has upper and lower bounds.

What distinguishes a finite-time signal?

A finite-time signal has zero values outside a specific time interval, meaning it is only active within the limits t1 < t < t2.

What is a SISO system in electrical engineering?

A SISO (Single Input Single Output) system has one input and one output terminal, characterized by the relationship y = Wˆ x.

What is the difference between a MIMO and a SIMO system?

A MIMO (Multiple Input Multiple Output) system has multiple inputs and outputs, while a SIMO (Single Input Multiple Output) system has one input and multiple outputs.

What does linearity in a system refer to?

A system is linear if the operator Wˆ in the excitation-response relation is additive and homogeneous, following the principle of superposition.

What is meant by invariance in a system?

A system is invariant if a temporal shift in the excitation results in the same temporal shift in the response.

What defines causality in a system?

A system is causal if the response depends only on present and past values of the excitation, not on future values.

What is stability in the context of a system?

A system is excitation-response stable (ER-stable) if every bounded excitation results in a bounded response.