Signals and Systems Key Concepts

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Questions and Answers

Which of the following is a key characteristic that distinguishes continuous-time signals from discrete-time signals?

Discrete-time signals cannot be represented mathematically.
Continuous-time signals are only defined for integer values of the independent variable.
Continuous-time signals are defined for every value of the independent variable, which is a continuous variable. (correct)
Discrete-time signals are defined for every real value of the independent variable.

What condition must be met for a discrete-time sinusoidal signal $x[n] = A \cos(\Omega n + \phi)$ to be considered periodic?

$\Omega$ must be an integer multiple of $\pi$.
$\Omega / 2\pi $ must be a rational number. (correct)
The amplitude $A$ must be equal to 1.
$\Omega$ must be an irrational number.

Given a continuous-time signal $x(t)$, which of the following integrals represents its total energy?

$\int_{0}^{\infty} |x(t)|^2 dt$
$\int_{-\infty}^{\infty} x^2(t) dt$
$\int_{-\infty}^{\infty} x(t) dt$
$\int_{-\infty}^{\infty} |x(t)|^2 dt$ (correct)

Which of the following statements accurately describes the sifting property of the unit impulse function $\delta(t)$?

$\int x(t)\delta(t-t_0) dt = x(t_0)$ (B) Signup and view all the answers

A system is defined such that its output $y(t)$ is the derivative of its input $x(t)$, i.e., $y(t) = \frac{d}{dt}x(t)$. What can be said about this system?

The system is linear and time-invariant. (A) Signup and view all the answers

What is the key characteristic of a causal system?

Its output depends only on present and past values of the input. (B) Signup and view all the answers

Which of the following functions is an example of an odd signal?

$x(t) = \sin(t)$ (D) Signup and view all the answers

If $x[n] = A \alpha^n$ represents a discrete-time real exponential signal, under what condition will the signal decay exponentially as $n$ increases?

$|\alpha| < 1$ (D) Signup and view all the answers

A continuous-time system is described by the input-output relationship $y(t) = x(t^2)$. Is this system time-invariant?

No, because the transformation $t^2$ introduces time scaling depending on the time origin. (B) Signup and view all the answers

What is the fundamental difference between energy signals and power signals?

Energy signals have finite energy and zero average power, while power signals have infinite energy, but finite average power. (D) Signup and view all the answers

Flashcards

What are Signals?

Signals are functions carrying information, representing a physical quantity's evolution.

Continuous-Time Signals

Signals defined for every time value (t), where t is a real number.

Cosine and Sine Signals

x(t) = A cos(ωt + φ) or x(t) = A sin(ωt + φ), where A is amplitude, ω is angular frequency, and φ is phase.