Signals and System

A signal is classified as a Power Signal if its total energy is _______.

• Zero.

• Finite and non-zero.

• Infinite, but the average power is finite.

• Infinite, but the average power is non-zero.

 A signal is said to be even if _______.

•  x(t) = x(-t)

• x(-t) = x(t)

• x(t) = 0

• x(t) = -x(-t)

The Unit Step Function u(t)and the Unit Impulse Function δ (t) are related by:

• u(t) = d/dt δ(t)

• δ(t)= d/dt u(t)

• u(t)=⨜ δ(𝒯)d 𝒯

• u(t) = -d/dt δ(t)

A discrete-time system processes signals defined at _______.

•  All real-time values

• Random continuous intervals

• Specific sampled instants

• Periodic time intervals only

A time-invariant system means _______.

• The system output depends on time

•  The behavior of the system does not change over time

• The system output scales with time

• The system parameters vary with time

The convolution sum for discrete-time systems is given by _______.

• y[n] = Σ x[k]h[n−k]

• y[n] = Σ x[-k]h[n−k]

• y[n] = Σ x[n−k]h[k]

• y[n] = Σ x[k]h[k−n]

The unit impulse response completely characterizes _______

• Random systems

• LTI systems

• Nonlinear systems

• Time Invariant systems

The convolution integral for continuous-time systems is _______.

• y(t) = ∫ x(τ)h(t−τ)dτ

• y(t) = ∫ x(τ)h(t−τ)dτ

• y(t) = ∫ x(τ)h(τ−t)dτ

•  y(t) = ∫ h(t)x(τ)dτ

Non-linear systems are commonly used in:

• Noise cancellation

• Amplification and modulation processes

• Ideal signal transmission

• Low-pass filtering

The distributive property of convolution states that _______.

• x(t) * [h1(t) − h2(t)]

• x(t) * [h1(t) − h2(t)]

• x(t) * h1(t) + h2(t)

• x(t)[h1(t) + h2(t)] =

  x(t) *h1(t) + x(t) * h2(t)