Signals & Systems Flashcards

The bilateral Laplace transform differs from the unilateral Laplace transform in that it integrates from:

Answer: -∞ to ∞

The bilateral (two-sided) Laplace transform integrates over all time from -∞ to ∞, capturing non-causal signals.

The frequency response H(e^(jω)) of a discrete-time system is evaluated from H(z) by substituting:

Answer: z = e^(jω)

The DTFT is obtained by evaluating the Z-transform on the unit circle, i.e., z = e^(jω).

An all-pass system has a magnitude response |H(jω)| that is:

Answer: Constant (unity) for all ω

An all-pass filter passes all frequencies with equal gain (unity magnitude) while altering only the phase.

The group delay of a system is defined as:

Answer: -dφ(ω)/dω

Group delay τ_g(ω) = -dφ(ω)/dω, representing the delay experienced by a narrowband signal centered at ω.

A signal x(t) is said to be even if:

Answer: x(t) = x(-t)

An even signal satisfies x(t) = x(-t), meaning it is symmetric about the vertical axis.

The output of a causal LTI system before the input is applied (t < 0) is zero because of:

Answer: Causality

Causality requires that the system output depends only on present and past inputs, so no output exists before excitation.

The CTFT of a rectangular pulse of width τ centered at the origin is:

Answer: A sinc function in frequency

The Fourier transform of a rectangular pulse rect(t/τ) is τ·sinc(fτ), a sinc function in the frequency domain.