Signals & Systems Flashcards

A continuous-time LTI system has impulse response h(t) = e^(-2t)u(t). What is the system's time constant?

Answer: 0.5 seconds

For h(t) = e^(-αt)u(t), the time constant τ = 1/α = 1/2 = 0.5 seconds.

The discrete Fourier transform (DFT) of a sequence of length N has how many unique frequency components?

Answer: N

The N-point DFT produces exactly N complex-valued frequency coefficients.

If X(jω) is the Fourier transform of x(t), then the Fourier transform of x*(t) is:

Answer: X*(-jω)

Conjugation in time corresponds to complex conjugation and frequency reversal: FT{x*(t)} = X*(-jω).

A second-order system has transfer function H(s) = ω_n²/(s² + 2ζω_n·s + ω_n²). For ζ = 0, the system is:

Answer: Marginally stable with pure oscillation

When ζ = 0, the poles are purely imaginary (±jω_n), producing undamped, sustained oscillation.

The region of convergence (ROC) of a right-sided sequence's Z-transform is:

Answer: Outside a circle

A right-sided (causal) sequence has an ROC that is the exterior of a circle |z| > r.

Parseval's theorem for continuous-time signals states that:

Answer: ∫|x(t)|²dt = (1/2π)∫|X(jω)|²dω

Parseval's theorem equates signal energy in time and frequency domains with the 1/2π normalization factor.

A linear phase FIR filter is preferred in applications requiring:

Answer: No phase distortion across all frequencies

Linear phase FIR filters introduce a constant group delay, preserving waveshape and avoiding phase distortion.