Signals & Systems Flashcards
7 cards from real BEE practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Signals & Systems flashcards as text
A discrete-time signal x[n] is defined as x[n] = u[n] - u[n-4]. What is the duration of this signal?
Answer: 4 samples
x[n] is nonzero for n = 0, 1, 2, 3, giving exactly 4 samples.
The Z-transform of δ[n - k] for k > 0 is:
Answer: z^(-k)
By the time-shifting property of the Z-transform, δ[n-k] ↔ z^(-k).
Which condition must hold for a system described by H(z) to be causal and stable?
Answer: All poles inside the unit circle
A causal, stable discrete-time LTI system requires all poles to lie strictly inside the unit circle.
The energy of the complex exponential signal x(t) = e^(jω₀t) over one period T₀ is:
Answer: T₀
|e^(jω₀t)|² = 1, so integrating over one period T₀ yields energy = T₀.
The cross-correlation of two signals x(t) and y(t) evaluated at τ = 0 equals:
Answer: The inner product ∫x(t)y(t)dt
R_xy(0) = ∫x(t)y(t)dt, which is the inner product of x and y.
A signal x(t) has Fourier transform X(jω). What is the Fourier transform of x(t - t₀)?
Answer: X(jω)·e^(-jωt₀)
The time-shift property gives FT{x(t-t₀)} = e^(-jωt₀)·X(jω).
The Nyquist sampling theorem states that to perfectly reconstruct a bandlimited signal with maximum frequency f_max, the sampling rate must be:
Answer: At least 2·f_max
The sampling rate must be at least twice the highest frequency component to avoid aliasing.