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
The convolution of u(t) with itself, u(t) * u(t), results in:
Answer: t·u(t)
Convolving two unit step functions yields the ramp signal r(t) = t·u(t).
The power spectral density (PSD) of a wide-sense stationary (WSS) random process is the Fourier transform of its:
Answer: Autocorrelation function
By the Wiener-Khinchin theorem, the PSD is the Fourier transform of the autocorrelation function.
A system is memoryless if its output at time t depends only on:
Answer: The input at the same instant t
A memoryless system's output depends solely on the present input value, with no dependency on past or future.
The Laplace transform of the unit ramp r(t) = t·u(t) is:
Answer: 1/s²
L{t·u(t)} = 1/s², valid for Re{s} > 0.
Gibb's phenomenon occurs when reconstructing a signal from its Fourier series near a:
Answer: Discontinuity
Gibbs phenomenon produces approximately 9% overshoot near jump discontinuities regardless of how many harmonics are included.
The transfer function of an ideal differentiator in the frequency domain is:
Answer: jω
Differentiation in time corresponds to multiplication by jω in the frequency domain.
Downsampling a discrete-time signal x[n] by factor M produces y[n] = x[Mn]. This operation in the frequency domain causes the spectrum to be:
Answer: Expanded by M with aliasing if not bandlimited
Downsampling by M expands the spectrum by M and introduces aliasing unless the signal is bandlimited to π/M.