Signals & Systems

Use this for “x(t) peaks at t = 2 s. Where does y(t) = x(2t − 4) peak?”

Use this for “Find the fundamental period of x[n] = cos(3πn ÷ 4).”

Use this for “Find the energy of x(t) = 2e⁻⁴ᵗu(t) and the average power of 2 cos(10t + 30°).”

Use this for “Is the system y(t) = t·x(t) linear? Is it time-invariant?”

Use this for “Convolve a 2 V pulse lasting 3 s with h(t) = 0.5 s⁻¹ for 1 s. Find the length and peak of y(t).”

Use this for “Convolve u(t) with h(t) = e⁻²ᵗu(t). Find y(t) at t = 1 s.”

Use this for “x(t) has a part at 5 kHz. Where is it in y(t) = x(2(t − 25 μs)), and what phase does the delay add there?”

Use this for “A 2 V pulse lasts 1 ms. Find its spectrum at 0 Hz and at 500 Hz, and the first frequency where it is zero.”

Use this for “Find the final value of x(t) when X(s) = 10 ÷ (s(s + 5)).”

Use this for “Find y[3] and the final value when y[n] = 0.5y[n − 1] + x[n] and x[n] is the unit step.”

Use this for “X(s) has poles at s = −1 ± j2. Does x(t) die out, oscillate forever or grow?”

Use this for “An 8-bit quantizer covers 2 V. Find the number of levels, the step size and the SQNR.”

Use this for “CD audio is sampled at 44.1 kHz with 16 bits in 2 channels. Find the bit rate and the size of one minute.”

Use this for “A 256-point DFT is taken of samples at 1 kHz. How far apart are the bins, and where does 100 Hz fall?”