b) A digital communication system uses a 4-ary signaling scheme. Assume that 4-symbols (-3,-1, 1, 3) are chosen with probabilities (1/8, 1/4, 1/2, 1/8), respectively. The channel is an ideal channel with AWGN, the transmission rate is 2x10 symbols/s, and the channei signal to noise ratio is known to be 15. Determine: 1. The source information rate.. 2. The minimum channel bandwidth required for error-free transmission.

Draw 5 circuits using a 4x1 multiplexer that is the only enable signal of the function F (a, b, c, d) = ∑ (0, 1, 3, 5, 8, 13). Draw 2 circuits using an 8x1 multiplexer and a 2x1 multiplexer to enable the function F (a, b, c, d) = ∑ (1, 2, 3, 5, 7, 11, 13). Draw a circuit that performs F (a, b, c) = a'.b'.c '+ b'.c using only a 1x2 decoder with the least active-0 enable signal. (The information that the enable signal is 1 behaves like normal decoder where all outputs are 0, 0.)

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4. Consider the series RLC circuit in Homework 7, Question 2. The component values are R = 1 ohms, inductance = 0.3 henries, and capacitance C = 0.6 farads. Enter w (double-u) for w (omega). x(t) L C (a) Find the frequency response function H(w) Y(w) = X(w) H(w) = (b) Find the positive linear frequency fo = wo in Hz at which |H(w) = 1. This is the resonant frequency or the center frequency of the bandpass filter. fo = (c) Find the two positive frequencies f₁₁ = 1 and (fcı < fœ₂) in Hz, at which |H(w)| = fc2 = These are the half-power frequencies of the bandpass filter. fc₁ = fc₂ = R www y(t)