Q5) A pass-band digital transmission system have four symbols. Encoder of the transmitter utilizes two or- thonormal bas
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Q5) A pass-band digital transmission system have four symbols. Encoder of the transmitter utilizes two or- thonormal basis to obtain signal vectors for each symbol. The modulator achieves quadrature phase shift modulation as described in the following. si (t) = sin (2πnt/T + in/2) represents message symbol mi, i = 1, 2, 3, 4. t is in the time-slot of corresponding symbol duration. EEE 492 Digital Communication Systems Sample Questions SPRING TERM, May 2022 Suppose that conditional probability distributions for the received (observation) vector x = [x₁, x₂] are as follows. fx (x\m₁) = g(x₁ - 1)g (x₂) fx (x\m₂) = g(x₂ + 1) g(x₁) g(x₁ + 1) g(x₂) fx (x\m3) = fx (x\m4) = g(x₂-1) g(x₁) where g (v) V (a) Sketch the constellation diagram. (b) Obtain values of the conditional probabilities for observation vector x = [0.75, 1.5] and determine the received message symbol by employing maximum likelihood decision rule.
Q5) A pass-band digital transmission system have four symbols. Encoder of the transmitter utilizes two or- thonormal basis to obtain signal vectors for each symbol. The modulator achieves quadrature phase shift modulation as described in the following. si (t) = sin (2πnt/T + in/2) represents message symbol mi, i = 1, 2, 3, 4. t is in the time-slot of corresponding symbol duration. EEE 492 Digital Communication Systems Sample Questions SPRING TERM, May 2022 Suppose that conditional probability distributions for the received (observation) vector x = [x₁, x₂] are as follows. fx (x\m₁) = g(x₁ - 1)g (x₂) fx (x\m₂) = g(x₂ + 1) g(x₁) g(x₁ + 1) g(x₂) fx (x\m3) = fx (x\m4) = g(x₂-1) g(x₁) where g (v) V (a) Sketch the constellation diagram. (b) Obtain values of the conditional probabilities for observation vector x = [0.75, 1.5] and determine the received message symbol by employing maximum likelihood decision rule.