Section A
Q1.
(a) In a narrow band digital communication system the symbol error probability for the in-phase channel is P_{eI} and for quadrature phase channel is P_{eQ}. Prove that the probability of symbol error for the overall system is given by (Pe): Pe = P_{eI} + P_{eQ} - P_{eI}P_{eQ}
(b) Consider a discrete time system with impulse response h[n] = 1/5)2n U[n]. Find the value of constant A such that h[n] - Ah[n-1] = δ[n] and δ[n] is a unit impulse signal.
(c)
A digital computer has a memory unit with 32 bits per word. The instruction set consists of 240 different operations. All instructions have an operation code part (opcode) and an address part (allowed for only one address). Each instruction is stored in one word of memory.
(i) How many bits are needed for the opcode ?
(ii) How many bits are left for the address part of the instruction ?
(iii) What is the maximum allowable size of the memory ?
(d)
The Radiation intensity of an antenna is
U(θ, \phi) = \begincases 2 sin θ sin3 \phi & 0 ≤ , 0 ≤ \\ 0 & \textelsewhere \endcases
Determine the directivity of the antenna.
(e) A graded index fiber has a characteristics refractive index profile of 1.85 and a core diameter of 60 \mum. Compute the insertion loss due to a 5 \mum lateral offset at an index matched fiber joint assuming the uniform illumination of all guided modes.
(f) A mobile network transmits data having bandwidth of 200 Hz using a carrier frequency of 800 MHz. If the maximum speed of a vehicle is 120 km/hr, calculate the bandwidth and the cut-off frequencies of the filter at the receiver input.
