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(a) Two 8-point discrete signals x1[n] = [12 0 12 0 0 0 12 12] and X2[n)= ( 4 4 0 0 4 0 0 4) are to be analysed. (1) Compute the energies in x-[n] and in xa[n] 2 marks (ii) It is known that one of the discrete signals contain a periodic component while the other is of a random nature. Using suitable technical analysis deduce which signal contains the periodic component. No marks will be awarded for guesswork. 6 marks The pole-zero diagram of a discrete system shown in Fig Q1(b) is characterised by a system function H(z), Frequency Response H(92) and an impulse response h[n]. (b) (i) Determine H(z) and h[n] 2 marks (ii) Using the pole zero diagram make a sketch of the frequency response of H(z) 2 marks (ii) Draw a realisation of the discrete system with input x[n] and corresponding output y[n]. 2 marks (iv) Determine the steady state output response of the system due to the following input: x[n] = 10 + 4 cos(+ n/2) + 2cos( nt n) + 6 cos(3 1 n/2) 2 marks A radar transmits pulses of duration 0.2ms with a bandwidth of 20 MHz at a pulse repetition frequency (PRF) of 2kHz. What is the total number of complex samples in the slow-time/fast-time (c)
data matrix if the radar acquires pulses for 0.4 seconds and samples the received echoes at the minimum sampling frequency? 1 O 0.8 0.6 0.4 0.2 3 Imaginary Part -0.2 -0.4 -0.6 E -0.8 -1 -1 -0.5 0.5 1 0 Real Part