# Pescs e inte N fr wx i. If x(n) is a sampled version of a periodic continuous-time signal x(t), stat

Pescs e inte N fr wx i. If x(n) is a sampled version of a periodic continuous-time signal x(t), state the conditions under which x(n) is also periodic. ii. Is the following discrete-time signal periodic? If yes, then give the fundamental period 16mn 2Imn. cos+2sin(for n z 0 x(n) (6 Marks) b) A discrete-time signal s(n)= sin(0.25mn) where n 2 0. The signal is corrupted by mean, unit variance Gaussian noise v(n) to give the signal x(n), where: zero- s(n)+ 0.5v (n) x(n) The signal x(n) is passed through a linear time invariant system to give y(n) where: y(n) 0.5[x(n)+ x(n- 8)] n 2 0 Determine: (i) The SNR (Signal-to-Noise Ratio) of x(n) in dB (ii) The SNR of y (n) in dB (8 Marks) 0.2 cos700tt is sampled at a rate of 400 samples per c) The signal x(t) second. The sampled waveform is the passed though bandwidth of 200Hz. Give an cos200tt an ideal lowpass filter with a expression for the filter output. Assume ideal sampling. (6 Marks) a) Consider a Butterworth analogue low pass filter with a OdB gain at dc. The filter is second order and has a cut-off frequency of I rad/sec. Give the following: (i) A sketch of the pole locations of the filter in the complex s-plane. (ii) The typical magnitude response from de to 20 rad/sec (8 Marks) b) Compare the magnitude response of a Butterworth filter to a Chebyshev filter of the same low pass filters with OdB gain at de and a 1 rad/sec cut-off order. Assume that both are frequency (3 Marks) c) A continuous-time signal x(t) is a rectangular pulse defined as: t) = 1 for Itl