Question

2 part a and b , 3 part a and b

7 marks 2. Consider the Fourier transform pair a) Use the appropriate Fourier transform properties to find the Fourier transform of te-lti 5 marks) b) Use the results from part (a) and the duality property to determine the Fourier transform of 4t f(t) = (1 +t2)2 [15 marks 3. For the discrete time system shown in fig. 1 a) Determine the transfer function Hint: The best starting point is to write the relation between W1 and W2 /15 marks b) Determine the range of K for which the system is stable. Hint: For stability the pole must be inside the unit circle. [5 marks] ay Gain W xIn] Unit Delay Gain Figure 1

Answer 1

For 2 (b) Frem duo Properd, Ef

Proper appl luo) スーdemam ナ ス I0 Kス -K(저) xcz)ス(HK)-10 (b) ス-H

cte.fhe Pole İsat スー10 For Shatin Fos Stolbi e lo The Systom gam K is to en al restive go for k>9.帆 system is stable