Answer Happy

[16 mare) [2 marles) [2 marks] [12 marks] and comment on your observation in term of signal transmission i Sketch is frequency spectrum Deduce from Part 3ic, the equation of the waveform that is being reconstructed from Fourier series! Given that a current pulse, f(t) =t.exp(-bt), show that the total energy acron a 10 resistor is given by 3. For the low pas fiter circuit shown in Fig 04. a periodic signal yit) of period is applied at its input. The Fourier coefficients Y. are given as follows: Yo = 0, Y = (1+). Y = 2 Y = 0 for > 2, where T = 2xRC. Determine the normalised power of y(t). 453 [8 marles] R . С F.B.CES OFFICE SICY Fig. 24 SECTION B DISCRETE TIME SYSTEMS ANALYSIS 5. Given that yk) = u(k)h(k), show that Y(z)=U(2) H(3) [2 marks] (1) Two identical systems H and H, with impulse response {N} = (4): k 2 0, are cascaded as shown in Fig Q5. If the input to the first system is a step = 1;k 20, a) Derive the input to the second system! [8 Marks] b) What is the output from the second system, using the z-transform! [5 Marks] c) Find the output expression for y using the convolution principle, and compare with the results obtained in Part b) [5 Marks) u. 2 H H: 6. Fig Q5 Design a non-recursive filter with impulse response given by 2.1.3.2 4 n= 0, 1, 2, 3, 4 h(n) = 70 n>4 [4 marks] il. Find the Fourier transform of the following functions by making use of appropriate transform properties