State the definitions of continuous and discrete systems, including examples. b) a) 25% 25% Describe

State the definitions of continuous and discrete systems, including examples. b) a) 25% 25% Describe how signals can be classified as even or odd For the signal shown in the figure below, make labelled sketches of the odd and even components. Verify that the addition of the components produces the original signal. c) de-e 50% 2 Evaluate y(t)- x(t) h(t) where x(t) and h(t) are shown in the figures below and sketch y(t). xit) h(t) 2 40% Consider the digital filter structures as shown in the figure below, where the impulse responses are h, (3,2,1,2) hy(1,2,3,4,5) hn xn) hln Determine the impulse response hin] of the composite filter 30% Page 2 of 4 Assume no previous inputs x-1)-0; x-2)= 0; and h[1]-0.25; h[2]-0.5; h[3])-0.25; what are the outputs when n)-(20 20 20 12 40 20 20 0.50 025 025 n 30% Find the complex exponential Fourier series coefficients, a for the periodic signal shown in the figure below (continues) joontinues) 2 4 4 50% Determine the amplitude and phase spectra of the signal x(t) eu(t ).(a is real and greater than 0) b) 50% Find the transfer functions, H(z), of the systems a) characterised by the following difference equations Also plot their pole-zero diagrams and determine their stability a1) yin] 2x(n]-xin- 11+3yln- 1]-2y[n-2 2) yin] – xn]- 2x[n 11+2.5y[n-1]-yin- 2] a3) yin) = xn]+ x[n-2]+ yln-11-0.5yln-2 60% Find the inverse Laplace transform of b. 2s +4 X(s) +45+3 for-3DATA SHEET Complex Exponential Fourier Transform -00 atr) 1- Relt)c -th 1-ar ar Rels)> 1-az -n-1 < Rela) 1-ar- --n-1 (1-az-y 1-2 cos 1-27cos 2 1- sna 1-2-1smc 1-r&#39;cos cos)um 1-2ar-00s > 1-2snag shn u T-2sin >Ja Rela)>-Rela) cswun Rel)-Rela) (sin n e”) Rel)>-Rela) ( 1 Rela)-Rela) Pape 4 of 4 k-E-E-E-E

 

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