State the difference equation which relates w[n] to x[n] and the equation which relates y[n] to w[n].

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Looking for answers for all 3 past exam papers. – Department of Electronic and Computer Engineering B365X Digital Signal Processing Semester 2 Examination 2 hours Instructions: Answer THREE Questions Additional Information: This is a closed book exDocument Preview:

School of Engineering B365X Digital Signal Processing Semester 2 Examination 2 hours Instructions: Answer THREE Questions Additional Information: This is a closed book exam Provided: Useful Formulae (attached) P203X Formula Book Any scientific, non-graphing, non-programmable calculator, for example Calculators: Casio FX 85 Series, or Casio FX 83 Series Examiners: Dr Alan Hewitt External Examiner: Dr A Rossiter1. Figure Q1 below represents a biquadratic digital filter in state-variable realisation. Figure Q1 (a) State the difference equation which relates w[n] to x[n] and the equation which relates y[n] to w[n]. From these, show that the z-domain transfer-function of the filter is given by 2 0.15z- 0.25z H (z)= . 2 z – 0.6z+ 0.08 [8 Marks] 0.25z 0.6- z ? ?? ? Show that the transfer function may also be written as H (z)= . (b) ? ?? ? z- 0.2 z- 0.4 ? ?? ? [2 Marks] (c) Carry out a partial-fraction expansion of H(z) to show that the impulse response of the filter k k may be expressed as h[k]= 0.25(0.4 )- 0.5(0.2 ). [6 Marks] (d) Draw a realisation of the filter as a parallel combination of two first-order filters. [4 Marks] (e) Starting from the transfer function, H(z), derive the difference equation which specifies the current output y[n] as a suitable combination of previous outputs and current and previous inputs. [5 Marks] B365X Digital Signal Processing Page 2 of 7 Academic Year 2011-20122. (a) T Th he e f fi ig gu ur re e b be el lo ow w s sh ho ow ws s a a b bl lo oc ck k-d di ia ag gr ra am m o of f t th he e p pr ro oc ce es ss si in ng g s si id de e o of f a a t tr ra an ns sf fe er r-function analyser. 

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