ELE 792 Midterm: ELE 792 Fall 2010 Midterm

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25 pts: a lti discrete-time system has the pole-zero diagram as shown in the gure. 4 pts c. determine all system characteristics that one can deduce from h(z). In par- ticular, determine/comment on the following system characteristics: fir or iir system, bibo stability, causality, linear-phase, all-pass. 2 pts d. determine the di erence equation describing the system. (assume that x[n] is the system input and y[n] is the system output. ) 4 pts e. sketch a signal- ow/block diagram which implements h(z) using a minimum number of addition, multiplication and storage elements. 6 pts f. we want to design an inverse system hi (z) such that the cascade connection of. H(z) with hi(z) will result in a at magnitude response, i. e. (cid:12)(cid:12) h(z)hi(z)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)z=ej . Determine hi(z), the system function of a stable and causal the inverse system such that the equalization condition of equation (1. 1) is satis ed. Also provide the z -transform of the equalized system h(z)hi (z).

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