3 iv Explain what is meant by l inear phase and show that your filter has a

# 3 iv explain what is meant by l inear phase and show

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3 iv) Explain what is meant by “l inear phase and show that your filter has a linear phase. Why may a linear phase characteristic be desirable? 4 b) A system is characterised by having the following difference equation: ] 2 [ 9604 . 0 ] 1 [ 6974 . 1 ] 2 [ 21 . 1 ] 1 [ 1 . 1 ] [ ] [ n y n y n x n x n x n y i) Find the transfer function H ( z ) of the system. 3 ii) Find the locations of the poles and zeros in the z plane. Hence, sketch the pole-zero diagram. 3 iii) At what frequencies (in degrees/sampling interval) will the magnitude of H ( z ) be a maximum and a minimum? 4 Total 25
PAPER CODE .................... ELEC309 ............... PAGE .... 6 ........ OF .............. 6 .......................... END Table of z-Transforms The z-transform of a discrete-time signal   n f is defined as:      n n z n f z F Note that   n u is the unit step defined as:   , 0 for 1 and , 0 for 0 n n n u and that   n is the unit impulse defined as:   0 for 1 and , 0 for 0 n n n   n f   z F 1   n 1 2 a n a z 3   n u 1 / z z 4   n u a n a z z / 5   n f   z F 6 a n f   z F z a 7   n f a n a z F / 8 sin ( an ) u ( n ) sin ( a ) z -1 /(1-2 cos ( a ) z -1 + z -2 ) Note: ) sin( ) cos( t j t e t j ) sin( ) cos( t j t e t j

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