2 ii Design a 10 th order Hamming windowed FIR low pass filter with cut off

2 ii design a 10 th order hamming windowed fir low

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2 ii) Design a 10 th order Hamming windowed FIR low-pass filter with cut- off frequency at 1000 Hz if the sampling frequency is 8000 Hz. Hence, find an expression for the multipliers a ( k ), k = 0, 1, 2,…10 of the designed filter. 8 iii) How would you use these values to design a high-pass filter with cut- off at 1000 Hz. Explain your answer. 3 Total 25 1; ( ) 0; c j LP c H e ) ( ) sin( ] [ c c c LP n n n h
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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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