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Function of discrete-time prototype low-pass filter

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Reference no: EM13889280

Let H/ z ) be the system function of a discrete-time prototype low-pass filter. Consider a new discrete-time low-pass filter whose system function H( z ) is obtained by replacing z in H/ z ) with ( z - a )/{1 -az ), where a is real.

(a) Show that

Hp( Z ) lz= I +hi = H ( Z ) lz= I +j 0

Hp( Z ) lz= - I +ju = H ( Z ) Iz = - I +ju

(b) Let flP 1 and fl1 be the specified frequencies ( 1r ) of the prototype low-pass filter and the new low-pass filter, respectively. Then show that sin[( npl - n ,)/2] a = sin[ ( npl + n , )/2]

Reference no: EM13889280

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