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**Unformatted text preview: **EE533 Problem Set-6 1. An input signal x ( · ) is passed through a stable filter with transfer function H ( z ) to produce v ( · ) . The signal { v (- n ) } is once again filtered by H ( z ) to yield w ( · ) . The final output is obtained as y ( n ) = w (- n ) . The coefficients of H ( z ) are real. Find the overall transfer function relating y ( · ) to x ( · ) , in both the z- and ω- domains. 2. Let x ( n ) be a causal signal that is zero outside the range 0 ≤ n ≤ M . When x ( · ) is input to a causal LTI system specified by the difference equation y ( n )- 0.36 y ( n- 2 ) = x ( n- 2 )- 0.36 x ( n ) , the output signal y ( · ) is found to have the same duration. What information does this behaviour convey about X ( z ) ? How does the energy of y ( · ) compare with that of x ( · ) ? 3. Five transfer functions with identical magnitude responses are given below: H 1 ( z ) = 0.5 + 0.25 z- 1 + 0.4 z- 2- 0.425 z- 3 + 0.75 z- 4- 0.75 z- 5 + 0.6 z- 6- 0.2 z- 7 H 2 ( z ) = 1- 0.50....

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