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**Unformatted text preview: **(b) Derive the magnitude response of H ( z ) , and sketch it for 0 . 5. Consider the second-order all-pole lter: H ( z ) = 1/ ( 1-2 r cos z-1 + r 2 z-2 ) , 0 < r < 1, 0 < < . (a) Derive an expression for the magnitude-squared response of H ( z ) . (b) Determine (in terms of r and ) the values of in the interval [ 0, ] at which the above response is a maximum or minimum. (c) While some of the values of determined above are always extremal points of the response, one value is an extremal point only when r and satisfy a specic condition. Determine this condition. 6. Design a rst-order all-pole IIR lowpass lter whose 3-dB cutoff is c = 0.3 . Ensure unity gain at = 0. END...

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