A linear time invariant (LTI) digital filter with input x[n] and output y[n] has the following system function H(z): (z?

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A Linear Time Invariant Lti Digital Filter With Input X N And Output Y N Has The Following System Function H Z Z 1 (63.45 KiB) Viewed 19 times

A linear time invariant (LTI) digital filter with input x[n] and output y[n] has the following system function H(z): (z? - 1) H(2) = (z? -0.52 +0.64)(z? + z +0.81) Y(2) where H(2) = and Y(z) = ZT[y[n]] and X(z) = ZT[x[n]] X(z) (a) Sketch the Pole Zero diagram for the digital filter. (b) Sketch the Magnitude of the frequency response of this filter from the Pole Zero diagram. (c) Is this digital filter a High Pass, Band Pass, Band Stop or Low Pass digital filter ? (d) Determine the linear difference equation for this digital filter. (e) Using the linear difference equation in part (d) draw a canonical realisation of this LTI digital filter (f) Using the property of LTI discrete systems, determine the steady state output response of this filter to an input: x[n]=4+4cos(Ttn)+2cos(Ttn/2)