A causal first order digital filter is described by the system function (a) Sketch the direct form I and direct form II realization of this filter and find the corresponding difference equations (b) For a 0 5 and b 0 6, sketch the pole zero pattern Is the system stable Why (c) For a 0 5 and b 0 5, determine b 0 So that the maximum value of H() is equal to 1 (d) Sketch the magnitude response H() and the phase response H() of the filter obtained in part (c) (e) In a specified application it is known that a 0 8 Does the resulting filter amplify high frequencies or low frequencies in the input Choose the value of b so as to improve the characteristics of this filter (i e , make it a better low pass or a better high pass filter)

Question: A causal first-order digital filter is described by the system function (a) Sketch the direct form I and direct form II realization of this filter

A causal first-order digital filter is described by the system function

(a) Sketch the direct form I and direct form II realization of this filter and find the corresponding difference equations

(b) For a = 0.5 and b = -0.6, sketch the pole-zero pattern. Is the system stable? Why?

(d) Sketch the magnitude response | H(ω)| and the phase response < H(ω) of the filter obtained in part (c).

(e) In a specified application it is known that a = 0.8. Does the resulting filter amplify high frequencies or low frequencies in the input? Choose the value of b so as to improve the characteristics of this filter (i.e., make it a better low pass or a better high pass filter).

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