Question

You are trying to create a 10th order IIR digital filter using a quantizer with only...

You are trying to create a 10th order IIR digital filter using a quantizer with only 4 bits. Consider robustness towards errors in coefficients.

a) Given a choice, would you choose a direct form implementation or a cascade form implementation? Explain why.

b) Given a choice, would you choose a direct form implementation or a parallel form implementation? Explain why.

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A quantizer with only 4 bits would introduce significant errors while performing the basic mathematical operations of addition and multiplication, both of which are required for the filter implementations. However, it is the multiplication operation which suffers the most due to errors, since the errors are carried forwrad to subsequent steps. Tus, we always choose that implementation, where there are lesser number of multiplications involved. From the given structures, the cascade form has the least number of muliplications, followed by the direct form.

a. Cascade form is chosen for the reason above

b. Direct form is chosen for the reason above.

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