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we are told to find coefficients and impulse response of IIR filter of order of 6. There are 6 zeros and 6 poles in the design. Pole and zero pairs are conjugate and poles are within the unit circle whereas zeros are on the unit circle and. I can write transfer function with no problem, but I cannot expand it as its order is too big to work with. I must work my way up to finding impulse response and filter input/output coefficients, but I am stuck terribly with the transfer function. What can I do? long divisions are used in second order polynomials, no example of it for larger orders. Is there a easy way? I am up for hours trying to figure it out.

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  • $\begingroup$ Since you say you have complex conjugate roots, split them into 2nd order sections. $\endgroup$ – a concerned citizen May 28 at 11:09
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You can write your transfer function as the sum of three 2-nd order transfer functions (partial fractions), and then the impulse response will be the sum of the impulse response of each.

To help you with the partial fractions you can use this calculator

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