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You correctly figured out that the system must have $3$ zeros. So you just have to define a corresponding transfer function $H(z)$ that satisfies $$H(z_i)=0,\qquad z_i=e^{j\omega_i},\quad i\in\{0,1,2\}$$ In other words, what is the minimum number of coefficients of a polynomial with $3$ zeros? Note that you might need to provide two solutions: one general ...

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