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For an all-pass system $H(z)= \frac{(z^{-1}-b)}{(1-az^{-1})}$, where $\mid H(e^{-j\omega }) \mid= 1,$ for all $\omega$. If $\text{Re}(a)\neq 0, \: \text{Im}(a)\neq 0,$then $b$ equals

  1. $a$
  2. $a^{*}$
  3. $1/a^{*}$
  4. $1/a$
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