A signal x[n] = \cos(2 \pi n/12) is passed through a filter with frequency response H_1(\hat{f}) = 1 + e^{-j 6 \pi \hat{f}}. The output signal is then passed through a second filter H_2(\hat{f}) . What is the value of |H_2(\hat{f} = 1/12)| so that the signal passes the combined filters unchanged? What is the required value of the phase of H_2(\hat{f} =1/12) , between -\pi and \pi ?

A signal x[n] = \cos(2 \pi n/12) is passed through a filter with frequency response

H_1(\hat{f}) = 1 + e^{-j 6 \pi \hat{f}}.

The output signal is then passed through a second filter H_2(\hat{f}) .   What is the value of |H_2(\hat{f} = 1/12)| so that the signal passes the combined filters unchanged?

What is the required value of the phase of H_2(\hat{f} =1/12) , between -\pi and \pi ?

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