If the low pass filter described by the difference equation y(n)=0.9y(n-1)+0.1x(n) is converted into a high pass filter, then what is the frequency response of the high pass filter?

If the low pass filter described by the difference equation y(n)=0.9y(n-1)+0.1x(n) is converted into a high pass filter, then what is the frequency response of the high pass filter? Correct Answer 0.1/(1+0.9e-jω)

The difference equation for the high pass filter is y(n)=-0.9y(n-1)+0.1x(n) and its frequency response is given as H(ω)=0.1/(1+0.9e-jω).

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