Question

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?

(a) 0.1/(1+0.9e^jω)

(b) 0.1/(1+0.9e^-jω)

(c) 0.1/(1-0.9e^jω)

(d) None of the mentioned

The question was asked in an interview for job.

My question is taken from LTI System as Frequency Selective Filters topic in section Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer 1

Right answer is (b) 0.1/(1+0.9e^-jω)

Explanation: 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).