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If hlp(n) denotes the impulse response of a low pass filter with frequency response Hlp(ω), then what is the frequency response of the high pass filter in terms of Hlp(ω)?

Correct Answer: Hlp(ω-π)
The impulse response of a high pass filter is simply obtained from the impulse response of the low pass filter by changing the signs of the odd numbered samples in hlp(n). Thus hhp(n)=(-1)n hlp(n)=(ejπ)n hlp(n) Thus the frequency response of the high pass filter is obtained as Hlp(ω-π).

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