Modulation and DeModulation I have a question regarding Modulation and Demodulation.
In question 5.21 (b) from the "Discrete-time Signal Processing" book by Oppennheim, he asks to find out the type of filter used in the attached figure:  


The question is what is the effect of $(-1)^n$ on the original filter and y[n].
I saw the answer to be high-pass filter, but I am not sure why.
Please help

Thanks
As hinted out, you firstly shift signal by π by multiplying it by cos(πn). Now, your low frequency components are around π. In the next step of diagram, you filter the components around frequency 0 since the filter in diagram is lowpass. But since your signal was shifted by π, you filter the high frequency components of the original signal. In the next step, you shift your original signal back to 0 frequency.

So, overall you filter the high frequency components.