# 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.
• Hint: $(-1)^n = \cos(\pi n)$. Multiplying $x(n)$ by $\cos(\pi n)$ is equivalent to which operation in the frequency domain? From this, you can sketch the effect of the modulation, the filter, and the second modulation on x's spectrum. – pichenettes Nov 18 '14 at 1:11