How to classify filters? In class, we have defined four types of filters: low-pass, high-pass, band-pass and band-stop. I have understood that in order to classify a filter into one of the fourth, one can use the signals:


DC: $1,1,1,\ldots$
Nyquist: $-1,1,-1,1,\ldots$
half-Nyquist: $1, 0, -1, 0, 1,\ldots$


Can you help me understand how to classify $y_n = x_n + x_{n-2}$ as a band stop filter?
Can you help me understand how to classify


Yes! 

Just draw the (discrete) spectra of your three test signals; then multiply them  piece-wise with the frequency response of your candidates, and compare with the response of your filter.