The signal $x[n]=1+\cos (n)+\cos (\pi n)$ is given as input to a high pass filter with a cut-off frequency of 2. Select the correct statement from the following: a: Both $x[n]$ and $y[n]$ are periodic b: $x[n]$ is periodic but $y[n]$ is not c: $y[n]$ is periodic but $x[n]$ is not d: Neither $x[n]$ or $y[n]$ are periodic

An LTI system with impulse response $h[n]=x[n]-x[n-1]$ acts as an a: low pass filter b: high pass filter c: band pass filter d: all pass filter

An LTI system with impulse response $h[n]=x[n]+x[n-1]$ acts as an a: low pass filter b: high pass filter c: band pass filter d: all pass filter