List of top Signals and Systems Questions on Discrete Time Fourier Transform (DTFT)

Consider the system described by the difference equation 
\[ y(n) = \frac{5}{6}y(n-1) - \frac{1}{6}(4-n) + x(n). \] Determine whether the system is linear and time-invariant (LTI). 
 

The discrete-time Fourier transform of a signal \(x[n]\) is \[ X(\Omega) = (1 + \cos \Omega) e^{-j\Omega} \] Consider that \(x_p[n]\) is a periodic signal of period \(N = 5\) such that \[ x_p[n] = x[n], \; n = 0,1,2, x_p[n] = 0, \; n=3,4 \] Note that \(x_p[n] = \sum_{k=0}^{N-1} a_k e^{j\frac{2\pi}{N}kn}\). The magnitude of the Fourier series coefficient \(a_3\) is ................ (Round off to 3 decimal places).