5) (20 pts) Determine the solutions for the following:
a) (6 pts) For each of the following systems (where $x[n]$ is the input and $y[n]$ is the output),
determine whether or not the system is a) linear, b) time-invariant, and c) causal: [answer
Yes/No clearly for each part]:
i. $y[n] = n x[n] + x[n-1]$
ii. $y[n] = |x[n]|$
b) (10 pts) Determine the 4-point DFT ($X[k]$) of the sequence $x[n] = \{1,0, 0, 1\}$.
c) (4 pts) Write the formula for a radix-2 FFT algorithm to implement the above 4-point DFT
assuming a n-point DFT of a sequence $x[n]$ is denoted by $DFT_N\{x[n]\}$.