1.
Linear: $ y[n]=x[n]+3x[n-1] $ Non Linear: $ y[n]=x[n]^2+x[n] $
Causal: $ y[t]=(1/3)x[t] $ Non Causal: $ y[n]=x[n+5]+x[n-2] $
With Memory: $ y[n]=x[n-1]^2 $ Without Memory: $ y[n]=sin(x[n]) $
Invertible: $ y[t]=16x[t] $ Non Invertible: $ y[t]=|x[t]| $
Stable: $ y[n]=x[n^2]+x[n-1] $ Unstable: $ y[n]=n!x[n] $
Time Variant: $ y[n]=x[n]/(n^2+1) $ Time Invariant: $ y[n]=x[n-2]^3 $
2.
3.
$ y(t)=cos(4t) $ The period is $ pi/2 $
