Problem 1. Determine the characteristic equation for each of the following IIR systems and determine whether each system is stable: \text { a. } y[n]=x[n]+0.5 y[n-1] \text { b. }

y[n]=x[n]-2 x[n-1]+0.5 y[n-2 \text { c. } y[n]=x[n]+0.5 x[n-2]+y[n-1]-0.25 y[n-2] \text { d. } y[n]=x[n]-1.5 y[n-1]-0.25 y[n-2]-0.375 y[n-3] \text { e. } y[n]=x[n]-\frac{1}{4} y[n-1]+\frac{1}{16} y[n-2]+\frac{1}{64} y[n-3]