Compute and plot the response of the following systems ynnn1

Compute and plot the response of the following systems:

y[n]=n/n+1 y[n-1]+x[n],y[-1]=0 y[n] = 0.9y[n - 1 ] 4- x[n], y[-1 ] = 0 to the inputs x[n] = 8[n] and x[n] = S[n - 5], for 0 less than or equals to n less than or equals to 20, and comment upon the obtained results.

Solution

y[0] = 0/1 y[-1] + x[0]

y[0] = 0 *0 + 0 =0

y[1] = 1/2 y[0] + x[1]

y[1] = 1/2 *0 +1

y[1] = 1

y[2] = 2/3 * y[1] + x[2]

y[2] = 2/3 + 1

y[2] = 5/3

y[3] = 3/4 y[2] +x[3]

y[3] = 3/4 * 5/3 + 1

y[3] = 5/4 +1

y[3] = 9/4

y[4] =4/5 y[3] + x[4]

=4/5 * 9/4 + 1

y[4] = 9/5 +1

y[4] = 14/5

like this we have to find values till 20

for second

y[0] = 0.9y[-1] + x[0]

y[0] = 0.9 *0 + 1

y[0] = 1

y[1] = 0.9 y[0] + x[1]

y[1] = 0.9 *1 + 1

y[1] = 1.9

y[2] = 0.9 *y[1] + 1

y[2] =2.71

y[3] = 0.9 y[2] +1

=2.439 +1

y[3] =3.439

y[4] =0.9*y[3] +1

y[4] = 2.195 +1

y[4] = 3.195

y[5] = 0.9*y[4] +1

y[5] = 0.9 *3.195 +1

y[5] = 2.8576 +1

y[5] = 3.8576