For the following sequences xn 4 5 1 2 3 0 2 3 lessthanoreq

For the following sequences: x[n] = {-4 5 1 -2 -3 0 2), -3 lessthanorequalto n lessthanorequalto 3 y[n] = {6 -3 -1 0 8 7 -2}, -1 lessthanorequalto n lessthanorequalto 5 w[n] = {3 2 2 -1 0 -2 5}, 2 lessthanorequalto n lessthanorequalto 8 generate the following sequences: e[n] = w[n + 2] u[n] = x[2n] + y[n] + w[n/2]

Solution

w[n+2] is the 2 unit delayed version of w(n) = { 3 2 2 -1 0 -2 5} 0<= n <= 6

x[n/2] gives you the expansion in time domain.in expansion x[n/a] means inserting two zeroes between the values

x[n] ={ -4 5 1 -2 -3 0 2 } and x[n/2] = { -4 0 0 5 0 0 1 0 0 -2 0 0 3 0 0 0 0 0 2 } x[2n] means removing the odd value as the n is multiplied with 2 and if n is multiplied by odd number then even values are removed. x[2n] = {5 -2 0}

- 1<n<1 and w[n/2] = { 3 0 0 2 0 0 2 0 0 -1 0 0 0 0 0 -2 0 0 5} where 4 < n < 16

adding all three sequences by according to the starting time of each sequence,

x[2n] = 5 -2 0                -1<n<1

y[n] =   6 -3 -1 0 8 7 -2     -1<n<5

w[n/2] =              3 0 0 2 0 0 2 0 0 -1 0 0 0 0 0 -2 0 0 5   4<n<12

adding all the three sequences u[n] = { 11 -5 -1 0 8 10 -2 0 2 0 0 2 0 0 -1 0 0 0 0 0 -2 0 0 5 }