Let

x(\\\\Omega )=2\\\\pi \\\\sum_(k=-\\\\infty )^(\\\\infty ) \\\\delta (\\\\Omega -(\\\\pi )/(4)-2\\\\pi k)

. Here

\\\\delta

is the continuous impulse function.\ (a) Use

x[n]=(1)/(2\\\\pi )\\\\int_(2\\\\pi ) x(\\\\Omega )e^(j\\\\Omega n)d\\\\Omega

to find

x[n]

. Show the steps.\ (b) Compute

\\\\sum_(n=-\\\\infty )^(\\\\infty ) |x[n]|^(2)

. Compute

(1)/(2\\\\pi )\\\\int_0^(2\\\\pi ) |x(\\\\Omega )|^(2)d\\\\Omega

. What do you observe?

3. Let X()=2k=(42k). Here is the continuous impulse function. (a) Use x[n]=212X()ejnd to find x[n]. Show the steps. (b) Compute n=x[n]2. Compute 2102X()2d. What do you observe