Computing the inverse dtft

Question

Assignment:

Question 1. Compute the DTFT of the discrete-time signal shown in the Figure below.

Question 2. For a discrete-time signal x[n] with the DTFT , X(Ω) = 1/ e^jΩ+ b where b is an arbitrary constant , compute the DTFT V(Ω) of v[n] = x[n] - x[n-1]

Question 3. Compute the inverse DTFT of  X(ω)=cos2Ω

Question 4. Compute the inverse DTFT of: X(ω)=sinΩ cosΩ

Question 5. Compute the rectangular form of the four-point DFT of the following signal, which is zero for n<0 and n>=4.

x[0]=1, x[1]=-1, x[2]=1, x[3]=-1

Provide complete and step by step solution for the question and show calculations and use formulas.