Hi. Here is one example from my book. Calculate Fourier transform of signal: Here is solution: We can write x(n) as: , where x1(n) is u(n+N)-u(n-N-1). We can write: (we used that cos(n)=(1/2)*(exp(j*n)+exp(-j*n)). Using properties of Fourier transform of discrete signal: , Fourier transform of our signal will be: We will find Fourier transform of x1(n): How they calculated that u(n+N)-u(n-N-1) equals 1 for -N<=n<=N and 0 for other values of N?