Let X(e j ) denote the Fourier transform of the sequence x[n] = (1/2) n u[n]. Let

Question:

Let X(e^jω) denote the Fourier transform of the sequence x[n] = (1/2)ⁿ u[n]. Let y[n] denote a finite-duration sequence of length 10; i.e., y[n] = 0, n < 0, and y[n] = n ≥ 10. The 10-point DFT of y[n], denoted by Y[k], corresponds to 10 equally spaced samples of X(e^jω); i.e., Y[k] = X(e^j2πk/10). Determine y[n]