A running integrator is defined by, where x (t) is the input, y (t) is the output,

Question:

A running integrator is defined by, where x (t) is the input, y (t) is the output, and T is the integration period. Both x (t) and y (t) are sample function of stationary processes X (t) and Y (t), respectively. Show that the power spectral density of the integrator output is related to that of the integrator input as SY (f) = T2 sinc2 (fT) SX(f)