Linear Systems with Random Inputs, Filtering, and Power Spectral Density
Alexander D. Poularikas · 2017
We first begin by defining the power spectrum of discrete random signals. The discrete-time Fourier transform (DTFT) pair is given by 6.1 https://www.w3.org/1998/Math/MathML"> x ( n ) = F D T − 1 [ X ( e j ω ) ] = 1 2 π ∫ 2 π X ( e j ω ) e j ω n T = 1 , ω = Ω T ( r a d ) , Ω ( r a d / s ) X ( e j ω ) = F D T { x ( n ) } = ∑ n = − ∞ ∞ x ( n ) e − j ω n T = 1 , ω = Ω T ( r a d ) , Ω ( r a d / s ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315112855/8fcaf561-84c8-4d3f-85f2-2d69ce935200/content/equ6_1.tif" xmlns:xlink=" https://www.w3.org/1999/xlink "/>