2.13. The autocorrelation sequence of a zero mean white noise process is rv (k) = v2 (k)...

2.13. The autocorrelation sequence of a zero mean white noise process is rv (k) =σ v2δ (k) and the power spectrum is ( ) v2 j

Pv e σ θ = , where 2

σ v is the variance of the process. For the random phase sinusoid the autocorrelation sequence is, rx (m) = A cos(m ) 1 2

2

ω 0 and the power spectrum is,

[ ( ) ( )]

2 1

( ) 0 0 0 0 P e jθ = π A2 u ω −ω + u ω +ω

x where:

u0 (ω −ω 0 ) represents an impulse at frequency ω 0 .

What is the power spectrum of the first-order autoregressive process that has an autocorrelation sequence of, m rx (m) =α

where:

|α| < 1