If the autocorrelation function of the sinusoidal signal x(t) = A cos (ω0 t + ϕ) is R(τ), then R(0) is given by (in terms of power spectral density of R(τ) = S(f))

Question

TuteeHUB · Accepted Answer

$R\left( 0 \right) = \mathop \smallint \limits_{ - \infty }^\infty \exp \left\{ {S\left( f \right)} \right\}df$

TuteeHUB · Answer

$R\left( 0 \right) = \mathop \smallint \limits_{ - \infty }^\infty S\left( f \right)df$

TuteeHUB · Answer

R(0) = S(f)|f = ∞

TuteeHUB · Answer

$R\left( 0 \right) = \mathop \smallint \limits_{ - \infty }^\infty lnS\left( f \right)df$

1.	If the autocorrelation function of the sinusoidal signal x(t) = A cos (ω0 t + ϕ) is R(τ), then R(0) is given by (in terms of power spectral density of R(τ) = S(f))
A.	\(R\left( 0 \right) = \mathop \smallint \limits_{ - \infty }^\infty S\left( f \right)df\)
B.	\(R\left( 0 \right) = \mathop \smallint \limits_{ - \infty }^\infty \exp \left\{ {S\left( f \right)} \right\}df\)
C.	R(0) = S(f)\|f = ∞
D.	\(R\left( 0 \right) = \mathop \smallint \limits_{ - \infty }^\infty lnS\left( f \right)df\)
Answer» B. \(R\left( 0 \right) = \mathop \smallint \limits_{ - \infty }^\infty \exp \left\{ {S\left( f \right)} \right\}df\)

If the autocorrelation function of the sinusoidal signal x(t) = A cos (ω0 t + ϕ) is R(τ), then R(0) is given by (in terms of power spectral density of R(τ) = S(f))

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