Find the Autocorrelation function of the following periodic function: X(t) = A sin(wt +θ) 21 With T=2π/w the period, A, θ, and w are constants.

Step-by-step explanation:

To find Autocorrelation function of the following periodic function

Given that:

X(t) = A sin(wt +θ)

with the period T=2π/w , A, θ, and w are constants.

The autocorrelation function  of periodic function with period  and phase θ can be expressed as:

where;

Then;

The term 2  is the cosine wave of frequency and the phase =

if we integrate that, the second term in the expansion for R(t) = zero

As such,

where ;

is constant

Then :

since

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step-by-step explanation:

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