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

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.

it would rotate about 180 degrees.