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Question 2: Autocorrelation and ESD / PSD a) Find the autocorrelation function and power spectral density of the periodic signal x(t) = ?_{n=1}^? a_n cos(2?nf_0t + ?_n), knowing that the signal cos(?t + ?) has autocorrelation ½cos(??). Show all your work. b) Consider the two input power spectral densities: ?_1(f) = K, -? < f < ? and ?_2(f) = ?(?f) What is the total power, P_1, P_2 of these two signals? Consider a third signal with autocorrelation function R_3(?) = 3 + 2 cos(2??). What are the total power, P_3 of this signal, its DC power and its AC power, all in terms of R_3(?) ? c) The signal with power spectral density ?_4(f) = ?(f - 1) + ?(f + 1) is filtered through an RC filter H(f) = 1/(1+j?RC), with RC = 1. Find the total output spectral power for the ?_4(f) input.

          Question 2: Autocorrelation and ESD / PSD

a) Find the autocorrelation function and power spectral density of the periodic signal x(t) = ?_{n=1}^? a_n cos(2?nf_0t + ?_n), knowing that the signal cos(?t + ?) has autocorrelation ½cos(??). Show all your work.

b) Consider the two input power spectral densities:
?_1(f) = K, -? < f < ? and ?_2(f) = ?(?f)

What is the total power, P_1, P_2 of these two signals?
Consider a third signal with autocorrelation function R_3(?) = 3 + 2 cos(2??). What are the total power, P_3 of this signal, its DC power and its AC power, all in terms of R_3(?) ?

c) The signal with power spectral density ?_4(f) = ?(f - 1) + ?(f + 1) is filtered through an RC filter H(f) = 1/(1+j?RC), with RC = 1. Find the total output spectral power for the ?_4(f) input.

Question 2: Autocorrelation and ESD / PSD

a) Find the autocorrelation function and power spectral density of the periodic signal x(t) = ?n=1^? an cos(2?nf0t + ?n), knowing that the signal cos(?t + ?) has autocorrelation ½cos(??). Show all your work.

b) Consider the two input power spectral densities:
?1(f) = K, -? < f < ? and ?2(f) = ?(?f)

What is the total power, P1, P2 of these two signals?
Consider a third signal with autocorrelation function R3(?) = 3 + 2 cos(2??). What are the total power, P3 of this signal, its DC power and its AC power, all in terms of R3(?) ?

c) The signal with power spectral density ?4(f) = ?(f - 1) + ?(f + 1) is filtered through an RC filter H(f) = 1/(1+j?RC), with RC = 1. Find the total output spectral power for the ?4(f) input.

Added by Jennifer M.

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