ELL727 Weekly Quiz-2

The autocorrelation function Ψ_g(τ) of a real-valued finite-energy signal g(t) can be computed as (⊗ denotes convolution)

• g(τ)⊗g(τ)

• g(τ)⊗g(-τ)

• g(-τ)⊗g(-τ)

• g(τ)⊗g(t+τ)

If a signal g(t) is real-valued and an even function, then it's Fourier transform G(f) is

• Real-valued and odd function

• Real-valued and even function

• Complex-valued and odd function

• Complex-valued and even function

Which of the following is a valid autocorrelation function defined in the range [-π/2, π/2]?

• sin²(t)

• tan (t)

• cos (t)

• sin (t)

Consider an LTI system with transfer function H(f) = -j sgn(f), where sgn(f) = 1 for f>0 and sgn(f) = -1 for f<0. What is the output y(t) for an input x(t) = cos(wt) to this system?