An audio signal s(t) generated by a loudspeaker is reflected at two different walls with reflection coefficients r1 and r 2 The signal x(t) recorded by a microphone close to the loudspeaker, after sampling, is x(n) s(n) r 1 s(n k 1 ) r 2 s(n k 2 ) where k 1 and k 2 are the delays of the two echoes (a) Determine the auto correlation r xx (l) of the signal x(n ) (b) Can we obtain r 1 , r 2 , k 1 and k 2 by observing r xx (l) (c) What happens if r 2 0

Question: An audio signal s(t) generated by a loudspeaker is reflected at two different walls with reflection coefficients r1 and r 2. The signal x(t) recorded

An audio signal s(t) generated by a loudspeaker is reflected at two different walls with reflection coefficients r1 and r_2.The signal x(t) recorded by a microphone close to the loudspeaker, after sampling, is

x(n) = s(n) + r₁s(n – k₁) + r₂s(n – k₂)

where k₁ and k₂are the delays of the two echoes.

(a) Determine the auto correlation r_xx (l) of the signal x(n.)

(b) Can we obtain r₁, r₂, k₁ and k₂by observing r_xx(l)?

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