5. Consider an auditorium with an echo problem. An initial acoustic impulse will be followed by...

 

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5. Consider an auditorium with an echo problem. An initial acoustic impulse will be followed by attenuated versions of the sound at regularly spaced intervals. Hence, the acoustic behavior of the auditorium can be modeled as an LTI system with an impulse response consisting of an impulse train with the 4th impulse in the train corresponding to the 4th echo, that is, h(t) = 1180 -kT 8(t - kT), where the factor e-KT represents the attenuation of the 4th echo. (a). (b). Determine the frequency response of the system. Design an inverse system that cancels the echoes and reproduce faithfully the original stage sounds. 5. Consider an auditorium with an echo problem. An initial acoustic impulse will be followed by attenuated versions of the sound at regularly spaced intervals. Hence, the acoustic behavior of the auditorium can be modeled as an LTI system with an impulse response consisting of an impulse train with the 4th impulse in the train corresponding to the 4th echo, that is, h(t) = 1180 -kT 8(t - kT), where the factor e-KT represents the attenuation of the 4th echo. (a). (b). Determine the frequency response of the system. Design an inverse system that cancels the echoes and reproduce faithfully the original stage sounds.