Question

As part of its "Think. Difference. Function." student strategy, SNaF2 University wants to add a live in-house band to accompany lectures and play musical interludes. Its President, an award winning media personality, points out that this will "be distinctive," has “co-creation in partnership and that its "collaborative, connected and active" learning will (Also, "jazzing it up" helps justify higher fees. :-) "sound education." lead to to a more To support this "blended learning," a microphone and speaker are added to every classroom. Consider the situation where a speaker outputs an amplified signals from a microphone, but where the microphone itself senses some of the sound coming from said speaker (shown above). The attenuating properties of the air decrease the strength of the speaker's signal picked up by the microphone. This increases with greater distance between the microphone and speaker. In addition, there is a time delay between the signal produced amplifier and then sent to the speaker and that sensed by the microphone. Initially assume the amplifier is KG(s), the speaker is Ks(), the attenuation the due to the air gap is KA(s), the delay due to the air gap is TA (in sec.), the microphone is given by KM(s), and the sampled signal is ZOH with a sampling period of Ts (in sec.). (a) Please draw the full block diagram from audio input to speaker output for the system assuming it is a fully digital i.e. the amplifier is digital) an in a negative feedback configuration. (b) What is the closed loop transfer function in both the domain? (i.e. TFe))? is the order of the overall closed loop transfer function in the z-domain? (d) If the terms KG, Ks, K4, KM, T4 and Ts are constants (and time-invariant), what can we say about the system's stability?

Please answer any parts that you can do / within your knowledge! Thank you very much in advance!

Answer 1

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