In a sound recording studio 11 microphones are placed at different locations. The data from each microphones are brought to a processing center over wires and are sampled, quantized, binary coded and time-division multiplexed. The multiplexed data are now transmitted to a master recording station. Assuming each signal bandwidth is 20 KHz, the acceptable error in sample amplitude is 0.25% of the peak signal amplitude and a sampling rate of twice the Nyquist rate. Determine the minimum cable bandwidth needed to transmit these data.
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8Sounds like homework assignment. What have you done so far? – Justme Dec 23 '19 at 09:28
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Is this the analog or digital kind of bandwidth? For analog you'd also need to know the signal-to-noise ratio of the multiplexed cable. – user253751 Dec 23 '19 at 11:26
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4I'm voting to close this question as off-topic because it is unattempted homework and underspecified. – Chris Stratton Dec 23 '19 at 11:46
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First we can calculate how many bits we need to represent a single sample with maximum 0.25% error: 100/0.25=400, so we need 400 different quantization values, to express them in a binary-coded form log_2(400) ~= 8.64 bits are necessary.
If we assume no compression is used (none is mentioned in the text) this means 9 bits. We need to transmit 4*20000 samples per second per mic (the 4 comes from "twice the Nyquist rate" the Nyquist rate is twice the signal bandiwdth of 20kHz). Since there are 11 time-dicision multiplexed mics this means 11*4*20kHz*9bits = 7920000 bits/sec = 7.92 MB/s.
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You should probably write Mbit/s to avoid any possible confusion with megabytes/second. – jcaron Dec 23 '19 at 13:17
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