In a satellite radio system, 128 stations of stereo quality are to be packaged i

Question

In a satellite radio system, 128 stations of stereo quality are to be packaged in one data stream. For each station, two(left and right) signals of bandwidth 15,000 hz are sampled, quantized, and binary coded into PCM signals. The transmitter must multiplex the data from the 128 stations into a single stream via time multiplexing.

A: If the maximum acceptable quantization error in sample amplitudes is 0.25% of the peak signal voltage, find the minimum number of bits needed for a uniform quantizer.

B: If the sampling rate must be 20% higher than the Nyquist rate, find the minimum bit rate of the multiplexed data stream based on the quantizer of part(A).

C: If 5% more bits are added to the multiplexed data for error protection and synchronization, determine     the minimum bandwidth needed to transmit the final data stream to receivers.

Explanation / Answer

A. For an N bit quantizer, the max error = 1/2^N try 10 bits --> 1/2^10 < 0.1% , too much try 9 bits --> 1/2^9 < 0.2 % enough try 8 bits --->1/2^8 = 0.39% .. uh not, failed to meet the spec. so we need to use 9 bits for the quantizer. B. For each channel, there is 15khz of bandwidth. so the nyquist sampling rate is 2 * 15khz = 30 Khz. 120% * 30khz = 36 KHz. so we need to sample at 36Khz (for each left / right) so for channel, we need 36Khz + 36Khz = 72K Samples per second. 72K samples per second * 9 bits per sample = 648 kbits / second C. add 5% more bits to the bit stream 1.05 * 648kbits /second = 680.4 kbits /s mininum bandwidth required = ? im not sure... but you need to send through 680.4Kbits/s ... good luck on the last part :)

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