1. A compact disk (CD) records audio signals digitally by using PCM. Assume that

Question

1. A compact disk (CD) records audio signals digitally by using PCM. Assume that the audio signal bandwidth equals 15 kHz.

(a). If the Nyquist sample are uniformly quantized into L=65,536 levels and then binary-coded, determine the number of binary digits required to encode a sample.
(b). If the audio signal has average power of 0.1 W and peak voltage of 1 V. Find the resulting ratio of signal to quantization noise (SQNR) of the uniform quantizer output in part (a).
(c). Determine the number of binary digits per second (bit/s) required to encode the audio signal and minimum bandwidth required to transmit the encoded signal.

Explanation / Answer

a) level=65536
so that no. of bit=16
b)
since peak voltage =1V
then
step size=(1/65536)=15.25uV
noise power=(step size)^2/12=19.40uwatt
signal power=0.1 watt
then the value of SNR is
(SNR)dB=10log(0.1watt/19.40uwatt)=97.12 dB

c)

sample frequency=2*15=30ksample

no. of bit=16*30k=480kbps

bandwidth=2*15kHz*16=480kHz

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