Question

A compact disk (CD) recording system samples each of two stereo signals with a 16-bit
analog-to-digital converter (ADC) at 44.1 kb/s.

a) Determine the output signal-to-quantizing ratio for a full-scale sinusoid.
Hint: Use Equation 4.47


b) The bit stream of digitized data is augmented by the addition of error-correcting bits, clock
extraction bits, and display and control bit fields. These additional bits represent 100 percent
overhead. Determine the output bit rate of the CD recording system.


c) The CD can record an hour’s worth of music. Determine the number of bits recorded on a
CD.

d) For a comparison, a high-grade collegiate dictionary may contain 1500 pages, 2 columns per
page, 100 lines per columns, 8 words per line, 6 letters per word, and 7 b per letter on
average. Determine the number of bits required to describe the dictionary, and estimate the
number of comparable books.

Answer 1

here v=16,
fs=44.1 kb/sec
1)s/n=1.76+6N=1.76+(6*16)=97.76dB
2)bit rate of two channels=v*fs
bit rate of two channels=2*v*fs=2*16*44.1*10*10*10=1.4112Mb/s
including the additional 100% overhead the output bit rate will be=2*1.4112*10(^6)=2.822Mb/s
3)cd can record an hours worth of music
therefore no of bits recorded=bit rate *no of secs/hr
=2.822*10^6*3600=10.16*10^9 bits

Answer 2

here v=16,
fs=44.1 kb/sec
1)s/n=1.76+6N=1.76+(6*16)=97.76dB
2)bit rate of two channels=v*fs
bit rate of two channels=2*v*fs=2*16*44.1*10*10*10=1.4112Mb/s
including the additional 100% overhead the output bit rate will be=2*1.4112*10(^6)=2.822Mb/s
3)cd can record an hours worth of music
therefore no of bits recorded=bit rate *no of secs/hr
=2.822*10^6*3600=10.16*10^9 bits
4) 1500*2*100*8*6*7= 100,800,000/2.822*10^6=35.719 approx36 CD's required 4books