A standard audio compact disc has 16-bit amplitude resolution. This means that i

Question

A standard audio compact disc has 16-bit amplitude resolution. This means that if the quietest noise the cd can represent is about 1 bit, then the loudest is about 215 = 32, 768 times the quietest.

(a) What is the dynamic range of a CD, expressed in dB? (The loudness referred to above is the amplitude, so use the usual dB formula for comparing two amplitudes.)

(b) What about the dynamic range of Bluray (which uses 24-bit audio)? How does this compare to the dynamic range of human hearing (120 dB)?

(c) Suppose that a Space Alien from the Planet Zorg has a dynamic range of hearing of 240 dB. How many bits of resolution are necessary for a digital recording to sound “perfect” to a Zorgian? Hint: For the last part, set up the dynamic range in dB for n bits, set it equal to 240 dB, and then use log x m = m log x to help you solve the resulting equation.

Explanation / Answer

a) = 20 log (2Q) where Q is bit

= 20 log ( 2^ 16) = 96db

b) = 20 log (2^24) = 144 db

human earing is 120 db

when playing back a CD, the amplifier is usually set so that the quietest sounds on the CD can just be heard above the noise floor of the listening environment (sitting room or cans). So if the average noise floor for a sitting room is say 50dB (or 30dB for cans) then the dynamic range of the CD starts at this point and is capable of 144dB (at least) above the room noise floor.

. If the full dynamic range of a CD was actually used (on top of the noise floor) =144 +50 = 294 db while human can bear upto 120 db

even if noise of sitting room is ignored even then it is well above human dynamic range.

c) ignoring room noise

240 = 20 log (2^Q)

Q = 240/log2 =39.8 = 40 bit

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