The first concern in storing a real-world analog, continuous-time audible signal is determining how the signal should be represented. Fundamental electrical engineering presents a simple and inexpensive solution. When sound waves are introduced to a microphone, the microphone produces a voltage. The voltage amplitude corresponds to the amplitude (loudness) of the sound. The voltage will vary in amplitude according to the changing air pressure from the sound. The air pressure changes in response to the underlying sinusoidal signal, so the time-varying voltage tracks the time-varying signal very well. Fourier showed how all real-world signals are accurately represented as a summation of sinusoids. Euler showed how a sinusoid could be represented in an exponential form. Therefor, any real-world signal can be represented with by Formula 1.
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Cn represents the coefficients of the exponential terms. w is the frequency of a sinusoidal term present in the signal. t represents time. |
The time-varying voltage levels from the microphone represent the cumulative effect of summing simultaneous sinusoids of different amplitudes present in the signal. These sinusoids are the frequencies that compose the signal being recorded. So, we simply need to record the amplitude of the signal as it continues in time, and we will record the signal with all of its frequency components. Quantization Fun Fact #1. It turns out that since the purpose is to record sound in the audible range, we only have to record enough different levels of amplitude so the difference in amplitude between two adjacent levels is the smallest difference (or less!) a listener can detect. With experimentation, the best result is to divide the audible range into 2^16, or 65536, intervals. This allows the representation of each quantified amplitude level of the signal with a single 16-bit binary number. Each 16-bit number is recorded on the CD-ROM as a pattern of reflective and non-reflective marks. The method for storing the signal is unimportant. Quantization Fun Fact #2. It turns out that sampling is not (and need not be) a continuous-time operation. A signal is measured, the value is stored, and the signal is then measured a certain time later. The question that arises is, how often must the sample be recorded to get the original signal back. This question leads to sampling theory.