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Appendix 4 - More on Digital Audio In a digital recording system, sound is represented as a series of numbers, with each number representing the voltage, or amplitude, of a sound wave at a particular moment in time. The numbers are generated by an analogue-to-digital converter, or ADC, which converts the signal from an analogue audio source (such as a guitar or a microphone) connected to its input into numbers. The ADC reads the input signal several thousand times a second, and outputs a number based on the input that is read. This number is called a sample. The number of samples taken per second is called the sample rate. On playback, the process happens in reverse: The series of numbers is played back through a digital-to-analogue converter, or DAC, which converts the numbers back into an analogue signal. This signal can then be sent to an amplifier and speakers for listening. In computers, binary numbers are used to store the values that make up the samples. Only two characters, 1 and 0, are used. The value of a character depends on its place in the number, just as in the familiar decimal system. Here are a few binary/decimal equivalents:
Figure 1. Binary numbers and their decimal equivalents Each digit in the number is called a bit, so the numbers in Figure 1 are 24-bits long, and the maximum value which can be represented is 16,777,215. The more bits that are used to store the sampled value, the more closely it will represent the source signal. In an 8-bit system, there are 256 possible combinations of zeroes and ones, so 255 different analogue voltages can be represented. A 16-bit system provides 65,535 possible combinations. A 24-bit system provides 16,777,215 possible combinations. A 24-bit signal is capable of providing far greater accuracy than a 16-bit signal. and 16-bit signal is capable of providing far greater accuracy than an 8-bit signal.
Figure 2 shows how this works.The more bits that are available, the more accurate the representation of the analogue signal and the greater the dynamic range. For example Pinnacle and Fiji sound cards analogue inputs use 20-bit ADCs, which means that the incoming signal can be represented by any of 1,048,575 possible values. The output DACs are also 20-bit; again, 1,048,575 values are possible. The S/PDIF inputs and outputs support signals with up to 24-bit resolution (16,777,215 possible values). The number of bits available also determines the potential dynamic range. Moving a binary number one space to the left multiplies the value by two (just as moving a decimal number one space to the left multiplies the value by ten), so each additional bit doubles the maximum value that may be represented. Each available bit provides 6dB of dynamic range. For example, a 16-bit system can theoretically provide 96dB of dynamic range, a 20-bit system can theoretically provide 120dB of dynamic range and a 24-bit system can theoretically provide 144dB of dynamic range The rate at which the numbers are generated by the ADC is equally important in determining the quality of a digital recording. To get a high level of accuracy when sampling, the sample rate must be greater than twice the frequency being sampled. The mathematical statement of this is called the Nyquist Theorem. When dealing with full-bandwidth sound (20Hz-20kHz), you should sample at greater than 40,000 times per second (twice 20kHz). Most modern sound cards allow you to sample at rates up to 48,000 times per second. If the sampling rate is lower than the frequency you are trying to record, entire cycles of the waveform will be missed, and the result will not resemble the proper waveform. When the sample rate is too low, the resulting sound has diminished high frequency content.
Figure 3. Increased sample rates yield a more accurate reproduction of the source signal. By the way, the circuits that generate the sample rate clock must be exceedingly accurate. Any difference between the sample rate used for recording and the rate used at playback will change the pitch of the recording, just as with an analogue tape playing at the wrong speed. Also, any unsteadiness, or jitter, in the sample clock will distort the signal as it is being converted from or to analogue form.
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