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Sampling Rates

from The AudioPro Home Recording Course By Bill Gibson
The process of sampling (digital encoding and decoding) breaks the time axis (horizontal) and the voltage axis (vertical) into a specific number of discrete steps. At each step along the time axis, a measurement is taken of voltage (amplitude) status. This process, called sampling, results in a stair-step picture of the analog waveform.

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The number of times per second the processor samples the voltage (amplitude) of the analog waveform is called the sample rate. The more times the processor samples the analog status of the waveform, the greater the potential accuracy of the system. According to the Nyquist Theorem?which set out to hypothesize the requirements of a digital recording system in order to accurately portrays the reality of a specified bandwidth?the sample rate must be at least twice the highest desired frequency. Therefore, to accurately and faithfully capture a bandwidth extending up to 20kHz (the upper range of human hearing) the sample rate must be at least 40kHz (2 x 20kHz). In order to insure accuracy and to provide headroom for the system, the standard audio CD sample rate was fixed at 44.1kHz.

Controversy follows the question of whether there is a need for higher sample rates and longer word length. Some feel that a sample rate of 44.1kHz is ample, since filters effectively eliminate any artifacts above 20kHz, and 20kHz is the upper limit of mankinds hearing range. Some feel that a 16-bit word provides more than adequate resolution for accurate audio. However, since all frequencies interact acoustically and work together to create a waveform, it seems believable and practical that capturing a broader frequency range and a more accurate resolution is justifiable. We dont yet realize the impact and result of high-frequency content above 20kHz on the emotional and physical perception of sound. Though the debate continues, many?I think, justifiably?contend that, at the very least, we should be archiving important audio material at the highest sample rate and most exact word length thats technologically feasible.

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The concern regarding sample rate isnt simply frequency-related. Since no one, not even the newest born baby, can hear above 25 or 26kHz anyway, the implied ideal sample rate might be 50 to 55kHz. However, theres more involved in our hearing and perception than frequency. Much of our perception comes from our stereo perception of localization and positioning on a three-dimensional plane. The messages that our brain responds to are based on a triangulation process involving both ears and the sound source. The brain calculates the time delay difference between the arrival of a sound at either ear. The time and EQ variations, as a sound moves around the head, are translated into left-right and front-back positioning cues. As the high frequencies are affected by the physical part of the outer ear, called the pinna, changes of equalization cue the brain about front-to-back positioning. Perception of left-right positioning is a product of the brains interpretation of timing differences between the arrival time of a sound at each ear. To complete the system, combined with level changes, the human hearing and localization systems are amazingly complex and efficient.

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Its been determined that time delay differences of 15 microseconds between left and right ears are easily discernible by nearly anyone. Thats less than the time difference between two samples at 48kHz (about 20 microseconds). Using a single pulse, one microsecond in length as a source, some listeners can perceive time delay differences of as little as five microseconds between left and right. It is therefore, indicated that, in order to provide a system with exact accuracy concerning imaging and positioning, the individual samples should be less than five microseconds apart. At 96kHz (a popularly preferred sample rate) there is a 10.417-microsecond space between samples. At 192kHz sample rate there is a 5.208-microsecond space between samples. This reasoning suggests that a sample rate of 192kHz is probably a good choice. As processors increase in speed and efficiency and as storage capacity expands high sample rates, long word length will become an insignificant concern and well be able to focus on the next audio catastrophe.

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