In other words, integers have round-off that is uniform, always rounding the LSB to 0 or 1, and floating point has SNR that is uniform, the quantization noise level is always of a certain proportion to the signal level. Rounding a large floating-point number results in a greater error than rounding a small floating-point number whereas rounding an integer number will always result in the same level of error. The trade-off between floating point and integers is that the space between large floating-point values is greater than the space between large integer values of the same bit depth. This greatly increases the SNR compared to an integer system because the accuracy of a high-level signal will be the same as the accuracy of an identical signal at a lower level. In floating-point representation, the space between any two adjacent values is in proportion to the value. The resolution of floating-point samples is less straightforward than integer samples because floating-point values are not evenly spaced. Signal-to-noise ratio and resolution of bit depths Multiple converters can be used to cover different ranges of the same signal, being combined to record a wider dynamic range in the long-term, while still being limited by the single converter's dynamic range in the short term, which is called dynamic range extension. Still, this approximately matches the performance of the human auditory system. As of 2011, digital audio converter technology is limited to a SNR of about 123 dB ( effectively 21-bits) because of real-world limitations in integrated circuit design.
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Therefore, 16-bit digital audio found on CDs has a theoretical maximum SNR of 96 dB and professional 24-bit digital audio tops out as 144 dB. Where Q is the number of quantization bits and the result is measured in decibels (dB). In an ideal ADC, where the quantization error is uniformly distributed between ± 1 2 The noise is nonlinear and signal-dependent.Īn 8-bit binary number (149 in decimal), with the LSB highlighted It is a rounding error between the analog input voltage to the ADC and the output digitized value. Quantization error introduced during analog-to-digital conversion (ADC) can be modeled as quantization noise. The bit depth has no impact on the frequency response, which is constrained by the sample rate. The bit depth limits the signal-to-noise ratio (SNR) of the reconstructed signal to a maximum level determined by quantization error.
The mantissa is expressed as a binary fraction in IEEE base-two floating point formats. The most common standard is IEEE 754 which is composed of three fields: a sign bit which represents whether the number is positive or negative, an exponent and a mantissa which is raised by the exponent.
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Unlike integers, whose bit pattern is a single series of bits, a floating point number is instead composed of separate fields whose mathematical relation forms a number. Both the WAV file format and the AIFF file format support floating point representations. Today, most audio file formats and digital audio workstations (DAWs) support PCM formats with samples represented by floating point numbers. Integer PCM audio data is typically stored as signed numbers in two's complement format. Thus, a 16-bit system has a resolution of 65,536 (2 16) possible values. The number of possible values that can be represented by an integer bit depth can be calculated by using 2 n, where n is the bit depth. Adding one bit doubles the resolution, adding two quadruples it and so on. The resolution of binary integers increases exponentially as the word length increases. The resolution indicates the number of discrete values that can be represented over the range of analog values. The amplitude is the only information explicitly stored in the sample, and it is typically stored as either an integer or a floating point number, encoded as a binary number with a fixed number of digits: the sample's bit depth, also referred to as word length or word size. Each sample represents the amplitude of the signal at a specific point in time, and the samples are uniformly spaced in time. A PCM signal is a sequence of digital audio samples containing the data providing the necessary information to reconstruct the original analog signal.
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