In digital audio using pulse-code modulation, bit depth is the number of bits of information
in each sample, and it directly corresponds to the resolution of each sample. Examples
of bit depth include Compact Disc Digital Audio, which uses 16 bits per sample, and
DVD-Audio and Blu-ray Disc which can support up to 24 bits per sample.
In basic implementations, variations in bit depth primarily affect the noise level from
quantization error—thus the signal-to-noise ratio and dynamic range. However, techniques
such as dithering, noise shaping and oversampling mitigate these effects without changing the
bit depth. Bit depth also affects bit rate and file size.
Bit depth is only meaningful in reference to a PCM digital signal. Non-PCM formats,
such as lossy compression formats like MP3, AAC and Vorbis, do not have associated bit
depths. For example, in MP3, quantization is performed on PCM samples that have been
transformed into the frequency domain.
Binary resolution A PCM signal is a sequence of digital audio
samples containing the data providing the necessary information to reconstruct the original
analog signal. Each sample represents the amplitude of the signal at a specific point
in time, and the samples are uniformly spaced in time. 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. The resolution of binary integers increases
exponentially as the word length increases. Adding one bit doubles the resolution, adding
two quadruples it and so on. The number of possible values that can be represented by
an integer bit depth can be calculated by using 2n, where n is the bit depth. Thus,
a 16-bit system has a resolution of 65,536 possible values.
PCM audio data is typically stored as signed numbers in two's complement format.
Floating point Many audio file formats and digital audio
workstations now support PCM formats with samples represented by floating point numbers.
Both the WAV file format and the AIFF file format support floating point PCM and major
DAWs such as Pro Tools, Reason, FL Studio, and Ableton Live support varied floating point
processing capabilities. 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. The most common standard is IEEE floating point
which is composed of three bit patterns: a sign bit which represents whether the number
is positive or negative, an exponent and a mantissa which is raised by the exponent.
The mantissa is expressed as a binary fraction in IEEE base two floating point formats.
Quantization The bit depth limits the signal-to-noise ratio
of the reconstructed signal to a maximum level determined by quantization error. The bit
depth has no impact on the frequency response, which is constrained by the sample rate.
Quantization noise is a model of quantization error introduced by the sampling process during
analog-to-digital conversion. It is a rounding error between the analog input voltage to
the ADC and the output digitized value. The noise is nonlinear and signal-dependent.
In an ideal ADC, where the quantization error is uniformly distributed between least significant
bit and where the signal has a uniform distribution covering all quantization levels, the signal-to-quantization-noise
ratio can be calculated from
where Q is the number of quantization bits and the result is measured in decibels.
24-bit digital audio has a theoretical maximum SNR of 144 dB, compared to 96 dB for 16-bit;
however, as of 2007 digital audio converter technology is limited to a SNR of about 124 dB
because of real-world limitations in integrated circuit design. Still, this approximately
matches the performance of the human auditory system.
The resolution of floating point samples is less straightforward than integer samples,
but the benefit comes in the increased accuracy of low values. In floating point representation,
the space between any two adjacent values is of the same proportion as the space between
any other two adjacent values, whereas in an integer representation, the space between
adjacent values gets larger in proportion to low-level signals. This greatly increases
the SNR because the accuracy of a high-level signal will be the same as the accuracy of
an identical signal at a lower level. 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. 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. 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.
A floating point noise floor will rise as the signal rises and fall as the signal falls,
resulting in audible variance if the bit depth is low enough.
Audio processing Most processing operations on digital audio
involve requantization of samples, and thus introduce additional rounding error analogous
to the original quantization error introduced during analog to digital conversion. To prevent
rounding error larger than the implicit error during ADC, calculations during processing
must be performed at higher precisions than the input samples.
Digital signal processing operations can be performed in either fixed point or floating
point precision. In either case, the precision of each operation is determined by the precision
of the hardware operations used to perform each step of the processing and not the resolution
of the input data. For example, on x86 processors, floating point operations are performed at
32- or 64-bit precision and fixed point operations at 16-, 32- or 64-bit resolution. Consequently,
all processing performed on Intel-based hardware will be performed at 16-, 32- or 64-bit integer
precision, or 32- or 64-bit floating point precision regardless of the source format.
However, if memory is at a premium, software may still choose to output lower resolution
16- or 24-bit audio after higher precision processing.
Fixed point digital signal processors often support unusual word sizes and precisions
in order to support specific signal resolutions. For example, the Motorola 56000 DSP chip uses
24-bit word sizes, 24-bit multipliers and 56-bit accumulators to perform multiply-accumulate
operations on two 24-bit samples without overflow or rounding. On devices that do not support
large accumulators, fixed point operations may be implicitly rounded, reducing precision
to below that of the input samples. Errors compound through multiple stages of
DSP at a rate that depends on the operations being performed. For uncorrelated processing
steps on audio data without a DC offset, errors are assumed to be random with zero mean. Under
this assumption, the standard deviation of the distribution represents the error signal,
and quantization error scales with the square root of the number of operations. High levels
of precision are necessary for algorithms that involve repeated processing, such as
convolution. High levels of precision are also necessary in recursive algorithms, such
as infinite impulse response filters. In the particular case of IIR filters, rounding error
can degrade frequency response and cause instability. Dither
The noise introduced by quantization error, including rounding errors and loss of precision
introduced during audio processing, can be mitigated by adding a small amount of random
noise, called dither, to the signal before quantizing. Dithering eliminates the granularity
of quantization error, giving very low distortion, but at the expense of a slightly raised noise
floor. Measured using ITU-R 468 noise weighting, this is about 66 dB below alignment level,
or 84 dB below digital full scale, which is somewhat lower than the microphone noise
level on most recordings, and hence of no consequence in 16-bit audio.
24-bit audio does not require dithering, as the noise level of the digital converter is
always louder than the required level of any dither that might be applied. 24-bit audio
could theoretically encode 144 dB of dynamic range, but based on manufacturer's datasheets
no ADCs exist that can provide higher than ~125 dB.
Dither can also be used to increase the effective dynamic range. The perceived dynamic range
of 16-bit audio can be as high as 120 dB with noise-shaped dither, taking advantage of the
frequency response of the human ear. Dynamic range
Dynamic range is the difference between the largest and smallest signal a system can record
or reproduce. Without dither, the dynamic range correlates to the quantization noise
floor. For example, 16-bit integer resolution allows for a dynamic range of about 96 dB.
Using higher bit depths during studio recording accommodates greater dynamic range. If the
signal's dynamic range is lower than that allowed by the bit depth, the recording has
headroom, and the higher the bit depth, the more headroom that's available. This reduces
the risk of clipping without encountering quantization errors at low volumes.
With the proper application of dither, digital systems can reproduce signals with levels
lower than their resolution would normally allow, extending the effective dynamic range
beyond the limit imposed by the resolution. The use of techniques such as oversampling
and noise shaping can further extend the dynamic range of sampled audio by moving quantization
error out of the frequency band of interest. Oversampling
Oversampling is an alternative method to increase the dynamic range of PCM audio without changing
the number of bits per sample. In oversampling, audio samples are acquired at a multiple of
the desired sample rate. Because quantization error is assumed to be uniformly distributed
with frequency, much of the quantization error is shifted to ultrasonic frequencies, and
can be removed by the digital to analog converter during playback.
For an increase equivalent to n additional bits of resolution, a signal must be oversampled
by
For example, a 14-bit ADC can produce 16-bit 48 kHz audio if operated at 16x oversampling,
or 768 kHz. Oversampled PCM therefore exchanges fewer bits per sample for more samples in
order to obtain the same resolution. Noise shaping
Oversampling a signal results in equal quantization noise per unit of bandwidth at all frequencies
and a dynamic range that improves with only the square root of the oversampling ratio.
Noise shaping is a technique that adds additional noise at higher frequencies which cancels
out some error at lower frequencies, resulting in a larger increase in dynamic range when
oversampling. For nth-order noise shaping, the dynamic range of an oversampled signal
is improved by an additional 6n dB relative to oversampling without noise shaping. For
example, for a 20 kHz analog audio sampled at 4x oversampling with second order noise
shaping, the dynamic range is increased by 30 dB. Therefore a 16-bit signal sampled
at 176 kHz would have equal resolution as a 21-bit signal sampled at 44.1 kHz without
noise shaping. Noise shaping is commonly implemented with
delta-sigma modulation. Using delta-sigma modulation, Super Audio CD obtains 120 dB
SNR at audio frequencies using 1-bit audio with 64x oversampling.
Applications Bit depth is a fundamental property of digital
audio implementations and there are a variety of situations where it is a measurement.
Bit rate and file size Bit depth affects bit rate and file size.
Bit rate refers to the amount of data, specifically bits, transmitted or received per second.
See also Audio system measurements
Color depth—corresponding concept for digital images
Effective number of bits Notes
References
Ken C. Pohlmann. Principles of Digital Audio. McGraw-Hill Professional. ISBN 978-0-07-134819-5.