Quantization (sound processing)
In signal processing
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

 and digital audio
Digital audio
Digital audio is sound reproduction using pulse-code modulation and digital signals. Digital audio systems include analog-to-digital conversion , digital-to-analog conversion , digital storage, processing and transmission components...

, quantization is the process of approximating a continuous range of values (or a very large set of possible discrete values) by a relatively small set of discrete symbols or integer values. This article describes aspects of quantization related to sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...


After sampling
Sampling (signal processing)
In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave to a sequence of samples ....

, sound signals are usually represented by one of a fixed number of values, in a process known as pulse-code modulation
Pulse-code modulation
Pulse-code modulation is a method used to digitally represent sampled analog signals. It is the standard form for digital audio in computers and various Blu-ray, Compact Disc and DVD formats, as well as other uses such as digital telephone systems...

 (PCM). Some specific issues related to quantization of audio signals follow.

Audio quantization

The telephone , colloquially referred to as a phone, is a telecommunications device that transmits and receives sounds, usually the human voice. Telephones are a point-to-point communication system whose most basic function is to allow two people separated by large distances to talk to each other...

 applications frequently use 8-bit quantization. That is, values of the analogue waveform are rounded to the closest of 256 distinct voltage values represented by an 8-bit binary number. This crude quantization introduces substantial quantization noise into the signal, but the result is still more than adequate to represent human speech.

By comparison, compact disc
Compact Disc
The Compact Disc is an optical disc used to store digital data. It was originally developed to store and playback sound recordings exclusively, but later expanded to encompass data storage , write-once audio and data storage , rewritable media , Video Compact Discs , Super Video Compact Discs ,...

s use a 16-bit digital representation, allowing 65,536 distinct voltage levels. This is far better than telephone quantization, but CD audio representing low signal levels would still sound noticeably 'granular' because of the quantizing noise. However, sometimes an addition of a small amount of noise is added to the signal before digitization. This deliberately added noise is known as dither
Dither is an intentionally applied form of noise used to randomize quantization error, preventing large-scale patterns such as color banding in images...

. Adding dither eliminates this granularity, and gives very low distortion, but at the expense of a small increase in noise level. Measured using ITU-R 468 noise weighting
ITU-R 468 noise weighting
ITU-R 468 is a standard relating to noise measurement, widely used when measuring noise in audio systems. The standard defines a weighting filter curve, together with a quasi-peak rectifier having special characteristics as defined by specified tone-burst tests...

, this is about 66dB below alignment level
Alignment level
The alignment level in an audio signal chain or on an audio recording is a defined anchor point that represents a reasonable or typical level...

, or 84dB below FS (full scale) digital, which is somewhat lower than the microphone noise level on most recordings, and hence of no consequence (see Programme levels for more on this).

Optimizing dither waveforms

In a seminar paper published in the AES
Audio Engineering Society
Established in 1948, the Audio Engineering Society draws its membership from amongst engineers, scientists, other individuals with an interest or involvement in the professional audio industry. The membership largely comprises engineers developing devices or products for audio, and persons working...

 Journal, Lipshitz and Vanderkooy pointed out that different noise types, with different probability density function
Probability density function
In probability theory, a probability density function , or density of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a given point. The probability for the random variable to fall within a particular region is given by the...

s (PDFs) behave differently when used as dither signals, and suggested optimal levels of dither signal for audio. Gaussian noise
Gaussian noise
Gaussian noise is statistical noise that has its probability density function equal to that of the normal distribution, which is also known as the Gaussian distribution. In other words, the values that the noise can take on are Gaussian-distributed. A special case is white Gaussian noise, in which...

 requires a higher level for full elimination of distortion than rectangular PDF or triangular PDF noise. Triangular PDF noise has the advantage of requiring a lower level of added noise to eliminate distortion and also minimizing 'noise modulation'. The latter refers to audible changes in the residual noise on low-level music that are found to draw attention to the noise.
An alternative to dither is noise shaping, which involves a feedback process in which the final digitized signal is compared with the original, and the instantaneous errors on successive past samples integrated and used to determine whether the next sample is rounded up or down. This smooths out the errors in a way that alters the spectral noise content. By inserting a weighting filter in the feedback path, the spectral content of the noise can be shifted to areas of the 'equal-loudness contours' where the human ear is least sensitive, producing a lower subjective noise level (-68/-70dB typically ITU-R 468 weighted).

24-bit quantization

24-bit audio is sometimes used undithered, because for most audio equipment and situations the noise level of the digital converter can be louder than the required level of any dither that might be applied.

There is some disagreement over the recent trend towards higher bit-depth audio. It is argued by some that the dynamic range presented by 16-bit is sufficient to store the dynamic range present in almost all music. In terms of pure data storage this is often true, as a high-end system can extract an extremely good sound out of the 16-bits stored in a well-mastered CD
Audio mastering
Mastering, a form of audio post-production, is the process of preparing and transferring recorded audio from a source containing the final mix to a data storage device ; the source from which all copies will be produced...

. However, audio with very loud and very quiet sections can require some of the above dithering techniques to fit it into 16-bits. This is not a problem for most recently produced popular music, which is often mastered so that it constantly sits close to the maximum signal (see loudness war
Loudness war
The loudness war or loudness race is a pejorative term for the apparent competition to digitally master and release recordings with increasing loudness.The phenomenon was first reported with respect to mastering practices for 7" singles...

); however, higher resolution audio formats are already being used (especially for applications such as film soundtracks, where there is often a very wide dynamic range between whispered conversations and explosions).

For most situations the advantage given by resolution higher than 16-bit is mainly in the processing of audio. No digital filter is perfect, but if the audio is upsampled and the audio is done in 24-bit or higher, then the distortion introduced by filtering will be much quieter (as the errors always creep into the least significant bit
Least significant bit
In computing, the least significant bit is the bit position in a binary integer giving the units value, that is, determining whether the number is even or odd. The lsb is sometimes referred to as the right-most bit, due to the convention in positional notation of writing less significant digits...

s) and a well-designed filter can weight the distortion more towards the higher inaudible frequencies (but a sample rate higher than 48kHz is needed so that these inaudible ultrasonic frequencies are available for soaking up errors).

There is also a good case for 24-bit (or higher) recording in the live studio, because it enables greater headroom (often 24dB or more rather than 18dB) to be left on the recording without encountering quantization errors at low volumes. This means that brief peaks are not harshly clipped, but can be compressed or soft-limited later to suit the final medium.

Environments where large amounts of signal processing are required (such as mastering or synthesis) can require even more than 24 bits. Some modern audio editors convert incoming audio to 32-bit (both for an increased dynamic range to reduce clipping, and to minimize noise in intermediate stages of filtering).

See also

  • Quantization (signal processing)
    Quantization (signal processing)
    Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set – such as rounding values to some unit of precision. A device or algorithmic function that performs quantization is called a quantizer. The error introduced by...

  • Pulse-code modulation
    Pulse-code modulation
    Pulse-code modulation is a method used to digitally represent sampled analog signals. It is the standard form for digital audio in computers and various Blu-ray, Compact Disc and DVD formats, as well as other uses such as digital telephone systems...

  • Sampling (signal processing)
    Sampling (signal processing)
    In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave to a sequence of samples ....

  • Audio bit depth
    Audio bit depth
    In digital audio, bit depth describes the number of bits of information recorded for each sample. Bit depth directly corresponds to the resolution of each sample in a set of digital audio data...

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