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42-406: DTS-HD MA can store up to 8 discrete channels of audio ( 7.1 surround ) at up to a 24 bit sample depth and 192 kHz sampling frequency (96 kHz for 6.1 or 7.1 surround). Although DTS-HD MA, and the related DTS-HD, allow virtually any number of channels in the abstract, these limits are imposed for practical reasons of limited storage and bitrate availability. A DTS-HD MA bitstream may have

84-531: A binary number with a fixed number of digits – the sample's bit depth , also referred to as word length or word size. The resolution indicates the number of discrete values that can be represented over the range of analog values. 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 an integer bit depth can represent can be calculated by using 2 , where n

126-650: A bit depth equal to 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, Direct Stream Digital achieves a theoretical 120 dB SNR at audio frequencies using 1-bit audio with 64× oversampling. Bit depth is a fundamental property of digital audio implementations. Depending on application requirements and equipment capabilities, different bit depths are used for different applications. 8-bit int, 16-bit int, 24-bit int, 32-bit int, 32-bit float, and 64-bit float mixing Bit depth affects bit rate and file size. Bits are

168-460: A bitrate no greater than 24.5 Mbit/s (instantaneous), of which no greater than 1.5 Mbit/s may be lossy DTS (as per the DTS CA specification). The Blu-ray specification stipulates DTS-HD MA as an optional codec, which means that some Blu-ray hardware may not decode it. This is the reason for the bifurcated nature of a DTS-HD MA audio stream; DTS CA, unlike its MA extension, is mandatory, so

210-430: A larger increase in dynamic range when oversampling. For n th-order noise shaping, the dynamic range of an oversampled signal is improved by an additional 6 n  dB relative to oversampling without noise shaping. For example, for a 20 kHz analog audio sampled at 4× 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

252-614: A player that is not MA-capable can automatically default to an MA-encoded disc's base DTS stream and simply ignore the supplementary data. Alternatively, even if a player is MA-capable, the base stream may be needed for backward compatibility with an older AV receiver (for example, one manufactured during the DVD era). DTS-HD MA is the encoding format for DTS:X , an object-based surround-sound format that competes with Dolby Atmos . A DTS-HD MA bitstream carrying DTS:X can contain up to 9 simultaneous sound objects, which are dynamically mapped to

294-402: A prior probability for the signal can be specified. Information field theory is then an appropriate mathematical formalism to derive an optimal reconstruction formula. Perhaps the most widely used reconstruction formula is as follows. Let { e k } {\displaystyle \{e_{k}\}} be a basis of L 2 {\displaystyle L^{2}} in

336-584: 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 means. 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 (IIR) filters. In

378-609: A reconstruction formula R that is also a linear map, then we have to choose an n -dimensional linear subspace of L 2 {\displaystyle L^{2}} . This fact that the dimensions have to agree is related to the Nyquist–Shannon sampling theorem . The elementary linear algebra approach works here. Let d k := ( 0 , . . . , 0 , 1 , 0 , . . . , 0 ) {\displaystyle d_{k}:=(0,...,0,1,0,...,0)} (all entries zero, except for

420-449: A user's speaker system during playback, unlike the rigid number and placement of speakers required by channel-based surround (a DTS marketing executive referred to DTS:X in an interview as "whatever.1"). DTS-HD MA is encoded in three steps. First, the audio master is fed to a DTS CA encoder, which generates the core (lossy) audio stream. Next, this lossy audio is decoded and compared to the master, with "residual" data being recorded wherever

462-431: 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

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504-531: 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 754 , which is composed of three fields: a sign bit representing whether the number is positive or negative, a mantissa , and an exponent determining a power-of-two factor to scale the mantissa. The mantissa is expressed as a binary fraction in IEEE base-two floating-point formats. The bit depth limits

546-598: Is as previously discussed, that is, quantization noise power has not been reduced, but the noise spectrum has been spread over 16× the audio bandwidth. Historical note—The compact disc standard was developed by a collaboration between Sony and Philips. The first Sony consumer unit featured a 16-bit DAC; the first Philips units had dual 14-bit DACs. This confused the marketplace and even in professional circles, because 14-bit PCM allows for 84 dB SNR, 12 dB less than 16-bit PCM. Philips had implemented 4× oversampling with first order noise shaping which theoretically realized

588-418: Is the basis of C n {\displaystyle \mathbb {C} ^{n}} given by (This is the usual discrete Fourier basis.) The choice of range k = ⌊ − n / 2 ⌋ , . . . , ⌊ ( n − 1 ) / 2 ⌋ {\displaystyle k=\lfloor -n/2\rfloor ,...,\lfloor (n-1)/2\rfloor }

630-567: Is the bit depth. Thus, a 16-bit system has a resolution of 65,536 (2 ) possible values. Integer PCM audio data is typically stored as signed numbers in two's complement format. Today, most audio file formats and digital audio workstations (DAWs) support PCM formats with samples represented by floating-point numbers. Both the WAV file format and the AIFF file format support floating-point representations. Unlike integers, whose bit pattern

672-464: Is the number of quantization bits, and the result is measured in decibels (dB). Therefore, 16-bit digital audio found on CDs has a theoretical maximum SNR of 98 dB, and professional 24-bit digital audio tops out as 146 dB. As of 2011 , digital audio converter technology is limited to an SNR of about 123 dB ( effectively 21 bits) because of real-world limitations in integrated circuit design. Still, this approximately matches

714-491: The k th entry, which is a one) or some other basis of C n {\displaystyle \mathbb {C} ^{n}} . To define an inverse for F , simply choose, for each k , an e k ∈ L 2 {\displaystyle e_{k}\in L^{2}} so that F ( e k ) = d k {\displaystyle F(e_{k})=d_{k}} . This uniquely defines

756-452: The signal-to-noise ratio (SNR) 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 error introduced during analog-to-digital conversion (ADC) can be modeled as quantization noise. It is a rounding error between the analog input voltage to the ADC and

798-409: The (pseudo-)inverse of F . Of course, one can choose some reconstruction formula first, then either compute some sampling algorithm from the reconstruction formula, or analyze the behavior of a given sampling algorithm with respect to the given formula. Ideally, the reconstruction formula is derived by minimizing the expected error variance. This requires that either the signal statistics is known or

840-614: The Hilbert space sense; for instance, one could use the eikonal although other choices are certainly possible. Note that here the index k can be any integer, even negative. Then we can define a linear map R by for each k = ⌊ − n / 2 ⌋ , . . . , ⌊ ( n − 1 ) / 2 ⌋ {\displaystyle k=\lfloor -n/2\rfloor ,...,\lfloor (n-1)/2\rfloor } , where ( d k ) {\displaystyle (d_{k})}

882-656: The bandwidth to carry DTS-HD MA (or PCM in more than 2 channels). A setup using S/PDIF audio may output DTS-HD MA as either lossy DTS (which S/PDIF can carry) or downmixed stereo PCM. Audio bit depth In digital audio using pulse-code modulation (PCM), 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

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924-416: The basic unit of data used in computing and digital communications. Bit rate refers to the amount of data, specifically bits, transmitted or received per second. In MP3 and other lossy compressed audio formats , bit rate describes the amount of information used to encode an audio signal. It is usually measured in kb/s . Signal reconstruction In signal processing , reconstruction usually means

966-648: The determination of an original continuous signal from a sequence of equally spaced samples. This article takes a generalized abstract mathematical approach to signal sampling and reconstruction. For a more practical approach based on band-limited signals, see Whittaker–Shannon interpolation formula . Let F be any sampling method, i.e. a linear map from the Hilbert space of square-integrable functions L 2 {\displaystyle L^{2}} to complex space C n {\displaystyle \mathbb {C} ^{n}} . In our example,

1008-528: 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, and 32-bit audio can achieve 192 dB, but this is almost impossible to achieve in the real world, as even the best sensors and microphones rarely exceed 130 dB. Dither can also be used to increase the effective dynamic range. The perceived dynamic range of 16-bit audio can be 120 dB or more with noise-shaped dither, taking advantage of

1050-461: 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. If the signal's maximum level is lower than that allowed by the bit depth, the recording has headroom . Using higher bit depths during studio recording can make headroom available while maintaining

1092-406: The expense of a slightly raised noise floor . Recommended dither for 16-bit digital audio measured using ITU-R 468 noise weighting is about 66 dB below alignment level , or 84 dB below digital full scale , which is comparable to the microphone and room noise level, and hence of little consequence in 16-bit audio. 24-bit and 32-bit audio does not require dithering, as the noise level of

1134-466: The frequency response of the human ear. 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. With the proper application of dither, digital systems can reproduce signals with levels lower than their resolution would normally allow, extending

1176-626: The full 96 dB dynamic range of the CD format. In practice the Philips CD100 was rated at 90 dB SNR in the audio band of 20 Hz–20 kHz, the same as Sony's CDP-101. 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

1218-455: The noise level from quantization error —thus the signal-to-noise ratio (SNR) and dynamic range . However, techniques such as dithering , noise shaping , and oversampling can mitigate these effects without changing the bit depth. Bit depth also affects bit rate and file size. Bit depth is useful for describing PCM digital signals . Non-PCM formats, such as those using lossy compression , do not have associated bit depths. A PCM signal

1260-461: The output digitized value. The noise is nonlinear and signal-dependent. In an ideal ADC, where the quantization error is uniformly distributed between ± 1 2 {\displaystyle \scriptstyle {\pm {\frac {1}{2}}}} least significant bit (LSB) and where the signal has a uniform distribution covering all quantization levels, the signal-to-quantization-noise ratio (SQNR) can be calculated from where b

1302-440: The particular case of IIR filters, rounding error can degrade frequency response and cause instability. 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 non-linear quantization error behavior, giving very low distortion, but at

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1344-497: The performance of the human auditory system . 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 . The resolution of floating-point samples is less straightforward than integer samples because floating-point values are not evenly spaced. In floating-point representation,

1386-465: 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 with single or double precision , and fixed-point operations at 16-, 32- or 64-bit resolution. Consequently, all processing performed on Intel-based hardware will be performed with these constraints regardless of

1428-433: 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 16× oversampling, or 768 kHz. Oversampled PCM, therefore, exchanges fewer bits per sample for more samples to obtain

1470-467: The re-quantization of samples and thus introduce additional rounding errors analogous to the original quantization error introduced during analog-to-digital conversion. To prevent rounding errors larger than the implicit error during ADC, calculations during processing must be performed at higher precisions than the input samples. Digital signal processing (DSP) operations can be performed in either fixed-point or floating-point precision. In either case,

1512-422: The same dynamic range. This reduces the risk of clipping without increasing quantization errors at low volumes. 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

1554-502: The same level of error. In other words, integers have a round-off that is uniform, always rounding the LSB to 0 or 1, and the floating-point format has uniform SNR, the quantization noise level is always of a certain proportion to the signal level. A floating-point noise floor rises as the signal rises and falls as the signal falls, resulting in audible variance if the bit depth is low enough. Most processing operations on digital audio involve

1596-408: The same resolution. Dynamic range can also be enhanced with oversampling at signal reconstruction, absent oversampling at the source. Consider 16× oversampling at reconstruction. Each sample at reconstruction would be unique in that for each of the original sample points sixteen are inserted, all having been calculated by a digital reconstruction filter . The mechanism of increased effective bit depth

1638-542: The source format. Fixed-point digital signal processors often supports specific word lengths to support specific signal resolutions. For example, the Motorola 56000 DSP chip uses 24-bit multipliers and 56-bit accumulators to perform multiply-accumulate operations on two 24-bit samples without overflow or truncation. On devices that do not support large accumulators, fixed-point results may be truncated, reducing precision. Errors compound through multiple stages of DSP at

1680-431: The space between any two adjacent values is in proportion to the value. The trade-off between floating-point and integer formats 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

1722-629: The two differ. Finally, the residual data is compressed losslessly and merged with the core into one bitstream. A DTS-HD MA decoder simply performs this process in reverse. DTS-HD MA audio, including DTS:X audio, can be created and edited using DTS's DTS:X Encoder Suite . The DTS-HD Master Audio Suite served the same function before the introduction of DTS:X, and can still be used for DTS-HD MA that does not carry DTS:X. DTS-HD Master Audio may be transported to AV receivers in 5.1 , 6.1, or 7.1 channels, in full quality, in one of three ways depending on player and/or receiver support: S/PDIF does not have

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1764-466: The vector space of sampled signals C n {\displaystyle \mathbb {C} ^{n}} is n -dimensional complex space. Any proposed inverse R of F ( reconstruction formula , in the lingo) would have to map C n {\displaystyle \mathbb {C} ^{n}} to some subset of L 2 {\displaystyle L^{2}} . We could choose this subset arbitrarily, but if we're going to want

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