Hope this may clear up some of the issues discussed:
Signal to noise: calculating the high-resolution-audio reality-to-hype ratio
By Brian Dipert, Technical Editor -- 2/6/2003
EDN
Music labels and equipment suppliers hope that high-resolution-audio formats, such as DVD-Audio and SACD (Super Audio CD), will be the latest in a string of mostly successful upgrade "pitches" (Reference 1). Beginning with the 78-rpm record and quarter-inch tape, the audio industry has sold consumers on a series of claimed ever-higher quality formats: 33.3-rpm albums, 45-rpm singles, and eight-track tapes, all of which audio CDs and cassettes and, less successfully, DAT and MiniDiscs have now superseded. Along the way, consumers have upgraded their audio gear, refreshed their music libraries, and purchased more expensive variants of new music. With history as a guide to future trends, why should this latest format jump be any different?
Well, with every generation up-tick, the incremental quality improvement has diminished. I'd argue, in fact, that the reason that audio CDs so quickly supplanted LPs had little or nothing to do with higher sonic quality, and the even more rapid acceptance of degraded-quality MP3 and other lossy- compression formats supports this claim. The embrace of the audio CD was all about portability and durability, not first-play sound quality, and some folks still insist that LPs sound better. The latest audio formats often offer surround sound, which is a credible upgrade motivator for at least some consumers. But will large samples and high sample rates further increase consumers' temptations to pull out their wallets? Will consumers care about these features? Or, as the actions of Sony (which refused to label recent two-channel re-releases of the Rolling Stones' library as the hybrid SACDs they in fact were and sells them at conventional-CD prices) suggest, will the plethora of formats have a detrimental effect on sales?
What's the theory behind the auditory benefit claims of the new high-resolution formats? And how well does this theory hold up outside the laboratory?that is, in the real world? To set a framework for the discussion that follows, let's make sure we're using the same vocabulary, and the same definitions for the words in that vocabulary. I adapted the descriptions that follow from an Analog Devices application note (Reference 2):
Decibel: describes the sound-level (sound-pressure-level) ratio or power and voltage ratios; dBVOLTS=20×log(Vo/Vi), dBWATTS=10×log(Po/Pi), dBSPL=20×log(Po/PI).
Dynamic range: the difference between the loudest and the quietest representable signal level or, if noise is present, the difference between the loudest (maximum level) signal to the noise floor; measured in decibels; dynamic range=(peak level)?(noise floor) dB.
SNR: the difference between the nominal level and the noise floor; measured in decibels; other authors define SNR for analog systems as the ratio of the largest representable signal to the noise floor when no signal is present, which more closely parallels SNR for a digital system.
Headroom: the difference between nominal line level and peak level where signal clipping occurs; measured in decibels; the larger the headroom, the better the audio system handles very loud signal peaks before distortion occurs.
Peak operating level: the maximum representable signal level at which clipping of the signal occurs.
Line level: nominal operating level (0 dB or, more precisely, ?10 to +4 dB).
Noise floor: the noise floor for human hearing is the average level of "just audible" white noise; analog-audio equipment can generate noise from components; with a DSP, noise can come from quantization errors.
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Analog Devices' documentation also points out that you can assume that the sum of headroom and SNR of an electrical analog signal is equal to the dynamic range, although this statement is not entirely accurate because signals can still be audible below the noise floor. It also points out that, in undithered DSP-based systems, you cannot directly apply the SNR definition because no noise is present in the absence of a signal. In the digital domain, which this article series will primarily discuss, dynamic range and SNR both often describe the ratio of the largest representable signal to the quantization error or noise floor.
More bits to represent a signal mean more available quantization levels (Figure 1 and Table 1). Having more levels means lower quantization noise, a wider dynamic range, and a more accurate representation of the original signal. Again quoting the Analog Devices literature, "The maximum representable signal amplitude to the maximum quantization error for an ideal A/D converter or DSP-based digital system is calculated as: SNRRMS (dB)=6.02×n+1.76 dB; dynamic range (dB)=6.02×n+1.76 dB6×n."
The documentation bases 1.76 dB on sinusoidal waveform statistics, and "this figure would vary for other waveforms"; n represents the data-word length. Providing more bits means providing better sound, then, at least to a point. How much accuracy between the sampled signal and the original is good enough, and how much is too much? Supporting more bits requires more processing muscle and more storage, both of which negatively impact cost. Ironically, Meridian Audio's Bob Stuart, one of the founding fathers of the 24-bit DVD-Audio format, along with a number of equally well-regarded peers, published a paper a few years ago that stated that 20-bit precision at a 48-kHz sampling rate and 14-bit precision at a 96-kHz sampling rate (in both cases incorporating noise shaping) were the maximum-required specifications for high-quality audio (Reference 3).
Thinking along similar lines, sound engineer Thomas Sandmann from Master Orange Entertainment points out that the theoretical quantization noise of a 24-bit A/D converter at ?144 dB is significantly lower than the thermal noise of a single resistor connected to the ADC input (Reference 4). And Sound and Vision editor David Ranada, in a recent review of DVD-Audio and SACD players, notes that even the best of them, with an effective dynamic range of 18 to 19 bits, delivers A-weighted noise levels approximately 34 dB "worse" than ideal, 24-bit PCM performance (Reference 5).
The human auditory system, in an ideal anechoic listening environment, discerns a 120-dB dynamic range. Literature often quotes the typical ambient masking-noise level in a living room as 45 dB SPL (sound-pressure level); the noise level in a moving automobile is significantly higher. Quantization noise, most noticeable in audio with low signal levels, must be near to (because it's correlated to the audio) or ideally above this ambient noise floor before it's audible. Even with 16-bit audio CDs, such a scenario would require extensive signal amplification, which would likely blow out speakers and eardrums when the audio returned to nominal levels (Table 2).
You may be getting the sense at this point that a 24-bit sample is overkill for audio storage. Even if you believe that 16-bit samples are insufficient, which I don't, a few bits' more resolution will keep sample size from becoming the weak link in the audio chain that begins in the recording studio and microphones and ends in the listening room and your ears. The choice of a 24-bit sample primarily results from the fact that modern memory, processing, and input/output circuits most readily handle information in 8-bit groups. But at least two scenarios exist for which I'd argue that 24 bits might not be enough.
The first situation occurs during the original recording, mixing, and mastering of the audio, before producers transfer it to optical storage, a downloadable file, or some other mass-distribution vehicle. Think about all of the operations that occur during music creation: Audio engineers combine, equalize, speed up, and slow down multiple tracks' worth of recordings; acoustically manipulate vocals to turn marginal singers into divas; and invariably compress the dynamic range of the final product for as-loud-as-possible radio broadcast. Each of these numerous steps involves arithmetic calculations that, with insufficient precision, result in overflow, rounding, and truncation errors. The effects of these incremental errors build on each other and may audibly degrade the final product (see sidebar "Put on a new record"). Even so, audio engineers are still grumbling over the significant amount of expensive hardware and software upgrades that larger samples, flowing into and out of machines at faster rates, require (references 6 to 8).
An analogous scenario occurs in the decoding and postprocessing stages of audio playback. The latest generation audio formats, such as DVD-Audio, DTS 96/24, WMA Professional, PCM-transformed SACD?which themselves require long data words and postdecoding tasks, such as surround virtualization and bass management?further add to the potential for calculation error and subsequent loss of acoustic "transparency." Even in the era of 16-bit audio, 32-bit, fixed- and floating-point DSPs commonly found use in midrange and high-end equipment. With the migration to 24-bit audio, the 32-bit DSP will likely become pervasive, and all but the lowest end systems will employ floating-point variants.
Samplification
To evaluate the validity of the high-sample-rate hype, first dust off your college textbooks and recall that according to the Nyquist theory, a given sampling rate perfectly reproduces all frequencies up to half that sample rate. Recall, too, that in a digital-audio-inclusive design, antialias filters find use during both audio capture and playback. During capture?that is, as part of the ADC stage?they keep audio frequencies above half the Nyquist rate from folding back into the passband. During playback?that is, as part of the DAC stage?they prevent inaudible, potentially damaging high-frequency energy from traveling beyond the filter stage to subsequent links in the playback chain, such as power amplifiers and transducers.
An ideal lowpass filter would have perfect transmission in the passband, perfect rejection above the cutoff frequency, and be acoustically "transparent" in all other respects to the audio passing through it (Figure 1). When was the last time you lived in the ideal world? In real life, design engineers must balance the desire for aggressive filtering against the need for low distortion near the cutoff frequency. Make the passband-to-rejection-band transition too steep, and you might create phase shift and ripple, depending on the complexity and cost of the filter architecture you choose. Make the transition too gentle, and you attenuate audible information, allow aliased information to become audible, or both.
Modern CD players minimize the acoustic effects of antialias filters by oversampling?most commonly at an 8× rate?the digital data, thereby moving aliased images of the audio beyond the 22.05- to 44.1-kHz range where 1× sampling would begin to place them. The resultant antialiasing filter can, as a result, be much gentler in its passband-to-rejection-band transition. DVD-Audio and its ilk extend this technique back before the media playback stage to the point at which the recording equipment captures and digitizes the original audio.
High sampling rates also deliver a potential benefit with regard to dithering, a random pattern added to the least significant bit of a signal during sample-length reduction (Figure 2). Although dither increases background noise, it does so in a way uncorrelated to the signal and therefore more pleasing to the ear than the effect that simply truncating bits creates. With 96-kHz sampling, the dither noise distributes to a frequency band more than twice as wide as that in 44.1-kHz sampling, but less than half of this wider frequency band is audible. Perceived noise drops by approximately 3 dB as a result, and noise shaping can further decrease the audible dither noise level (see Web-only sidebar "Reading 'bitween' the lines").
Notice that in all the discussion so far, I haven't mentioned the most commonly touted marketing advantage of the new formats: their ability to capture sonic information higher than an audio CD's 22.05-kHz Nyquist-dictated cutoff. In reality, even the keenest-hearing children barely perceive audio information at 20 kHz, and, by middle age, even the sharpest ear can't hear anything higher than 15 kHz. Research data even suggests that the human auditory system lumps all frequencies higher than approximately 12.5 kHz into a single frequency "bin," in which humans cannot differentiate the various frequencies present. Noise shaping, a core technology that most modern audio formats use, takes advantage of these phenomena.
Though the frequency-domain benefits of ultrasonic-captured information are at best dubious, time-domain advantages may be more compelling (references 2 and 3). Ripple near an alias filter's cutoff frequency translates to "smearing" of sharp transients in the time domain. When listeners report that DVD-Audio discs and SACDs (Super Audio CDs) sound crisper, they may be noting the reduced blurring effect that an optimized antialias filter has on abrupt edges, such as the "attacks" that percussion and brass instruments produce, and on the higher order harmonics that instruments such as distorted guitars generate (Reference 4). Even if the ears and brain don't consciously acknowledge the presence of a stimulus, it may still have an effect?a phenomenon that subliminal advertising also harnesses. Recent studies indicate increased brain activity in response to high-resolution audio, even when listeners don't report any audible difference between that audio and more conventional music formats (Reference 5).
One claimed benefit of high-resolution audio that likely holds no water is the belief that high sampling rates and consequent ultrasonic frequencies aid in precisely locating a sound source. This phenomenon, the Haas effect, refers to the fact that the phase?that is, time?difference between when a sound hits one ear and when it hits the other is one of two means by which you acoustically place its source in 3-D space. (The other means is the intensity difference you perceive between one ear and the other.) The time difference between any two 44.1- kHz samples is approximately 23 µsec, yet the human auditory system can resolve phase- and time-delay differences of only a few microseconds (defined in part by the distance between an average person's ears).
As Thomas Sandmann from Master Orange Entertainment notes, "One frequent opinion states that the higher sampling rate with its shorter time distance between two samples is better suited for replicating such phase-delay differences. However, this theory is without any foundation because it is indeed possible to present shorter time distances in a digital signal than the distance of two samples. The phase position of a digital audio signal is quite continual with respect to its value since the quantization and the resultant numeric values always apply only to the current amplitude in a discrete time pattern.
"The reconstruction in the D/A-conversion process results in the original waveform and also in the original phase position of the signal. Here, simply raising the sampling frequency does not result in an advantage" (Reference 6). Claims of listeners' locating sound sources better at high sample rates also ignore the results of studies indicating that at high frequencies, the ears and brain rely on intensity, not phase or time, to discern direction (Reference 7).
Can't get no (sonic) satisfaction
If the benefits of a migration beyond 16-bit, 44.1-kHz audio are so obscure, then why do so many people claim that the new formats sound so much better, especially when they're auditioning in nonideal listening environments? One pragmatic answer is that brains are fickle organs; if someone wants to believe that one thing is better than another, the brain happily distorts its sensory inputs to create the desired result. If you've just spent tens of thousands of dollars to upgrade your gear and music collection, that investment can be a strong perception incentive. Also, folks notice subtle differences much more when they're testing multiple options at once than when they listen to any of the options stand-alone (Reference 8).
As noted in Part 1, a well-engineered surround mix can be a powerful motivation for migrating from one format too another. An equally powerful incentive is a reformatted version of an old music classic, slowly and carefully remastered on modern equipment that is free of overflow, rounding, and truncation artifacts and employs the latest and greatest antialias filter technology. This benefit is analogous to the remastered audio CDs that sound so much better than the original, rushed mixes that audio engineers unfamiliar with the new and evolving rules of the then-nascent digital age created. As the person sitting next to me at an audition of the two-channel SACD remix of the Rolling Stones' Street Fighting Man at last October's Audio Engineering Society Convention said, "I never heard the master tape hiss so clearly before."
Remastering a music catalog has its place. However, various vendors are targeting brute-force upsampling equipment at audiophiles. Don't let their sales pitches fool you. This gear connects to a CD player's digital outputs and claims to transform your audio CDs into 24-bit, 96- or 192-kHz "higher quality" presentations. Remember that you can't out of thin air create more meaningful bits than those that existed in the source; padding a sample with zeros doesn't count. Also, "upsampling" doesn't differ from the "oversampling" that CD players perform. An audiophile box may use a more robust antialias filter than a bargain-basement CD player, which may lead to a slight sonic improvement, but that's the extent of the gain.
As John Atkinson from Stereophile writes, other than making active the lowest 8 bits of a 24-bit word, none of these products create any new audio information. As susceptibility to word-clock jitter increases with sampling frequency, upsampling audio data can even make things worse rather than better; and no matter how good these upsampling products can sound, they offer no conceptual advantage over traditional CD-playback systems. Atkinson is "convinced that the sonic differences...are due to the...choices in digital filters [that these products' designers] make with respect to the number of taps, passband ripple, and stopband rejection and to changes in the jitter performance" (Reference 9).
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