Normalized Audio and 0dBFS+ Exposure

Because an analog-to-digital converter or sample rate converter sample clock generally has an arbitrary time relationship to a given piece of program material applied to its input, the same audio can be represented in an infinite number of ways if correctly dithered before the quantizer. Many CDs produced today are normalized to 0dBFS in the digital domain by digital signal processing that is not oversampled and is thus unaware of the peak values of the waveform following playback device D/A converters. Following reconstruction into the analog domain, the peak level of the audio waveform can exceed 0dBFS, a phenomenon commonly known as “0dBFS+,” “intersample peak clipping,” or “true peak clipping.” If the digital-to-analog converter in a consumer playback device does not have 3dB of headroom (3dB being the maximum possible increase in peak level if the reconstruction filter is phase-linear), the converter can produce massive clipping and aliasing distortion components on top of any distortion components introduced by the digital signal processing. Add these to the artifacts produced by the MP3/AAC encode/decode process and it is no wonder that much of today’s aggressively mastered music sounds so unpleasantly distorted.

What is particularly pernicious is that if mastering engineers monitor their work through converters having the required 3dB of headroom and do not use meters that show intersample peaks, these engineers will be completely unaware of the additional distortion that many consumer playback devices will produce. Mastering engineers who do not use intersample peak meters are therefore likely to process more aggressively than would if they were able to hear the additional distortion introduced by poorly designed playback components.

Over-processed audio simply creates bad sound. Bad sound in, more bad sound out. It is really no wonder at all why it is so difficult to make radio stations and netcasts sound good with modern material, because it is all grossly pre-distorted! We are pleased to note that in the last year or so, the mastering community has finally started to become more aware of the intersample peak problem, but we are still seeing many major-label CDs that produce intersample peaks above 0 dBFS.

Version 2 of the free Orban Loudness Meter includes an intersample peak meter (bottom meter) that is sampled at 384 kHz and is thus accurate to approximately 0.2 dB. This software can indicate and log these peak values in real time. www.orban.com/meter

With its “Mastered for iTunes” guide (released in early 2012), Apple Computer has helped make the mastering community aware of this problem. www.apple.com/itunes/mastered-for-itunes

The International Telecommunications Union’s BS.1770-2, “Algorithms to measure audio programme loudness and true-peak audio level,” provides a technical guide for metering intersample peaks. See “Appendix 1 to Annex 2” in this document: www.itu.int/dms_pubrec/itu-r/rec/bs/R-REC-BS.1770-4-201510-I!!PDF-E.pdf

Assuming that the analog path following the D/A converter is DC-coupled and that the frequency response and group delay of the reconstruction filter are flat, the following example shows the worst case and demonstrates that it is never wise to normalize the maximum digital sample value to 0dBFS.

Oversampling

Oversampling the audio reduces (but does not entirely eliminate) the 0dBFS+ phenomenon. 8x oversampling is generally considered sufficient to render the problem negligible because limiting the digital audio samples to a maximum peak level of –0.17dBFS is sufficient to completely eliminate the possibility of clipping upon D/A conversion. Many digital signal processing software and plug-ins are not oversampled and hence have the potential to produce serious distortion caused by 0dBFS+ unless their operators monitor the peak output levels with oversampled peak level meters and reduce the output level of the processing software until the oversampled peak level meter shows no “overs”.

What must a broadcaster or netcaster do to prevent 0dBFS+ problems with commercial recordings, where the peak limiting technology used to prepare the recording is almost never revealed to the recording’s end user? Without completely analyzing a file intended for broadcast or netcast with an oversampled peak level meter, there is no way of knowing the peak levels such a recording will produce after reconstruction. However, there is a simple formula that can be used to guarantee that 0 dBFS+ clipping will never occur downstream: attenuate the audio data by 3 dB in the digital domain.

This should be done by using a competently designed application that correctly dithers the audio data prior to attenuation. (If dither is not added, reducing gain will not only raise the effective noise level by 3dB but will also introduce low-level nonlinear distortion.) When correctly dithered, audio in the digital domain has the same resolution and bandwidth as audio in the analog domain having the same bandwidth and noise floor as the digital representation; the bandwidth in the digital domain is limited to less than one-half the sample frequency and the bit depth determines the noise floor. Few digital audio applications and hardware get this 100% right. It all depends upon the software implementation and mathematical accuracy. These are the kinds of details that separate the “toys” from the “good stuff.” Buyer/user beware!

Although reducing gain by 3dB reduces the resolution of the audio by about a one-half bit, the resulting 3dB loss of signal-to-noise ratio will never be heard with 16-bit or higher audio while the audible benefit of eliminating 0dBFS+ overshoots is dramatic, particularly if the signal is subject to further audio signal processing as it typically is in broadcasting and netcasting. Much of the music today is listened to on portable music players. This is probably the main reason why music is heavily processed in mastering. For much the same reason that broadcasters fight loudness wars, now there are the downloadable music file wars. Unfortunately, these same audio files are used by broadcasters and netcasters despite long-standing broadcast industry pleas to record companies for “mastered for broadcast” material. (Such material has the same processing applied in mastering as is applied to the consumer version of the file except that clipping and aggressive digital peak limiting are not used and the average level of the file is reduced as necessary.)

Here is what 0dBFS+ looks like on the world’s most popular portable music player, which also works as a phone.

The Imperfect World of 1x Digital Audio

To our knowledge, this is the first 3D depiction of the 0dBFS+ phenomenon. The graph shows the peak magnitude of the reconstructed signal plotted against frequency and against the phase difference between the zero crossings of the test signal and the sample clock, where the “phase difference” refers to the phase of the test signal. It shows that the worst case is 3 dB, which occurs when the frequency is one-quarter of the sampling frequency and the phase difference is 45 degrees from 0, or p/4 radians. This corresponds to the second chart from the top of this page.

To observe the amount of 0dBFS+ accumulation from a CD source audio file, extract the CD to linear PCM format (.wav). Open the file in an audio editor such as Adobe Audition and reduce the audio level by 3dB. Check the resulting digital peak levels by running the Amplitude Statistics > Peak Amplitude analysis. The result should be very close to –3dB if the source is modern over-processed audio. Then Convert Sample Type (upsample) to 4x or 176.4kHz, which approximates the digital-to-analog conversion process to an accuracy of about ±0.6 dB. Run Amplitude Statistics again. With most modern source material, this will show that the upsampling process has introduced samples whose peak levels are higher than –3 dBFS.

Most audio editing software displays audio data by showing the amplitude of the digital samples. When zoomed in, Adobe Audition automatically applies a reconstruction filter to the digital samples, allowing the user to view the reconstructed audio as it would appear at the output of a D/A converter. However, Audition’s digital audio level meters show the levels of the digital samples, not the reconstructed audio. This can confuse users who are unaware of this behavior. For example, if one opens the first two supplied test files, Adobe Audition will display the first file as 0dBFS and the second file as –3dBFS. If you zoom in, you see that both files actually reconstruct to 0dB, as they were generated. The third file, however, is clipped. If the third file level is reduced by 3dB, it will then reconstruct to 0dB, clearly indicating why it is a good idea to reduce the level of all currently produced audio by 3dB.

Other audio editing software applications, such as iZotope RX, has a very good feature to view 0dBFS+ or true peak levels in the audio editor. The additional peaks are displayed on top of the normal digital sample peaks and shown in red. This makes it very easy to observe 0dBFS+ peak levels and also reveals the density of the 0dBFS+ build-up, so you know the severity of the problem. This waveform display feature is enabled in Edit > Preferences… > Display and tick Show analog waveform.

Assuming correct dithering, audio in the digital domain has the same resolution and bandwidth as audio in the analog domain having the same bandwidth and noise floor as the digital representation. (The bandwidth in the digital domain is limited to less than one-half the sample frequency and the bit depth determines the noise floor.) However, as we have shown above, the D/A converter must allow headroom for 0 dBFS+ to ensure correct reconstruction. Few digital audio applications and hardware get this 100% right, particularly regarding the need to add dither to audio prior to any level reduction. It all depends upon the software implementation and mathematical accuracy. These are the kinds of details that separate the “toys” from the “good stuff.” Buyer/user beware!

The Real World

Enough theory. This is what is “out in the wild.” Record companies take note! You may not be understanding what is really happening to your audio product.

Here is an example of a song that reached #12 on the Billboard Hot 100 Chart in 2010. It is a digital rip of Track 1. This is what happens in the real world.

CD – Track 1 – Linear PCM

Direct digital rip of CD – Track 1 – Entire Track – Gain adjusted to –3dB – Upsampled 4x Note that even though this view is in bit view mode, up-sampling provides a reconstruction filter approximation, and peak levels start to rise, since the original signal was only peak limited using a 1x sample rate peak limiter.

CD – Track 1 – Linear PCM

Direct digital rip of CD – Track 1 – Entire Track – Gain adjusted to -3dB – Zoomed in to 20ms – HPF 3rd Order 20Hz

Close in view of highly clipped low frequency audio program material. The third-order filter introduces more tilt than the first-order filter, even though they are both 3 dB down at 20 Hz.

This is a technical work in progress. More information will be added here on this topic, including what happens when MP3/AAC encoding/decoding is introduced into the signal chain.
A technical paper is being prepared on all the information here.