Overload in Signal Conversion Søren H. Nielsen and Thomas Lund ¡ TC Electronic A/S, Risskov, Denmark Correspondence should be addressed to Søren H. Nielsen ([email protected]) ¢¤£¦¥¨§ © ¢ § ¤!"#%$'&%()(*+ ,-%$'./!"0*1%$'&%$2/3*%546/65 3$'70$8(*%65,9&:$';<=$'.<348?>=>=?.=@./%6=$"?0:0 0!"?. 4848=&*8ACBD6=?$+%65?*E?. :*%$8,C4'.¤4'5*%$+(*F:$8.=$'&G,H#%?05$I:6=$J*1 =.5 (*G ,-:$8.@*1$'70$8&:$8?K¦0=%? 0.?K (*1% 0&%%$2 ?. :6=$JL: ¦0.5? 0M4N .<7$8&*1? 0. >=&% 48$'*:*GE%6=$J??*1%$'.=$8&E$'.5@=$+% ¦(04O" ,C6=$'&: < !P.Q:6=$3&%$'>=&% 4R%? 0.¨A ST5&%$'KU?0:G>=&: 4N$'*:*%.=V*%546W*X*:!¦>=?$ &#%$¤4N 0.Y7$8&*1? 0.U.5W>$'&:48$8>:5G4N $'4'* !"ZK[$N\6=?]=M%65$¤*:!¦$ >=&: 0]5$'!QA_^E6=(*¤>5>`$8&Q$'*:4N&:]`$'* !M$20*%=&:$8!¦$8.<:*"% a;<50.<%,9Kb:6=$/>=&: 0]5$'!Qcd0.5e.=$'fg:$'*1:*¤>$'&1,9 &%!¦$2a . 48 0!¦!¦$8&4N(&:$'4N &:=.=<*C% X=$8!¦ 0.5*1%&#:$E%6=$>=6=$'.= 0!¦$8.=A)h==&%%6=$'&%!¦ &%$c0!¦$N:6= =*: XZ70 ?X%6=$+(*F: 0&%%? 0."&:$ (*:4N5*:*1$2¤0.5Q$8!¦ 0.*F:&:%$'iA 1 INTRODUCTION more abused. Most pop releases now get so much distortion added during reproduction The final signal processing stage in produc- that 16 bit resolution is completely overkill. tion of audio material is called mastering. While the art of mastering 20 years ago in- The distortion problems arise because of volved getting the best results from a con- more or less conscious use of clipping in the sumer LP reproduction, it seems now to have digital domain during production and mas- become the process in which every tune is tering. Digital processors may have famil- normalized to digital full scale. Because iar names like "Limiter" or "Compressor", but there are no spectral restraints from the LP there is no guarantee they will have much emphasis/de-emphasis process, and no level in common with their analog counterparts, restriction besides from an ancient rule of and not even that they obey the fundamen- how many consecutive samples are allowed tal sampling criteria. Clipping can also be at full scale, mastering has actually turned hidden inside computer processors, DAWs or into a loudness war. The mastering engineer digital mixers, making later recovery difficult is its field marshall, with a number of secret or in many cases impossible. weapons to squeeze the last 0.1 dB of loud- ness out of any song or movie. Figure 1 shows a block diagram of a music or post production studio with a computer The loudness war, as we shall see, has now workstation or a digital mixer at the heart of become so furious that equipment down- it. Headroom critical areas exist around all stream of mastering is not able to pass or digital or analog filters, plug-in or external reproduce the audio material without adding processing, summing busses, limiters, sam- significant distortion to it. It appears to be ple rate converters and digital to analog con- a contradiction that the professional audio verters. Sufficient indication of internal clip industry promotes better standards such as in computers or processing plug-ins even on 96 kHz sampling, 24 bit resolution, DSD, ex- single sources is mandatory, if contamina- otic dither schemes etc. and the hi-fi world tion of the final mix is to be prevented. It is becoming conscious about jitter-rejection is also worth considering if studio speaker etc. – while the current main delivery for- monitoring should include 0 dBFS+ artifacts mat, 16 bit/44.1 kHz, is becoming more and or not, and how signal should be displayed AES 23RD INTERNATIONAL CONFERENCE, COPENHAGEN, DENMARK, 2003 MAY 23–25 1 NIELSEN AND LUND OVERLOAD IN SIGNAL CONVERSION AD CONV MIXER showing clipping due to inter-sample peaks. DOut AIn Out In AOut It may be argued that a single occational EDITOR AD CONV overshoot is inaudible, but this short over- In Out LIMITER Out In shoot does not necessarily stay short. Due AIn Out In Out In In In Out to recursive filters, analog domain latch-up, protection systems or other prolonging ef- CD ASRC FX fects in downstream processing or reproduc- Out In Out In Out tion equipment an originally short overhoot Clk Clk In Out may become much more audible. CLOCK MASTER REC The problem of inaccurate peak level estima- Ref AES1 In tion at certain frequencies has been recog- nised also by the IEC, as stated in Annex A.3 Figure 1: Typical digital studio set-up. (Amplitude-frequency response) in [3]: “(...) However, a response irregularity may occur at specific frequencies related to the sample on level meters or histograms. frequency. The requirement therefore does While frequent clipping in the digital do- not apply at these exceptional frequencies.” main can cause listening fatigue, things are In order to further test how critical the over- made worse during mastering when clipped shoots are in practice several measurements material is normalized to digital full scale. were carried out using both artificial test sig- Such material will later be subject to addi- nals and commercially available recordings tional distortion during data-reduction, sam- as test signals. First of all, the severity of ple rate conversion and digital to analog con- the problem in existing equipment, both dig- version. ital to analog and digital to digital converters, At first glance it seems to be a paradox that was determined. Next, various strategies for overload at these stages can happen but it is avoiding the problem were tested. not. The phenomenon is not limited to con- version into the analog domain. Also purely 2 THEORETICAL CONSIDERATIONS digital processing such as sample rate con- As trivial as it may sound, the basic cause version or data rate reduction coding is criti- of overload in signal conversion is lack of cal. waveform preservation in the conversion pro- Both narrow-band and broadband (e.g. cess. There are several possible causes for clipped) signals can have a theoretical peak this waveform change: value larger than the actual representation in the digital format. The simplest example The very nature of sampled signal repre- is a high frequency sine wave. Depending on sentation frequency and phase the peak value of the Change of phase digital sine wave representation may be up to 3 dB lower than the theoretical, or ana- Change of bandwidth log, peak value. If this headroom is used for increasing the digital gain, the peak value of Non-linear distortion such as clipping the reconstructed analog signal will be higher than the DC value representing digital full Often, a combination of these factors cause scale, 0 dBFS. the trouble. Unfortunately, this is not just a theoretical 2.1 Phase change problem. In practice, all digital converters Even the simplest of waveforms, the sine are equipped with interpolation filters which wave, can be sensitive to phase changes in a by their very nature cause overshoot. way which causes overload by a conversion Earlier work by the authors [1, 2] have indi- process. This is very easily demonstrated: ¡ cated this problem and presented measure- Consider a cosine wave at s ¢¤£ . At a starting ments on the analog outputs of CD players phase of ¥§¦ , the digital representation of the AES 23RD INTERNATIONAL CONFERENCE, COPENHAGEN, DENMARK, 2003 MAY 23–25 2 NIELSEN AND LUND OVERLOAD IN SIGNAL CONVERSION 1 maximum peak value [4, 5]. This is done by changing the phase over a broad fre- quency range containing the problematic sig- 0.5 nal, thus causing peaks to be spread out in time. Depending on the input signal the 0 phase rotation may also have the opposite ef- value [FS] fect, however, by increasing the peak value of signals with rather flat tops. -0.5 Encoding 4-2-4 matrixed surround [6] sound typically also involves a large change of -1 phase over most of the audio frequency range 0 0.04 0.08 0.12 0.16 0.2 time [ms] in order to maintain a constant phase differ- ence between the front and surround chan- Figure 2: Analog and a possible digital repre- nels. The possible audibility of these phase- sentation of 8 kHz ( ¢¡¤£¢¥ ) sampled at 48 kHz. rotator types of phase change will not be dis- cussed here. waveform includes the maximum theoretical 2.2 Bandwidth change magnitude of the waveform. With a starting Removing part of the spectral content of a phase of ¦¨§ © , however, the digital represen- broadband signal is very likely to cause a tation contains only the values times the peak level increase – despite the reduced en- theoretical maximum of the wavefor m, cor- ergy in the resulting signal. responding to -3 dB. At other frequencies re- lated in a simple way to the sampling fre- A very simple example of this is a low fre- quency, a similar difference between theoret- quency limitation, i.e. a high pass filter, ical and practical peak value occurs, see for which is present at most analog interfaces example Figure 2. in order to avoid DC offset. Filtering a low frequency square wave with just a first or- If the digital samples were derived from an der high pass filter will result in a peak level analog source without overload and not pro- increase of up to 6 dB. Sometimes, such fil- cessed in the digital domain, there would be ters occur also within the digital domain. The no potential overload problem at the conver- effect of low frequency, high pass filtering a sion to analog, or to another sample rate. square wave is illustrated in Figure 3. It may Typically some digital processing takes place, be argued that some of the peak level in- however, for example a gain and/or phase crease is caused by the phase change rather change.