Re: dynamic range and sample bit depth (Geoff Martin )


Subject: Re: dynamic range and sample bit depth
From:    Geoff Martin  <GGM@xxxxxxxx>
Date:    Thu, 4 Dec 2014 07:42:11 +0000
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

--_000_141767893176082378bangolufsendk_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Hi, In my opinion, the answer to your question is: "it depends" The calculation of converting bits depth to usable dynamic range is a bit (= sorry...) too simple to make a decision for all cases. If the signal is TPDF dithered, then the simplified calculation is 6.02*Num= berOfBits - 3.01 dB. (The 3.01 is to allow for the noise floor caused by th= e dither.) However, remember that the dither is wide-band noise, and that the measurem= ent of its level is a wide-band RMS measurement and therefore averaged over= time. The signal, however, it probably not wide-band at any given moment. = This means that if, for example, you have a sine tone at -93 dB FS in a 16-= bit system, the math says that your sine tone will be at the same level as = the noise floor. However, it will still be easily audible, since the noise = floor's energy is distributed over a much wider bandwidth. However, if you don't dither your signal, and you drop the sine tone down t= o -93 dB FS, it won't be a sine tone any more. It will be a nasty square wa= ve-like thing. http://www.tonmeister.ca/seeing_dither/? shows some visual analogies that m= ight make this more intuitive. It is also oversimplifying to say that the dither will be below the thresho= ld of audibility for the same reason (of bandwidth). However, it should be = considered whether the dither will be below the noise floor of the playback= system itself (i.e. the amplifiers driving the headphones/loudspeakers) In addition to this, you have to consider that, in cases where you are usin= g "home-made" stimuli recorded for the experiment, it is possible that the = initial recording was not done "properly" (whatever that might mean. For ex= ample, if your initial recording peaked at 20 dB below full scale and, in o= rder to normalise the various stimuli, you then wind up applying 20 dB of g= ain to that recording, you're also bringing up the dither noise floor of th= e original recording by 20 dB. This means that, when you compare the variou= s stimuli, you may be "infecting" the experiment with different noise floor= s (like listening to some of Glen Gould's recordings that are tape spliced = from different recordings on different days - the piano keeps playing the G= oldberg Variation, but the tape hiss abruptly changes throughout the piece) Of course, using stupidly high sampling rates and insane bit depths are ext= remes that are very likely unnecessary - however, if you don't know whether= you'll have a problem or not by fiddling with the gain of the stimuli, it'= s a brute-force way of buying insurance... Cheers -geoff? --_000_141767893176082378bangolufsendk_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable <html> <head> <meta http-equiv=3D"Content-Type" content=3D"text/html; charset=3Diso-8859-= 1"> <style type=3D"text/css" style=3D"display:none"><!-- p { margin-top: 0px; m= argin-bottom: 0px; }--></style> </head> <body dir=3D"ltr"> <div id=3D"divtagdefaultwrapper" style=3D"font-size:12pt;color:#000000;back= ground-color:#FFFFFF;font-family:Calibri,Arial,Helvetica,sans-serif;"> <p>Hi,<br> </p> <p><br> </p> <p>In my opinion, the&nbsp;answer to your question is: &quot;it depends&quo= t;<br> </p> <p><br> </p> <p>The calculation of converting bits depth to usable dynamic range is a bi= t (sorry...)&nbsp;too simple to make a decision for all cases.<br> </p> <p><br> </p> <p>If the signal is TPDF dithered, then the simplified&nbsp;calculation is = 6.02*NumberOfBits - 3.01 dB. (The 3.01 is to allow for the noise floor caus= ed by the dither.)<br> </p> <p><br> </p> <p>However, remember that the dither is wide-band noise, and that the measu= rement of its level is a wide-band&nbsp;RMS measurement and therefore avera= ged over time. The signal, however, it probably not wide-band at any given = moment. This means that if, for example, you have a sine tone at -93 dB FS in a 16-bit system, the math says that y= our sine tone will be at the same level as the noise floor. However, it wil= l still be easily audible, since the noise floor's energy is distributed ov= er a much wider bandwidth.<br> </p> <p><br> </p> <p>However, if you don't dither your signal, and you drop the sine tone dow= n to -93 dB FS, it won't be a sine tone any more. It will be a nasty square= wave-like thing.<br> </p> <p><br> </p> <p><a href=3D"http://www.tonmeister.ca/seeing_dither/" id=3D"lnk123699">htt= p://www.tonmeister.ca/seeing_dither/</a>&#8203; shows some visual&nbsp;anal= ogies that might make this more intuitive.<br> </p> <p><br> </p> <p>It is also oversimplifying to say that the dither will be below the thre= shold of audibility for the same reason (of bandwidth). However, it should = be considered whether the dither will be below the noise floor of the playb= ack system itself (i.e. the amplifiers driving the headphones/loudspeakers)<br> </p> <p><br> </p> <p>In addition to this, you have to consider that, in cases where you are u= sing &quot;home-made&quot; stimuli recorded for the experiment, it is possi= ble that the initial recording was not done &quot;properly&quot; (whatever = that might mean. For example, if your initial recording peaked at 20 dB below full scale and, in order to normalise the various st= imuli, you then wind up applying 20 dB of gain to that recording, you're al= so bringing up the dither noise floor of the original recording by 20 dB. T= his means that, when you compare the various stimuli, you may be &quot;infecting&quot; the experiment with = different noise floors (like listening to some of Glen Gould's recordings t= hat are tape spliced from different recordings on different days - the pian= o keeps playing the Goldberg Variation, but the tape hiss abruptly changes throughout the piece)<br> </p> <p><br> </p> <p>Of course, using stupidly high sampling rates and insane bit depths are = extremes that are very likely unnecessary - however, if you don't know whet= her you'll have a problem or not by fiddling with the gain of the stimuli, = it's a brute-force way of buying insurance...<br> </p> <p><br> </p> <p>Cheer<span style=3D"font-size: 12pt;">s</span></p> <p><span style=3D"font-size: 12pt;">-geoff&#8203;</span></p> </div> </body> </html> --_000_141767893176082378bangolufsendk_--


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