Subject: Re: [AUDITORY] Question about level conversions From: "Richard F. Lyon" <dicklyon@xxxxxxxx> Date: Thu, 9 Mar 2023 19:21:42 +1100--0000000000006ad62305f67356f8 Content-Type: text/plain; charset="UTF-8" Step 2 looks like a wrong sign. If the tone level is fixed, the tone energy should be an increasing function of duration, but you show a decreasing function of duration. Did this come from Richards or Ahumada? The use of units like dB/Hz makes my skin crawl; but I think what you've done with it makes sense for the noise. In communication theory, we use measures like Eb/N0, that is, energy per bit relative to noise spectral density. So the E_tone/N0 seems sensibly analogous as a non-dimensional quantity. It will be easier to see it's non-dimensional if you get out of the dB realm. By the way, I haven't heard from Al Ahumada for a while, but he was a bit of a bud about 25 years ago, in Silicon Valley. Dick On Thu, Mar 9, 2023 at 4:14 PM Alejandro Osses <ale.a.osses@xxxxxxxx> wrote: > Dear list, hello! > > I have a technical question about presentation levels and signal-to-noise > ratios (SNRs), as expressed in the current literature and in more classical > studies (some of the papers I have recently investigated: Richards (1992, > JASA - doi:10.1121/1.402831) and Ahumada et al (1975, JASA - > doi:10.1121/1.380453)). > > I have some thoughts, which I will share next, please feel free to comment > on any of these aspects in terms of maths or concepts, or in terms of > conceptual accuracy.... > > In classical papers (think also of the work by David Green and > colleagues), SNRs are often expressed as energy with respect to N0, often > reported as E/N0. In this expression E is typically the energy of a target > signal (e.g., a tone) which is embedded in a noise, whose spectrum level is > N0. *I am interested to know the mathematical expressions needed to > convert between noise levels to the appropriate target sound level*. I > will now give an example about how I am currently doing such a conversion. > > The example: Let's say I have a Gaussian noise (duration=0.5 s) with > frequencies between 0 and 5 kHz, with a total RMS level of 70 dB SPL. On > the other hand, my target sounds have a centre frequency of 500 Hz, a > duration of 0.1 s, temporally centred in the noise. I want to know the > level of the tone, if E_tone/N0 needs to be 11.8 dB (this is actually from > Ahumada et al (1975)). > > My calculations are as follows: > > - *Step 1*: N0 = 33 dB/Hz (because N0 = lvl_noise - 10*log10(BW) = 70 > - 10*log10(5000) = 33 dB/Hz) > - *Step 2*: The energy of the tone E_tone can be calculated from the > normalised level to a duration of 1 second: E_tone = lvl_tone - > 10*log10(dur_tone) = lvl_tone + 10 dB (using dur=0.1 s) > - *Step 3*: At the same time: E_tone needs to have a E_tone/N0 of 11.8 > dB or E_tone = N0 + 11.8 dB > - *From Step 3 and 4*: N0+11.8 = lvl_tone + 10 -----> for the current > values: lvl_tone = 33+11.8-10 = 34.8 dB > > So, my tone will have a level of 34.8 dB SPL for this example. > > Am I correct with my calculation method or am I missing any important > concept? > > Thank you for the feedback, > > Alejandro Osses > > > --0000000000006ad62305f67356f8 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable <div dir=3D"ltr"><div class=3D"gmail_default" style=3D"font-size:small">Ste= p 2 looks like a wrong sign.=C2=A0 If the tone level is fixed, the tone ene= rgy should be an increasing function of duration, but you show a decreasing= function of duration.=C2=A0 Did this come from Richards or Ahumada?<br></d= iv><div class=3D"gmail_default" style=3D"font-size:small"><br></div><div cl= ass=3D"gmail_default" style=3D"font-size:small">The use of units like dB/Hz= makes my skin crawl; but I think what you've done with it makes sense = for the noise.</div><div class=3D"gmail_default" style=3D"font-size:small">= <br></div><div class=3D"gmail_default" style=3D"font-size:small">In communi= cation theory, we use measures like Eb/N0, that is, energy per bit relative= to noise spectral density.=C2=A0 So the E_tone/N0 seems sensibly analogous= as a non-dimensional quantity.=C2=A0 It will be easier to see it's non= -dimensional if you get out of the dB realm. <br></div><div class=3D"gmail_= default" style=3D"font-size:small"><br></div><div class=3D"gmail_default" s= tyle=3D"font-size:small">By the way, I haven't heard from Al Ahumada fo= r a while, but he was a bit of a bud about 25 years ago, in Silicon Valley.= <br></div><div class=3D"gmail_default" style=3D"font-size:small"><br></div>= <div class=3D"gmail_default" style=3D"font-size:small">Dick</div><div class= =3D"gmail_default" style=3D"font-size:small"><br></div></div><br><div class= =3D"gmail_quote"><div dir=3D"ltr" class=3D"gmail_attr">On Thu, Mar 9, 2023 = at 4:14 PM Alejandro Osses <<a href=3D"mailto:ale.a.osses@xxxxxxxx">ale= .a.osses@xxxxxxxx</a>> wrote:<br></div><blockquote class=3D"gmail_quote= " style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);= padding-left:1ex"><div dir=3D"ltr"><div>Dear list, hello!</div><div><br></d= iv><div>I have a technical question about presentation levels and signal-to= -noise ratios (SNRs), as expressed in the current literature and in more cl= assical studies (some of the papers I have recently investigated: Richards = (1992, JASA - doi:10.1121/1.402831) and Ahumada et al (1975, JASA - doi:10.= 1121/1.380453)). <br></div><div><br></div><div>I have some thoughts, which = I will share next, please feel free to comment on any of these aspects in t= erms of maths or concepts, or in terms of conceptual accuracy....<br></div>= <div><br></div><div>In classical papers (think also of the work by David Gr= een and colleagues), SNRs are often expressed as energy with respect to N0,= often reported as E/N0. In this expression E is typically the energy of a = target signal (e.g., a tone) which is embedded in a noise, whose spectrum l= evel is N0. <b>I am interested to know the mathematical expressions needed = to convert between noise levels to the appropriate target sound level</b>. = I will now give an example about how I am currently doing such a conversion= .</div><div><br></div><div>The example: Let's say I have a Gaussian noi= se (duration=3D0.5 s) with frequencies between 0 and 5 kHz, with a total RM= S level of 70 dB SPL. On the other hand, my target sounds have a centre fre= quency of 500 Hz, a duration of 0.1 s, temporally centred in the noise. I w= ant to know the level of the tone, if E_tone/N0 needs to be 11.8 dB (this i= s actually from Ahumada et al (1975)).</div><div><br></div><div>My calculat= ions are as follows: <br></div><div><ul><li><b>Step 1</b>: N0 =3D 33 dB/Hz = (because N0 =3D lvl_noise - 10*log10(BW) =3D 70 - 10*log10(5000) =3D 33 dB/= Hz)</li><li><b>Step 2</b>: The energy of the tone E_tone can be calculated = from the normalised level to a duration of 1 second: E_tone =3D lvl_tone - = 10*log10(dur_tone) =3D lvl_tone + 10 dB (using dur=3D0.1 s)</li><li><b>Step= 3</b>: At the same time: E_tone needs to have a E_tone/N0 of 11.8 dB or E_= tone =3D N0 + 11.8 dB</li><li><b>From Step 3 and 4</b>: N0+11.8 =3D lvl_ton= e + 10 -----> for the current values: lvl_tone =3D 33+11.8-10 =3D 34.8 d= B <br></li></ul><div>So, my tone will have a level of 34.8 dB SPL for this = example.</div><div><br></div><div>Am I correct with my calculation method o= r am I missing any important concept?<br></div></div><div><br></div><div>Th= ank you for the feedback, <br></div><div><br></div><div>Alejandro Osses<br>= </div><div><br></div><div><br></div></div> </blockquote></div> --0000000000006ad62305f67356f8--