Subject: Re: swept sine accuracy From: Jan Schnupp <jan@xxxxxxxx> Date: Fri, 6 Mar 2009 09:30:31 +0000 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>--001636c599eab2729e04646fef10 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit Hi James, I would have thought if the system truly is linear then it does not matter how fast you sweep the sine. The problem is only that most systems are only approximately linear. As long as the input overall has enough bandwidth and enough energy to allow you to measure the response at a sufficiently good signal to noise ratio, then your done. Think about it this way: If you make the FM sweep effectively infinitely fast, then you get a kind of click, and you can collect the impulse response of the system by deconvolving the click from the recording. In theory that's great, but in practice there can be a problem with that because, in doing so, you 'pack a lot of bandwidth' into a short time, so you may need to output a lot of power to get a decent S/N. Your stimulus delivery might start distorting. Slow FM would be one way to deliver substantial stimulus at potentially modest stimulus power (you simply spread it out in time, hence less distortion, and potentially 'cumulatively' a good S/N. Does that make sense? All the best, Jan 2009/3/6 James W. Beauchamp <jwbeauch@xxxxxxxx> > Guys, > > This is a not strictly an auditory question, but it could be > useful for people doing acoustic measurements. If you use a > swept sine wave to measure the frequency response of a linear > system, what is the limitation on the speed of the sweep in > terms of how accurate the result would be? I imagine it has > something to do with how smooth the actual frequency response > is. If it has some pronounced bumps, they could be smoothed > out if the sweep is too fast. > > In practice, you could sweep at some arbitrary rate, and then > slow it by a factor of two, and if the result is the same > (within an acceptable tolerance) you could say that you've > converged on the solution. > > But I'd like to have a theoretical result. > > Jim Beauchamp > Univ. of Illinois at Urbana-Champaign > -- Dr Jan Schnupp University of Oxford Dept. of Physiology, Anatomy and Genetics Sherrington Building - Parks Road Oxford OX1 3PT - UK +44-1865-272513 www.oxfordhearing.com --001636c599eab2729e04646fef10 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Hi James,<br><br>I would have thought if the system truly is linear then it= does not matter how fast you sweep the sine. The problem is only that most= systems are only approximately linear.<br><br>As long as the input overall= has enough bandwidth and enough energy to allow you to measure the respons= e at a sufficiently good signal to noise ratio, then your done. Think about= it this way: If you make the FM sweep effectively infinitely fast, then yo= u get a kind of click, and you can collect the impulse response of the syst= em by deconvolving the click from the recording. In theory that's great= , but in practice there can be a problem with that because, in doing so, yo= u 'pack a lot of bandwidth' into a short time, so you may need to o= utput a lot of power to get a decent S/N. Your stimulus delivery might star= t distorting. Slow FM would be one way to deliver substantial stimulus at p= otentially modest stimulus power (you simply spread it out in time, hence l= ess distortion, and potentially 'cumulatively' a good S/N.<br> <br>Does that make sense?<br><br>All the best,<br><br>Jan<br><br><div class= =3D"gmail_quote">2009/3/6 James W. Beauchamp <span dir=3D"ltr"><<a href= =3D"mailto:jwbeauch@xxxxxxxx">jwbeauch@xxxxxxxx= </a>></span><br> <blockquote class=3D"gmail_quote" style=3D"border-left: 1px solid rgb(204, = 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">Guys,<br> <br> This is a not strictly an auditory question, but it could be<br> useful for people doing acoustic measurements. If you use a<br> swept sine wave to measure the frequency response of a linear<br> system, what is the limitation on the speed of the sweep in<br> terms of how accurate the result would be? I imagine it has<br> something to do with how smooth the actual frequency response<br> is. If it has some pronounced bumps, they could be smoothed<br> out if the sweep is too fast.<br> <br> In practice, you could sweep at some arbitrary rate, and then<br> slow it by a factor of two, and if the result is the same<br> (within an acceptable tolerance) you could say that you've<br> converged on the solution.<br> <br> But I'd like to have a theoretical result.<br> <br> Jim Beauchamp<br> Univ. of Illinois at Urbana-Champaign<br> </blockquote></div><br><br clear=3D"all"><br>-- <br>Dr Jan Schnupp<br>Unive= rsity of Oxford<br>Dept. of Physiology, Anatomy and Genetics<br>Sherrington= Building - Parks Road<br>Oxford OX1 3PT - UK<br>+44-1865-272513<br><a href= =3D"http://www.oxfordhearing.com">www.oxfordhearing.com</a><br> --001636c599eab2729e04646fef10--