On 22 September 2012 12:52, Fons Adriaensen <fons@xxxxxxxxxxxxxx> wrote: > On Sat, Sep 22, 2012 at 04:19:48AM +0200, Robin Gareus wrote: > >> Fons - author of JAAA and JAPA - is on this list and may chime in sooner >> or later. > > Eccomi. > > Confusion as to what JAPA actually measures is a recurring thing... > Unfortunately it's not that easy to explain without going into a > bit of theory. > > Any spectrum analyser is in the end just a set of bandpass filters > acting on the input signal. The outputs levels of these filters are > then displayed as a function of frequency. > > The differences are about how these filters are distributed over > the audio range. In all cases we'll assume that together they cover > this range, and that they overlap in a 'sensible' way, for example > the filter curves intersect at the -3dB points [1]. So the distances > between the center frequencies and the bandwidth of the filters > are related. > > A second thing to consider is the nature of the signal that is being > measured. This could have a line spectrum, i.e. consist of a set of > discrete frequencies (sine waves), or it could be a noise-like signal, > or a mix of the two. The point about noise signals is that their energy > is not concentrated into single frequencies but distributed over a > continuous frequency range. If you could measure them at exactly one > single frequency (not possible, it would take infinite time), you > would find zero. But if you measure them over a finite frequency > interval you find a non-zero value. Noise is characterized by its > _density_, that is the power per Hz. > > White noise has the same density at all frequency (within some range). > There is as much energy between say 5000 and 5010 Hz as there is between > 100 and 110 Hz, or 20 and 30 Hz etc. If you send white noise through two > bandfilters, one with a bandwidth B and one with a bandwidth 2 * B, then > the output level of the second one would be 3 dB (a factor of 2 in power) > higher than the first one. > > Pink noise has a density that is inversely proportional to frequency. > That means that if you integrate over an interval corresponding to > some fixed _ratio_ (rather than difference) of frequencies, you find > the same value. For example there is as much power between 1000 and > 2000 Hz as there is between 100 and 200 Hz, or between 10 and 20 Hz. > > Returning to the analyser, the simplest case is a set of filters that > all have the same bandwidth (measured in Hz, not octaves) and the same > gain at their center frequencies. That's the case for e.g. JAAA. Since > all filters have the same gain, sine waves will be measured correctly. > White noise will produce the same output level for all filters, and > be displayed as a flat trace. Pink noise will result in a trace that > goes down by 3 dB per octave, since its density is proportional to the > inverse of frequency. > > Now imagine the set of filters used in e.g. a 1/3 octave analyser. > Center frequencies are a factor of around 1.26 apart, e.g. 100, 125, > 160, 200, 250, 315, etc [2]. The bandwidths of the filters increase in > the same way - they are proportional to the center frequencies instead > of being all the same. The filter centered at 1 kHz is ten times as wide > (in Hz) as the one at 100 Hz. If all filters have again the same gain, > then sine waves (at the center frequencies) will be measured correctly. > But now, since the bandwidths increase with frequency, white noise > will appear as spectrum that rises +3dB / octave, and pink noise will > be shown as a flat spectrum. > > What this shows is that, at least for noise-like signals, or when > you are not interested in single frequencies but more in the general > shape of the spectrum, there is no single 'correct' way to show it, > it's a matter of interpretation. Which one of the two above is the > more relevant depends on the application [3]. > > The filter set used by JAPA is something in between the two shown > above. At least in the medium frequency range, the filter bandwidths > are proportional to the 'critical bandwidths' of the human hearing > mechanism [4]. You can get an idea of how the filters are distributed > by selecting the 'warped' frequency scale. With this option, all > filter have the same width *on the display*. You will see that the > very low and very high frequency ranges are 'compressed' compared > to a logarithmic scale, there are less filters there, while the > resolution in the mid frequency range is increased. How exactly > this is done depends on the 'warp factor' which you can select > on the right panel. The same filters are used if you select the > normal logarithmic scale, only the display is different. > > With the response set to 'flat', all filters have the same gain. > So a slow sine sweep would produce a flat trace. But since the > filter bandwidts are neither constant nor proportional to frequency, > neither white nor pink noise will be shown as a flat spectrum. > > What happens if you select the 'prop' response is that the filter > _gains_ are modified so you get a flat trace for pink noise. The > consequence is that sine waves will not be measured correctly, so > it depends on your application which response makes sense. > > Ciao, > > [1] In both JAAA and JAPA there are actually about twice as much > filters as would be suggested by this, but that doesn't change > the principle. > > [2] Actually 1/3 octave is a misnomer, all real-life analysers > use a ratio of 1/10 decade in order to have a set of 'round' > center frequencies including e.g. 100, 1k, 10k. > 10^(1/10) = 1.2589... while 2^(1/3) = 1.2599... > > [3] This also means that if you would modify e.g. JAPA to have > a log frequency scale it would still be the same analyser, it > will still show -3 dB/octave for pink noise. Which is not what > one would expect from a 'log' analyser. > That said, I think I'd like a JAAA (that's what you meant, right?) with a log frequency scale. The unevenly spaced bands and (default) uneven response of JAPA have always troubled me. Thanks for explaining things, and of course thanks for sharing all your software with the world, Fons. mH > [4] This is not directly related to Fletcher-Munson or other > equal loudness curves. The critical bandwidths are about > masking, that is to what extent one frequency can hide the > presence of another, which in turn is related to what level > of detail in a spectrum is relevant to human hearing. > > -- > FA > > A world of exhaustive, reliable metadata would be an utopia. > It's also a pipe-dream, founded on self-delusion, nerd hubris > and hysterically inflated market opportunities. (Cory Doctorow) > > _______________________________________________ > Linux-audio-user mailing list > Linux-audio-user@xxxxxxxxxxxxxxxxxxxx > http://lists.linuxaudio.org/listinfo/linux-audio-user _______________________________________________ Linux-audio-user mailing list Linux-audio-user@xxxxxxxxxxxxxxxxxxxx http://lists.linuxaudio.org/listinfo/linux-audio-user
