Re: [LAU] users of japa

On 09/22/2012 01:52 PM, Fons Adriaensen 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.

Ecce Fonso.

Wow. Many Thanks for this explanation:

> 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.
>
> [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.
>
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Received on Sat Sep 22 16:15:02 2012