From: Fons Adriaensen <fons@...>

To: <linux-audio-user@...>

Subject: Re: [LAU] users of japa

Date: Saturday, September 22, 2012 - 11:52 am

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

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.

[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)

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Re: [LAU] users of japa, Fons Adriaensen, (Sat Sep 22, 11:52 am)

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