[LAU] Frequency-response analyzer for Linux?

[Fons Adriaensen]

On Fri, Jul 17, 2009 at 07:18:30PM -0700, Ken Restivo wrote:

> The white noise was similarly not flat:
> http://restivo.org/misc/white.png

To get a flat trace for pink noise, you have to
set the 'Resp' (response) control at the bottom
to 'Prop' (proportional). 

To understand what's happening here you need to
grok the following.

A spectrum analyser uses a set of bandpass filters
to measure signal levels at different frequencies
(the implementation maybe different, but the basic
idea is set of filters).

There are two well-known types: 

- A 'linear scale' analyser uses a set of filters
with a constant _difference_ of center frequency 
between adjacent filters, and all filters have the
same bandwidth. This is what you get using a simple
FFT, as used for example in Jaaa.

- A 'logarithmic scale' analyser uses a set of filters
with a constant _ratio_ of center frequency between
adjacent filters, and the bandwidth of each filter is
proportional to center frequency. This is the case e.g.
for a 1/3 octave analyser.

Now assume that you design each analyser so it will 
indicate the correct level for a sine tone at the 
exact center frequency of one of the filters.

Then the two types of analyser will react differently
to noise.

The 'linear' one will indicate a flat spectrum for
white noise, and a slope of -3dB/octave for pink.

The 'logarithmic' analyser will indicate a flat
spectrum for pink noise, and a slope of +3dB/oct
for white.

The analyser used in Japa is neither linear nor
logarithmic. It uses a 'warped' frequency scale
that is adapted to human hearing. You can see the
scale if you set the 'Scale' control (bottom) to
'Warp'. With this setting, each filter corresponds
to the same width on the screen.

The 'Warp' control (right) will select on of three
'warp factors'. The first and default one called
'Bark' corresponds closely to the so-called 'Bark
scale' used in psycho-acoustics (there's no relation
to dog sounds).

Since Japa is neither 'lin' nor 'log', it will
normally not display a flat spectrum for either
white or pink noise. Setting the 'Resp' control
to 'Prop' will adjust the filter gains so you
get a flat trace for pink noise. This setting is
for _noise_ measurements only, it will produce
wrong results for sine tones. For these use
the 'Flat' setting.

Measuring FR using noise can be difficult since
noise by its very nature is random, and you have
to select a slow analyser response to get any
accurate readings. 

Japa allows to use a trick to make this more
practical:

Connect the pink noise out to the app to be
measured, _and_ to one of Japa's own inputs.
Connect the output of the tested app to one
of the other Japa inputs.

Now select the app's out on channel A, and the
noise loopback on channel B, and set the display
to 'A/B'. The resulting trace is the difference
(in dB) of the two signals and it will move a
lot less since most of the randomness cancels.
Since we are using a relative measurement, the
'Resp' setting doesn't matter in this case.

Ciao,

--
FA