# Re: Pascal per Hertz

On Jun 23,  Laszlo Toth wrote:

> This Praat fft must be magic. I give you a series of numbers, don't tell
> anything about how its amplitude/sampling rate is related to the real world,
> and it gives back values in Pascal/Hertz??

Praat is not Matlab. The sound is in a Sound object, which has information
about the time domain and about the sampling, and is considered to carry
samples that represent air pressures in Pascal. The "fft" converts this
Sound object into a Spectrum object, which has information about the
frequency domain and its sampling, and is considered to carry samples
that represent the real and imaginary values of a spectral density
in Pascal / Hertz. Squaring and summing the values of the Sound,
and multiplying by the sample period, gives an energy in
Pascal-squared-seconds.
Squaring and summing the values of the Spectrum, and multiplying by its
frequency resolution, gives the SAME energy in Pascal-squared-seconds.
That's Parseval's theorem at work.

> By the way, something I never understood: Let's suppose I have an auditory
> model (software) and nice articles about how the model behaves for speech
> signals at a given SPL. I have a PC with a soundcard. My software gets a
> series of samples as input. No SPL's, just a series of integers. One turn
> on the mike-preamp's knob, and the amplitude of the samples is different. One
> move in the soundcard's mixer program, and the amplitude of the samples is
> different. One multiplication with a constant, and the amplitude of the
> samples is different. So, even if my talker talks at a nice 70dB SPL
> normal conversational level, as he's supposed, is there any way I can
> relate the absolute power of the signal to the amplitude of my samples?
> I'm afraid not.

In Praat, the maximum absolute value of the samples is 1, which, if considered
Pascals, corresponds to an intensity of 94 dB re auditory threshold.
There will always be a distance from the mouth to the microphone
for which the sample values represent true air pressures.
Of course, you will not usually know what distance that is,
so in order to have calibrated air-pressure values that you can use
for modelling basilar excitation patterns, you should use a dB meter once,
with your computer set to a maximum input gain, and use the same gain
setting for all subsequent recordings. My old Indy underestimates the pressure
by 4 dB, and my newer Indigo by 24 dB, so I could multiply the signal after
recording if I want to compute cochleagrams. However, the signal I get on my
Indigo is quite weak, so I have to hold my mouth very close to the microphone,
so I multiply the distance instead. Does this sound outrageous?
The point is, no-one talks at 70 dB (perhaps 70 dB at 1 metre).

--
Paul Boersma
Institute of Phonetic Sciences, University of Amsterdam
Herengracht 338, 1016CG Amsterdam, The Netherlands
tel:  +31-20-5252385 / 5252183 (fax: 5252197)
http://www.fon.hum.uva.nl/paul/