# Why does the deconvolved response and impulse response in soundcheck have units of Pa/s?

I recently tried to figure out the time selective response algorithm of soundcheck. I found:

1. It uses a logarithmic sweep sine as a stimulus, `x(t)` for example, with unit of Volt.

2. The excitation signal is sent to the sound card to achieve D / A conversion, and then sent to the speaker through the power amplifier. While the speaker plays the sound, the microphone collects the sound to obtain the signal `y(t)`, the unit is Pa. Assuming the sensitivity of the microphone is `s0` V/Pa, we can convert the unit of `y(t)` to Volt (same as x(t)), for example `y1(t)=y(t)[Pa]*s0`[V/Pa].

3. According to Farina's paper “Advancements in impulse response measurements by sine sweeps”, firstly I calculate the inverse filter `f(t)=Am*fliplr(x(t))`, where `Am` is an amplitude modulation. Then I perform the deconvolution:

``````deconv=conv(y(t),f(t)),
``````

it should be unit-less.

4. However, the de-convolved response in soundcheck has a unit of Pa/s, and is much smaller than the results I calculated, even though they have exactly the same shape.

Here below are some pictures:

Can anybody give me some tips? Thanks!

• Not having used soundcheck before, but having had quite a bit of experience with inverse convolution, I would say initially that the result could be due to the gain structure of the sensing microphone. Everything else looks as per expectations.
– Mark
Mar 6, 2020 at 11:16
• The thing that I do observe, which gives me cause for concern, is the considerable pre-ring in the resulting impulse response which should not be there. I suspect this is something to do with your filtering. I have not read Angelo's paper yet, so will do so, but I am unsure as to why there is a need to associate Amplitude Modulation with the filter and why you can't just proceed straight to a deconvolution. Will read the paper and hopefully will have a better understanding of what he is trying to do there.
– Mark
Mar 6, 2020 at 23:29
• @Mark, thanks for your suggestion. while the amplitude modulation is used to correct the spectrum of stimulus signal. In fact, a pure exponential sweep sine signal without amplitude modulation doesn't have a white (flat) spectrum: due to the fact that the instantaneous frequency sweeps slowly at low frequencies, and much faster at high frequencies, the resulting spectrum is pink (falling down by -3 dB/octave in a Fourier spectrum). So, the inverse filter must compensate for this: a proper amplitude modulation is consequently applied to the reversed sweep signal, so that its amplitude is now in Mar 10, 2020 at 7:32