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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:

enter image description here

Can anybody give me some tips? Thanks!

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    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
    Commented 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
    Commented 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
    – bactone
    Commented Mar 10, 2020 at 7:32

1 Answer 1

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I believe that the units of Pa/s come from the formal definition of the impulse response, which is the system's (the speaker's, in this case) response when being driven by an impulse function, δ(t). The impulse function is the time derivative of the unit step function, u(t), where u(t) is 0 for t<0, and 1 for t>=0, and is unit-less. This function can not exist in the real world since it changes infinitely fast from 0 to 1. Similarly, neither can the impulse function exist in the real world since it represents the rate of change of a function that is changing infinitely fast. That said, the units of δ(t) are 1/seconds, since it is the time derivative of the unit-less step function, u(t). So driving a speaker with a 1-Volt impulse function is equivalent to applying an input of (1V)δ(t), which results in units of V/s. The speaker has a sensitivity of some number of Pa/V, so its output, in this case, will have units of Pa/s.

As far as the magnitude of the impulse response in SoundCheck, this is the result of the entire signal chain: relationship of the digital values in SoundCheck to the actual voltages on the digital-to-analog and analog-to-digital converters of the sound card, and the sensitivity of the measurement microphone (and any pre-amplification). The "calibration" steps in SoundCheck establish these relationships so that Volts and Pascals in the real world are the same in the program. If the calibration is off, the magnitudes in the program will be off too.

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