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I have conducted an experiment in which the impulse was exerted on sound bowl (it was hit by a hammer). As a result I have obtained acceleration from accelerometer on 3 axis, calculated net acceleration ($\sqrt{x^2+y^2+z^2}$) and tried to obtain frequency components of the response.

What I need to do is to identify input impulse but I have no idea on how to do that.

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  • $\begingroup$ what about the input impulse do you need to identify? The way I look at it, you have more unknowns than you have data points: You're observing the convolution of the unknown input impulse with the unknown sound bowl impulse response [convolved with the (hopefully linear) impulse response of your sensor system, but let's assume that's mostly an identity operation]. $\endgroup$ – Marcus Müller Jan 26 '20 at 10:29
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  1. Compute the position function from the accelerometer data using a scaled aggregator of some kind presumably, with initial conditions about resting position and velocity of the sound bowl. If you don't want to model the hammer's impact exactly, and want to think of it as an impulse, then the position function is the impulse response. Otherwise, go to 2.

  2. Model the impact of a hammer as a non-ideal impulse function in time. Deconvolve the position function and the hammer model to get the impulse response. You could try to use the 3d fft on both these functions and find their ratio, and the compute its inverse 3d fft.

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