# Advice on seperation of impulse responses for harmonic distortion orders

I am working based on Angelo Farinas paper: Simultaneous measurement of impulse response and distortion with a swept-sine technique.

The purpose of the work is part of a loudspeaker measurement and analysis system.

At present my "measurement" data is generated via a non-linear transducer model, so simulated to include typical electroacoustic transducer non-linearities. The simulation is time-domain based and outputs displacement, velocity and acceleration data.

The process as it stands is:

1. Excite the transducer model with a exponential sweep defined by:

$$x(t)=\sin\left(\frac{\omega_1T}{\ln(\frac{\omega_2}{\omega_1})}(e^{\frac{t\ln(\omega_2)}{\omega_1}}-1)\right)$$

1. Create an inverse filter

(which gives a delayed Dirac delta function when convolved with the input function $$x(t)\circledast f(t)\rightarrow\delta(t)$$):

$$f(t) = \frac{x_\text{inv}(t)}{e^{\frac{t\cdot \ln(\frac{\omega_2}{\omega_1})}{T}}}$$

1. Convolve the transducer model output signal $$y(t)$$ with the inverse filter to retreive the systems impulse response $$h(t)$$:

$$h(t)=y(t)\circledast f(t)$$

$h(t)$" />

1. Isolate and plot the FFT of each impulse in the system impulse response (right to left) in order of harmonics:

My main questions are, am I on the right track with this? Are there alternative methods I have missed? What improvements I can make?

3. However, we can't set $$\omega_1=0$$, and in some cases low frequency can cause pre-ringing as well. In this case you may use frequency-domain deconvolution with proper regularization.