AES Journal Forum

Authors are too much briefly describing the concept of the start and the final frequency of the sweep. It means that the spectrum of such sweep will have components very close to zero in bands before the start frequency and after the final frequency that will be causing division by zero in the „deconvolution” process or in another words – the deconvolution filter will have enormous high gain in mentioned bands and will bring up all noses and errors of the real measurement in that bands.

The spectrum of the synchronized swept-sine signal have components very close to zero in bands before the start frequency and after the final frequency. This is normal (and intuitive) for all the chirp-like signals.

The division by zero problem in the „deconvolution” process appears in the classical methods (Eq.4). In our method, the deconvolution process consists in designing the "inverse filter" directly in frequency domain in an analytical way (Eq.43, derived in Appendix A.1). The deconvolution is then made using (Eq.50) in which no division appears. Since the inverse filter X_tilde(f) is designed analytically, there are no enormous high gains in you mentioned.

You can check this out using the Matlab code from Appendix A.2.4 in which the inverse filter is defined as:
X_ = 2*sqrt(f_ax/L).*exp(-j*2*pi*f_ax*L.*(1-log(f_ax/f1)) + j*pi/4);

Note, that the vector f_ax goes from 0 to fs, so that the filter X_ is defined also outside the region <f1,f2>