Linear sweeps and the characterisation of linearly time-varying acoustical systems

Sine sweeps are widely used as test signals in the experimental characterisation of linear and non-linear acoustical systems' responses. One of the reasons for their popularity is that their immunity against time variance is assumed to be superior to that of other types of test signals. This paper explores and quantifies the consequences of linear time variance on the characterisation of acoustical systems with linear sweeps. The first result is a novel compact closed-form expression for the spectrum of a linear sweep. Second, a similar expression for the frequency response of a linearly time-varying delay to a linear sweep is derived. Additionally, this work demonstrates the application of these expressions through a numerical investigation into the frequency response of a time-invariant bandpass filter when the measurement chain exhibits linear time variance and the attenuation between a ground-borne point source and a receiver in front of a façade under the assumption of a homogeneous atmosphere subject to realistic temperature changes.