Spectral Estimation of the Pass-by Noise of an Acoustic Source

The identification of a moving noise source is important in reducing the source power of the transport systems such as airplanes or high speed trains. However, the direct measurement using a microphone running with noise source is usually difficult due to wind noise, while the source motion distorts the frequency characteristics of the pass-by sound measured at a fixed point. In this study the relationship between the spectra of the source and the pass-by sound signal is analyzed for an acoustic source moving at a constant velocity. Spectrum of the sound signal measured at a fixed point has an integral relationship with the source spectrum. Nevertheless direct conversion of the measured spectrum to the source spectrum is ill-posed due to the singularity of the integral kernel. Alternatively a differential equation approach is proposed, where the source characteristics can be recovered by solving a differential equation relating the source signal to the distorted measurement in time domain. The parameters such as the source speed and the time origin, required beforehand, are also determined only from the frequency-phase relationship using an auxiliary measurement. With the help of the regularization method, the source signal is successfully recovered. The effects of the parameter errors to the estimated frequency characteristics of the source are investigated through numerical simulations.