A spectrum-of-spectrum filtering method to extract direct and multipath arrivals from simulations and measurements

In measurements and numerical modelling of wave propagation, undesired interference between direct and multipath arrivals can be reduced using Fourier-based signal processing methods. Existing methods, such as cepstral analysis and time-signal gating, are not applicable to all cases. Here, an alternative Fourier-based signal processing method is presented, called spectrum-of-spectrum (SoS) filtering. Its main advantage over existing methods is its ability to extract single direct or multipath arrivals for relatively short propagation distances even when subsequent arrivals do not become successively weaker. The method is based on the following steps: • Apply a lowpass filter to the real and imaginary parts of an input frequency spectrum individually, using a digital finite impulse response (FIR) filter in the frequency domain. • Recombine the filtered real and imaginary parts of the frequency spectrum to get the frequency spectrum of the direct arrival. • For extraction of the first multipath arrival, subtract the filtered frequency spectrum from the input frequency spectrum and repeat the previous steps. Repeat multiple times to extract subsequent multipath arrivals.