Figure 6 - uploaded by Eivind Nag Mosland
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Magnitude of í µí°» í µí±í µí± (í µí°¿, í µí±) and the parts of í µí°» í µí±í µí± (í µí°¿, í µí±) containing the direct, first multipath, second multipath, and third multipath arrivals, respectively, obtained using SoS filtering, shown for í µí°¿ = 0.10 m over the frequency range 50-200 kHz.
Source publication
Different signal processing methods are explored to extract individual arrivals from frequency spectra that include interfering direct and multipath arrivals. Specifically, spectrum-of-spectrum (SoS) filtering of the frequency spectrum, cepstrum filtering, and time-signal gating techniques are investigated for an ultrasonic transmit-receive measure...
Contexts in source publication
Context 1
... magnitude of the parts of í µí°» í µí±í µí± (í µí°¿, í µí±) containing only the direct arrival and the first, second, and third multipath arrivals, respectively, obtained using SoS filtering, are shown in Figure 6 for í µí°¿ = 0.10 m over the frequency range 50-200 kHz. The iterative procedure for multipath extraction described in [1] is used. ...
Context 2
... gradually decaying ripples at either end of the frequency spectra in Figure 4 and Figure 6 are effects resembling the Gibbs effect, both for the filtering methods and the time-signal gating results. In Figure 6, they increase for each subsequent arrival, probably due to the iterative procedure used which inherits these effects from the preceding arrivals. ...
Context 3
... gradually decaying ripples at either end of the frequency spectra in Figure 4 and Figure 6 are effects resembling the Gibbs effect, both for the filtering methods and the time-signal gating results. In Figure 6, they increase for each subsequent arrival, probably due to the iterative procedure used which inherits these effects from the preceding arrivals. The ripples are an inherent feature of the filtering process and may be difficult to reduce. ...
Context 4
... limitations caused by this assumption are discussed in Appendix B. From the increasing deviation between the cepstrum results and the SoS filtering and time-signal gating results in Fig- ure 4, it can be inferred that the multipath arrivals become gradually too strong to fulfill this requirement, starting from approximately 160 kHz. For the frequency range 177-200 kHz, the magnitude of the first multipath arrival is larger than that of the direct arrival, as seen in Figure 6, possibly due to near-field effects. ...
Context 5
... SoS filtering is used to find the multipath results in Figure 6, since it is only SoS filtering that yields relatively good results for the entire studied frequency range, for the example case with í µí°¿ = 0.10 m. However, it is assumed that cepstrum filtering would yield similar multipath results as SoS filtering, for frequencies up to approximately 160 kHz, and that time-signal gating would yield similar multipath results as SoS filtering outside the frequency band around the resonances. ...
Citations
... However, it may also be unnecessary or have adverse effects [4][5][6] . For the special case where the magnitudes of interfering multipath arrivals do not decrease compared to the direct arrival, cepstral filtering will likely yield erroneous results, as shown in [7] . ...
... Time-signal gating is typically used for multipath removal or extraction in frequency domain transfer functions derived from numerical simulations were harmonic time dependence (continuous waves) is assumed [ 2 , 7 ]. It may be used for the special case described above, but generally yields poor results at short distances and for narrowband transducers, for which steady-state conditions may not be not achieved [7] . ...
... An alternative method is presented here, denoted spectrum-of-spectrum (SoS) filtering, which has improved performance compared to the cepstral and time-signal gating methods for the special case where the magnitude of interfering multipath arrivals does not decrease [7] . SoS filtering of the frequency spectrum can be used to extract the direct arrival or any multipath arrival, and can be applied to, e.g., acoustic, electroacoustic, or electromagnetic problems. ...
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.
... In this work, a more complete FE-based system modeling approach that avoids these limitations is implemented, here denoted system Funded by the Research Council of Norway, grant No. 303169. model B, based on [4], [6], [7]. Full FE modeling of the piezoelectric transmitter, fluid medium, and piezoelectric receiver inherently accounts for near-and far-field sound propagation effects, and transmission, reception, and diffraction as experienced by real transducers. ...
... Since these conditions may not always be achieved in measurements with relatively short burst signals, the effects of short signals are included in the system model using timesignal gating. This Fourier-synthesis method [7], adapted from [10], is applied to the calculated H V V 0m6 (L, f ) using burst length and window settings as in the measurements. ...
... An FE model of the transmitter, medium, and receiver is used in system model B. It is based on [10], but reimplemented with improved PML performance and convergence [6]. Since the output of this model is the superposition of the direct arrival and all subsequent multiple reflection between the transmitter and receiver, SoS filtering [7] is applied to extract the direct arrival [6]. ...