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Low-Order Filter Implementations

Figure 47: Removing the peak of the measured radiation response at $ 127$ Hz. The plot shows the signal from time 0 to $ 3$ s.
Image rad_response_peak_removed

Figure 48: FFT of the measured radiation response with the peak at $ 127$ Hz removed. The plot shows the magnitude at frequencies between $ 50$ Hz to $ 500$ Hz.
Image rad_response_peak_removed_fft

Using the same techniques described in Section 4.3.1, a reduction in the length of the resulting transfer function can be made by factoring out frequency components of the signal with the most energy and replacing them with low-order resonators. Both Complex Spectral Subtraction and inverse-filtering methods can be used. However, as done for the body response, we opt to use inverse-filtering. Figures 47 and  48 show the results of removing the peak centered around $ 127$ Hz with a bandwidth of $ 10$ Hz. Similar to the results obtained in Section 4.3.1, the radiation response is significantly shortened. As Figure 47 shows, the residual signal approaches 0 within $ 0.1$ s. Whereas, as shown in Figure 45 shows, the radiation response lasts for well over $ 1$ s. Furthermore, the peak in the spectral domain is entired removed. As shown in Figure 48, the peak is close to $ 60$ dBs lower than the peak at $ 127$ Hz in the original radiation response shown in Figure 46.

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``Virtual Stringed Instruments'', by Nelson Lee and Julius O. Smith III,
REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .
Released 2008-02-20 under the Creative Commons License (Attribution 2.5), by Nelson Lee and Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University