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Error Analysis of Sound Source Directivity Interpolation Based on Spherical Harmonics

Szwajcowski Adam, Krause Daniel, Snakowska Anna

Archives of Acoustics

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2021

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Vol. 46, No. 1

95--104

EN

Precise measurement of the sound source directivity not only requires special equipment, but also is time-consuming. Alternatively, one can reduce the number of measurement points and apply spatial interpolation to retrieve a high-resolution approximation of directivity function. This paper discusses the interpolation error for different algorithms with emphasis on the one based on spherical harmonics. The analysis is performed on raw directivity data for two loudspeaker systems. The directivity was measured using sampling schemes of different densities and point distributions (equiangular and equiareal). Then, the results were interpolated and compared with these obtained on the standard 5° regular grid. The application of the spherical harmonic approximation to sparse measurement data yields a mean error of less than 1 dB with the number of measurement points being reduced by 89%. The impact of the sparse grid type on the retrieval error is also discussed. The presented results facilitate optimal sampling grid choice for low-resolution directivity measurements.

2

Offset compensated baseline restoration and computationally efficient hybrid interpolation for the brain PET

Qaisar S. M.

Bio-Algorithms and Med-Systems

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2018

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Vol. 14, no. 4

art. no. 20180031

EN

The acquisition of positron emission tomography (PET) pulses introduces artifacts and limits the performance of the scanner. To minimize these inadequacies, this work focuses on the design of an offset compensated digital baseline restorer (BLR) along with a two-stage hybrid interpolator. They respectively treat the incoming pulse offsets and limited temporal resolution and improve the scanner performance in terms of calculating depth of interactions and line of responses. The offset of incoming PET pulses is compensated by the BLR and then their interesting parts are selected. The selected signal portion is up-sampled with a hybrid interpolator. It is composed of an optimized weighted least-squares interpolator (WLSI) and a simplified linear interpolator. The processes of calibrating the WLSI coefficients and characterizing the BLR and the interpolator modules are described. The functionality of the proposed modules is verified with an experimental setup. Results have shown that the devised BLR effectively compensates a dynamic range of bipolar offsets. The signal selection process allows focusing only on the relevant signal part and avoids the unnecessary operations during the post-interpolation process. Additionally, the hybrid nature allows improving the signal temporal resolution with an appropriate precession at a reduced computational complexity compared to the mono-interpolationbased arithmetically complex counterparts. The component-level architectures of the BLR and the interpolator modules are also described. It promises an efficient integration of these modules in modern PET scanners while using standard and economical analog-to-digital converters and field-programmable gate arrays. It avoids the development of high-performance and expensive application-specific integrated circuits and results in a costeffective realization.

3

On approximation and interpolation errors of analytic functions

Kumar D.

Fasciculi Mathematici

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2007

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Nr 38

47-56

EN

Kasana and Kumar [5] obtained the (p. q)—growth parameters in terms of Chebyshev and interpolation errors for entire functions on a compact set E of positive transfinite diameter. Rizvi and Nautiyal [9] studied the order and type in terms of these errors for the functions which are not entire. But these results do not give any specific information about the growth of non-entire functions if maximum modules is increasing so rapidly that the order of function is infinite. In this paper an attempt has been made to extend the results contained in [9] for functions having rapidly increasing maximum modulus.