Abstract
Discrete Fourier transform (DFT) is the basic means of spectrum analysis in the field of digital signal processing, and the fast Fourier transform (FFT) has become the most popular algorithm which decreases the computational complexity from quadratical to linearithmic. However, engineers are often challenged to detect a single or just a few of the frequency components. For this kind of sparse spectrum analysis, the FFT no longer has advantage because it always computes all the frequency components. This paper proposes a recursive single-bin DFT (RSB-DFT) algorithm to compute one specific frequency spectrum, whose theoretical derivation is elaborated and implementation steps are given as a flow diagram. A 16-point RSB-DFT calculation example is also given to exhibit computation process of the algorithm. An application example for bioimpedance spectroscopy (BIS) measurement demonstrates that the proposed RSB-DFT algorithm can compute specific single spectral lines accurately. The computation efficiency of the proposed RSB-DFT algorithm is demonstrated as the highest compared with the DFT, FFT, Goertzel algorithm, which means that the RSB-DFT algorithm has the potential to become an alternative and efficient tool for sparse spectrum analysis.
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References
Lyons, R.G.: Understanding Digital Signal Processing, 3rd edn. Prentice Hall, Englewood Cliffs (2011)
Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19(90), 297–301 (1965)
Sysel, P., Rajmic, P.: Goertzel algorithm generalized to non-integer multiples of fundamental frequency. EURASIP J. Adv. Sig. Proc. 2012(1), 1–8 (2012)
Ayhan, T., Dehaene, W., Verhelst, M.: A 128:2048/1536 point FFT hardware implementation with output pruning. In: 2014 22nd European Signal Processing Conference (EUSIPCO), pp. 266–270 (2014)
Orallo, C.M., Carugati, I., Donato, P.G., Maestri, S.: Study on Single-bin Sliding DFT algorithms: comparison, stability issues and frequency adaptivity. Measurement 69, 9–19 (2015)
Seoane, F., Ward, L.C., Lindecrantz, K., Lingwood, B.E.: Automated criterion-based analysis for Cole parameters assessment from cerebral neonatal electrical bioimpedance spectroscopy measurements. Physiol. Meas. 33(8), 1363–1377 (2012)
Ward, L.C., Essex, T., Cornish, B.H.: Determination of Cole parameters in multiple frequency bioelectrical impedance analysis using only the measurement of impedances. Physiol. Meas. 27(9), 839–850 (2006)
Wang, T.T.: The segmented chirp-transform and its application in spectrum analysis. IEEE Trans. Instrum. Meas. 39(2), 318–323 (1990)
Duhamel, P., Vetterli, M.: Fast fourier transforms: a tutorial review and a state of the art. Signal Process. 19(4), 259–299 (1990)
Sorensen, H.V., Burrus, C.S.: Efficient computation of the DFT with only a subset of input or output points. IEEE Trans. Signal Process. 41(3), 1184–1200 (1993)
Goertzel, G.: An algorithm for the evaluation of finite trigonometric series. Am. Math. Mon. 65(1), 34–35 (1958)
Sorensen, H., Heideman, M., Burrus, C.: On computing the split-radix FFT. IEEE Trans. Acoust. Speech Signal Process. 34(1), 152–156 (1986)
Onchis, D.M., Rajmic, P.: Generalized Goertzel algorithm for computing the natural frequencies of cantilever beams. Signal Process. 96, Part A, 45–50 (2014)
Liang, L., Tianwei, X., Hong, L.: A recurrence algorithm of FFT. J. Yunnan Normal Univ. 20(2), 20–23 (2000). in Chinese
Yang, Y., Wang, J., Yu, G., Niu, F., He, P.: Design and preliminary evaluation of a portable device for the measurement of bioimpedance spectroscopy. Physiol. Meas. 27(12), 1293–1310 (2006)
Pliquett, U., Barthel, A.: Interfacing the AD5933 for bio-impedance measurements with front ends providing galvanostatic or potentiostatic excitation. J. Phys. 407(1), 012019 (2012)
Sanchez, B., Louarroudi, E., Jorge, E., Cinca, J., Bragos, R., Pintelon, R.: A new measuring and identification approach for time-varying bioimpedance using multisine electrical impedance spectroscopy. Physiol. Meas. 34(3), 339–357 (2013)
Sanchez, B., Bragos, R., Vandersteen, G.: Influence of the multisine excitation amplitude design for biomedical applications using impedance spectroscopy. In: Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 3975–3978 (2011)
Wang, C., Huang, C., Zhang, X., Wang, H.: Mixing Frequency Bio-impedance Measurement, based on DFT and Virtual Reference Vector. In: International Conference on BioMedical Engineering and Informatics, 2008 (BMEI 2008), pp. 455–459 (2008)
Min, M., Pliquett, U., Nacke, T., Barthel, A., Annus, P., Land, R.: Broadband excitation for short-time impedance spectroscopy. Physiol. Meas. 6, S185–S192 (2008)
Gawad, S., Sun, T., Green, N.G., Morgan, H.: Impedance spectroscopy using maximum length sequences: application to single cell analysis. Rev. Sci. Instrum. 78(5), 054301–054307 (2007)
Sanchez, B., Rojas, C.R., Vandersteen, G., Bragos, R., Schoukens, J.: On the calculation of the D-optimal multisine excitation power spectrum for broadband impedance spectroscopy measurements. Meas. Sci. Technol. 23(8), 085702 (2012)
Sanchez, B., Vandersteen, G., Bragos, R., Schoukens, J.: Optimal multisine excitation design for broadband electrical impedance spectroscopy. Meas. Sci. Technol. 22(11), 115601 (2011)
Sanchez, B., Vandersteen, G., Bragos, R., Schoukens, J.: Basics of broadband impedance spectroscopy measurements using periodic excitations. Meas. Sci. Technol. 23(10), 105501 (2012)
Yang, Y., Kang, M., Lu, Y., Wang, J., Yue, J., Gao, Z.: Design of a wideband excitation source for fast bioimpedance spectroscopy. Meas. Sci. Technol. 22(1), 013001 (2011)
Nahvi, M., Hoyle, B.S.: Electrical impedance spectroscopy sensing for industrial processes. Sens. J. IEEE 9(12), 1808–1816 (2009)
Grimnes, S., Martinsen, Ø.G.: Bioimpedance and Bioelectricity Basics, 2nd edn. Elsevier Academic Press, London (2008)
Armstrong, S., Jennings, D.: Current injection electrodes for electrical impedance tomography. Physiol. Meas. 25(4), 797 (2004)
Gonzalez, S.A., Garcia-Retegui, R., Benedetti, M.: Harmonic computation technique suitable for active power filters. IEEE Trans. Industr. Electron. 54(5), 2791–2796 (2007)
Zhang, Y., Song, J., Huang, W.: Harmonie distortion analysis of seismic data acquisition system based on single-bin DFT. In: IEEE 10th International Conference On Signal Processing Proceedings, pp. 34–37 (2010)
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This study has been supported by grants from the Scientific Research Plan of Education Bureau of Shaanxi Province (No. 16JK1370) and the Scientific Research Plan of Science and Technology Bureau of Shaanxi Province (2016GY-051).
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Wang, W., Tang, Y., Zhang, X. et al. Design of a recursive single-bin DFT algorithm for sparse spectrum analysis. Cluster Comput 20, 1483–1492 (2017). https://doi.org/10.1007/s10586-017-0866-8
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DOI: https://doi.org/10.1007/s10586-017-0866-8