## Main Article Content

## Abstract

Different approaches for a high-resolution analysis of narrow-band spectra are reviewed and compared. Partial-band algorithms are proved to be zoom-FFT's. In this contribution, three new modifications of the (Subband-FFT) SB-FFT are presented. In the first modification the chirp z-transform substitutes the small FFT which calculates the band of interest. In the second modification, the idea of zero-padding the input signal is applied to the SB-FFT with pruning at both input and output. Lastly zooming a small band of frequencies using a method of transforming by parts is applied for a narrow-band signal using the adaptive SB-FFT. A newly introduced version of the subband technique is included also in this work. In this version the subband decomposition technique is combined with the linear prediction method for higher spectrum resolution. Application of the SB-FFT and its modified versions and the new version in measuring the Doppler-frequency directly and indirectly for the purpose of vehicle-speed measurements is introduced in this paper. Comparison between all methods in terms of complexity and resolution is given. A new idea of channel test is included to keep the real-time successive measurements of Doppler frequency stable and consistent as well as simple.

## Keywords

## Article Details

*How to Cite*

*The Journal of Engineering Research [TJER]*,

*8*(1), 1–11. https://doi.org/10.24200/tjer.vol8iss1pp1-11

* * References

- Besson, O. and Castanie, F., 1990, "Doppler Frequency Estimator Performance Analysis," Proceedings ICASSP'90, Albuguerque.
- Blanchet, G. and Charbit, M., 2006, "Digital Signal and Image Processing using MATLAB," Wiley-ISTE.
- Claeben, S., 1991, "Untersuchung Zur Auswertung Von Dopplersignalen Mit Parametrichen Spektralanalyseverfahren," Diplomarheit, AG Digitale Signalverarbeitung, Ruhr- Universität Bochum (in German).
- Harris, F.J., 2004, "Multirate Signal Processing," Prentice Hall.
- Hossen, A.N. and Heute, U., 1993, "Fully Adaptive Evaluation of Sub-Band DFT," Proc. Of IEEE Int. Symp. on Circuits and Syst., Chicago, pp. 655-658.
- Hossen, A.N. and Heute, U., 1994, "Different Approaches for a High-Resolution Narrow-Band Spectrum," Proceedings of EUSIPCO'94, Edinburgh, pp. 1716- 1719.
- Hossen, A. and Heute, U., 2004, "Parametric Modeling of Decomposed Sub-bands: Resolution Improvement and Applications for Narrow-Band Signals," Signal Processing Journal, Vol. 84, pp. 2195-2206.
- Kay Steven, M., 1988, "Modern Spectral Estimation Theory and Applications," Prentice Hall.
- Kleinhempel, W., Stammler, W. and Bergmann, D., 1992” Radar Signal Processing for Vehicle Speed Measurements," EUSIPCO-92, pp. 1829-1832.
- Kuo, S.M. and W-Seng Gan, 2005, "Digital Signal Processing, Architecture, Implementations, and applications," Pearson Education.
- Liu, B. and F. Mintzer, 1978, "Calculation of Narrow- Band Spectra by Direct Decimation," IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-26(6), pp. 529-534.
- Mahafza, B.R. and Elsherbeni, A., 2003, "MATLAB Simulations of Radar System Design," Chapman & Hall/CRC.
- Mahafza, B.R., 2008, "Radar Signal Analysis and Processing using MATLAB," Chapman & Hall/CRC .
- Markel, J.D., 1971, "FFT Pruning," IEEE Trans. Audio and Electroacoustics," Vol. AU-19(4), pp. 305-311.
- Marple Lawrence, S., 1987, "Digital Spectral Analysis with Applications," Prentice Hall. "Matlab Signal Processing Toolbox," 1996, The MathWorks.
- Mitra, S.K., 2006, "Digital Signal Processing, A Computer Based Approach," McGraw-Hill.
- Nagai, K., 1986, "Pruning the Decimation-in-time FFT Algorithm with Frequency Shift," IEEE Trans. Acoust., Speech, Signal Processing, VoI. ASSP-34(4), pp. 1008-10l0.
- Rabiner, L. and R. Schafer., 1969, "The Chirp z- Transform Algorithm and Its Application," Bell Systems, Tech. J. Vol. 48, pp. 1249-1292.
- Rabiner, L.R., Schafer, R.W. and Rader, C.M., 1969, "The Chirp Z-Transform Algorithm and its Application," Bell Syst. Tech. J., Vo1. 48, pp. 1249- 1292.
- Richards, M.A., 2005, "Fundamentals of Radar Signal Processing," McGraw-Hill.
- Roche, C., 1992, "A Split-Radix Partial Input/Output Fast Fourier Transform Algorithm," IEEE Trans. on Signal Processing, Vo1. 40(5), pp.1273-1276.
- Shentov, O.V., Hossen, A.N., Mitra, S.K. and U. Heute, 1991, "Sub-Band DFT-Interpretation, Accuracy, and Computational Complexity," Proc. of 25th Annual Asilomar Conf.Sig., Syst., Comp., Pacific Grove, CA, pp. 95100.
- Sorensen, H.V., Heideman, M.T. and Burrus, C.S., 1986, "On Computing the Split-Radix FFT," IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-34(1), pp. 152-156.
- Sorensen, H.V., Burrus, C.S. and Jones, D..L., 1988, "A New Efficient Algorithm for Computing a Few DFT Points," Proc. of IEEE Int. Symp. on Circuits and Syst., Finland, pp. 1915-1918.
- Sorensen, R.V. and Burrus, C.S., 1993, "Efficient Computation of the DFT with only a Subset of Input or Output Points," IEEE Trans. on Signal Processing, Vol. 41(3), pp. 1l84-1l99.
- Sreenivas, T.V. and Rao, P.V.S., 1980, "High-Resolution Narrow-Band Spectra by FFT Pruning," IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-28(2), pp. 254-257.
- Thrane, N., 1980, "Zoom FFT," Brüel & Kjaer Technical Review, pp. 3-45.
- Weeks, M., 2007, "Digital Signal Processing Using Matlab and Wavelets," Infinity Science Press.
- Wild, R. de., Nieuwkerk, L.R. and Van Sinttruyen, J.S., 1987, "Method for Partial Spectrum Computation," IEE Proceedings, Vol. 134(7), Pt. F, pp. 659-666.

#### References

Besson, O. and Castanie, F., 1990, "Doppler Frequency Estimator Performance Analysis," Proceedings ICASSP'90, Albuguerque.

Blanchet, G. and Charbit, M., 2006, "Digital Signal and Image Processing using MATLAB," Wiley-ISTE.

Claeben, S., 1991, "Untersuchung Zur Auswertung Von Dopplersignalen Mit Parametrichen Spektralanalyseverfahren," Diplomarheit, AG Digitale Signalverarbeitung, Ruhr- Universität Bochum (in German).

Harris, F.J., 2004, "Multirate Signal Processing," Prentice Hall.

Hossen, A.N. and Heute, U., 1993, "Fully Adaptive Evaluation of Sub-Band DFT," Proc. Of IEEE Int. Symp. on Circuits and Syst., Chicago, pp. 655-658.

Hossen, A.N. and Heute, U., 1994, "Different Approaches for a High-Resolution Narrow-Band Spectrum," Proceedings of EUSIPCO'94, Edinburgh, pp. 1716- 1719.

Hossen, A. and Heute, U., 2004, "Parametric Modeling of Decomposed Sub-bands: Resolution Improvement and Applications for Narrow-Band Signals," Signal Processing Journal, Vol. 84, pp. 2195-2206.

Kay Steven, M., 1988, "Modern Spectral Estimation Theory and Applications," Prentice Hall.

Kleinhempel, W., Stammler, W. and Bergmann, D., 1992” Radar Signal Processing for Vehicle Speed Measurements," EUSIPCO-92, pp. 1829-1832.

Kuo, S.M. and W-Seng Gan, 2005, "Digital Signal Processing, Architecture, Implementations, and applications," Pearson Education.

Liu, B. and F. Mintzer, 1978, "Calculation of Narrow- Band Spectra by Direct Decimation," IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-26(6), pp. 529-534.

Mahafza, B.R. and Elsherbeni, A., 2003, "MATLAB Simulations of Radar System Design," Chapman & Hall/CRC.

Mahafza, B.R., 2008, "Radar Signal Analysis and Processing using MATLAB," Chapman & Hall/CRC .

Markel, J.D., 1971, "FFT Pruning," IEEE Trans. Audio and Electroacoustics," Vol. AU-19(4), pp. 305-311.

Marple Lawrence, S., 1987, "Digital Spectral Analysis with Applications," Prentice Hall. "Matlab Signal Processing Toolbox," 1996, The MathWorks.

Mitra, S.K., 2006, "Digital Signal Processing, A Computer Based Approach," McGraw-Hill.

Nagai, K., 1986, "Pruning the Decimation-in-time FFT Algorithm with Frequency Shift," IEEE Trans. Acoust., Speech, Signal Processing, VoI. ASSP-34(4), pp. 1008-10l0.

Rabiner, L. and R. Schafer., 1969, "The Chirp z- Transform Algorithm and Its Application," Bell Systems, Tech. J. Vol. 48, pp. 1249-1292.

Rabiner, L.R., Schafer, R.W. and Rader, C.M., 1969, "The Chirp Z-Transform Algorithm and its Application," Bell Syst. Tech. J., Vo1. 48, pp. 1249- 1292.

Richards, M.A., 2005, "Fundamentals of Radar Signal Processing," McGraw-Hill.

Roche, C., 1992, "A Split-Radix Partial Input/Output Fast Fourier Transform Algorithm," IEEE Trans. on Signal Processing, Vo1. 40(5), pp.1273-1276.

Shentov, O.V., Hossen, A.N., Mitra, S.K. and U. Heute, 1991, "Sub-Band DFT-Interpretation, Accuracy, and Computational Complexity," Proc. of 25th Annual Asilomar Conf.Sig., Syst., Comp., Pacific Grove, CA, pp. 95100.

Sorensen, H.V., Heideman, M.T. and Burrus, C.S., 1986, "On Computing the Split-Radix FFT," IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-34(1), pp. 152-156.

Sorensen, H.V., Burrus, C.S. and Jones, D..L., 1988, "A New Efficient Algorithm for Computing a Few DFT Points," Proc. of IEEE Int. Symp. on Circuits and Syst., Finland, pp. 1915-1918.

Sorensen, R.V. and Burrus, C.S., 1993, "Efficient Computation of the DFT with only a Subset of Input or Output Points," IEEE Trans. on Signal Processing, Vol. 41(3), pp. 1l84-1l99.

Sreenivas, T.V. and Rao, P.V.S., 1980, "High-Resolution Narrow-Band Spectra by FFT Pruning," IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-28(2), pp. 254-257.

Thrane, N., 1980, "Zoom FFT," Brüel & Kjaer Technical Review, pp. 3-45.

Weeks, M., 2007, "Digital Signal Processing Using Matlab and Wavelets," Infinity Science Press.

Wild, R. de., Nieuwkerk, L.R. and Van Sinttruyen, J.S., 1987, "Method for Partial Spectrum Computation," IEE Proceedings, Vol. 134(7), Pt. F, pp. 659-666.