Abstract
A simple but versatile hyperbolic cosine window function is presented in this paper, which has two terms in the time domain. A parameter p in the window can be varied to make the mainlobe width of the window function to approach that of a rectangular window (\(\pm 1/T,\)) while maintaining higher sidelobe decay (12 dB/octave.) Even though such behavior has been demonstrated by the two-term polynomial window, it suffers from the limitation that only some discrete values of mainlobe widths can be achieved in the range, \(\pm 1/T\) to \(\pm 1.5/T\). The proposed hyperbolic cosine window has no such limitation; one can achieve any desired value of mainlobe width in the above range. The proposed window can be employed for applications involving spectral resolution.
Similar content being viewed by others
References
R.N. Bracewell, The Fourier Transform and Its Applications, 3rd edn. (Tata McGraw-Hill, New Delhi, 2003), p. 152
F.J. Harris, On the use of windows for harmonic analysis with discrete Fourier transform. Proc. IEEE 66(1), 51–83 (1978)
R.G. Kulkarni, S.K. Lahiri, Improved sidelobe performance of cosine series functions. IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC–46(2), 464–466 (1999)
R.G. Kulkarni, Asymptotic behavior of cosine windows. Microwav. J. 43(10), 96–104 (2000)
R.G. Kulkarni, Polynomials for narrowband signal processing. IEE Proc. Vis. Image Signal Process. 149(3), 159–161 (2002)
R.G. Kulkarni, Polynomial windows with fast decaying sidelobes for narrow-band signals. Signal Process. 83(6), 1145–1149 (2003)
D.C. Malocha, C.D. Bishop, The classical truncated cosine series functions with applications to SAW filters. IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC–34, 75–85 (1987)
A.H. Nuttall, Some windows with very good sidelobe behavior. IEEE Trans. Acoust. Speech Signal Process. ASSP – 29(1), 84–91 (1981)
K.J. Parker, Apodization and windowing functions. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60(6), 1263–1271 (2013)
S. Starosielec, D. Hagele, Discrete-time windows with minimal RMS bandwidth for given RMS temporal width. Signal Process. 102, 240–246 (2014)
Acknowledgements
The author thanks the management of PES University for supporting this work. The valuable comments of Associate Editor and the anonymous referees improved the manuscript considerably.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kulkarni, R.G. A Versatile Hyperbolic Cosine Window for Spectral Resolution. Circuits Syst Signal Process 38, 2380–2386 (2019). https://doi.org/10.1007/s00034-018-0964-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-018-0964-8