Fixed Windows in Fractional Fourier Domain

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Rahul Pachauri 1,* Sanjeev N. Sharma 2 Rajiv Saxena 1

1. Jaypee University of Engineering & Technology, Guna (M.P.), India

2. Samrat Ashok Technological Institute, Vidisha (M.P.), India

* Corresponding author.


Received: 3 Oct. 2013 / Revised: 3 Nov. 2013 / Accepted: 28 Nov. 2013 / Published: 8 Jan. 2014

Index Terms

Fractional Fourier Transform, Null Bandwidth, Half Main Lobe Width, Maximum Side Lobe Level


In this study, some mathematical relations have been derived for the useful parameters of fixed window functions in fractional Fourier transform (FRFT) domain. These reported expressions are also verified with the simulation studies. The FRFT provides an important extension to conventional Fourier transform with an additional degree of freedom by which these parameters of window functions can be controlled while inherent time domain behavior of the windows remains intact. The behavior of fixed windows on time-frequency plane has been varied by varying the FRFT order. The obtained variability in the window functions has been applied in the designing of FIR filters.

Cite This Paper

Rahul Pachauri,Rajiv Saxena,Sanjeev N. Sharma,"Fixed Windows in Fractional Fourier Domain", IJIGSP, vol.6, no.2, pp.1-13, 2014. DOI: 10.5815/ijigsp.2014.02.01


[1]L.R. Rabiner, B. Gold. Theory and Applications of Digital Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1975.

[2]F. J. Harris. On the use windows for harmonic analysis with discrete Fourier transform. Proc. IEEE, 1978, 66(1):51-83.

[3]L. B. Almeida. The fractional Fourier transform and time-frequency representation. IEEE Trans., Signal Processing, 1994, 42(11): 3084-3093. 

[4]V. Namias. The fractional order Fourier transform and its application to quantum mechanics. J. Inst. Math., 1980, Appl. 25:241-265.

[5]H. M. Ozaktas, Z. Zalevsky, M. A. Kutey. The Fractional Fourier transform with Applications in Optics and Signal processing. 1st ed., Wiley, Newyork, 2001.

[6]S. Kumar, K. Singh, R. Saxena. Analysis of Dirichlet and Generalized Hamming window functions in fractional Fourier transform domain. Signal Processing, 2011, 91:600-606.

[7]S. N. Sharma, R. Saxena, S. C. Saxena. Tuning of FIR filter transition bandwidth using fractional Fourier transform. Signal Processing, 2007, 87: 3147-3154.

[8]R. Saxena. Synthesis and characterization of new window families with their applications. Ph. D. Dissertation, Department of Electronics and Computer Engineering, University of Roorkee (Presently IIT Roorkee), India, 1996.

[9]D. L. Donoho, P.B. Stark. Uncertainty principles and signal recovery. SIAM J. Apll. Maths. 1989, 49(3): 906-931.

[10]J. G. Proakis, D. G. Manolakis. Digital signal processing, principles, algorithms, and applications. Prentice-Hall, 2007. 

[11]J. K. Gautam, A. Kumar, R. Saxena. On the modified Bartlett-Hanning window (family). IEEE Trans., Signal Processing, 1996, 44 (8): 2098-2102. 

[12]N. C. Geckinli, D. Yavuz. Some novel windows and a concise tutorial comparison of window families. IEEE Trans., Acoustics, speech, and Signal Processing, 1978, 26 (6): 501-507.

[13]A. Antoniou. Digital signal processing: signals, systems, and filters. McGraw-Hill, 2005.