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Analysis of Dirichlet, Generalized Hamming and Triangular window functions in the linear canonical transform domain

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Abstract

Linear canonical transform is a four-parameter class of integral transform that plays an important role in many fields of optics and signal processing. Well-known transforms such as the Fourier transform, the fractional Fourier transform, and the Fresnel transform can be seen as the special cases of the linear canonical transform. This paper presents a new mathematical model for obtaining the linear canonical transforms of Dirichlet, Generalized “Hamming”, and Triangular window functions. The different window function parameters are also obtained from the simulations. By changing the value of four parameters and then changing the adjustable parameter, the main-lobe width, −3 dB bandwidth, −6 dB bandwidth and correspondingly, the minimum stop-band attenuation of the resulting window functions can be controlled. It has been shown that by using linear canonical transform, we are able to obtain all window parameters successfully as compared to fractional Fourier transform.

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Authors and Affiliations

  1. Electronics and Communication Engineering Section, YCOE, Punjabi University Guru Kashi Campus, Talwandi Sabo, India

    Navdeep Goel

  2. Department of Electronics and Communication Engineering, Thapar University, Patiala, India

    Kulbir Singh

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  1. Navdeep Goel
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  2. Kulbir Singh
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Correspondence to Navdeep Goel.

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Goel, N., Singh, K. Analysis of Dirichlet, Generalized Hamming and Triangular window functions in the linear canonical transform domain. SIViP 7, 911–923 (2013). https://doi.org/10.1007/s11760-011-0280-2

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  • DOI: https://doi.org/10.1007/s11760-011-0280-2

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