Analysis of Dirichlet and Generalized “Hamming” window functions in the fractional Fourier transform domains

Fixed Windows in Fractional Fourier Domain

“…, Prior to this work, analysis of some window functions in FRFT domain has been carried out by Kumar et al [6], and it has been observed that the window parameters can be varied by changing the FRFT order. However, no mathematical relationships have been established between window parameters and FRFT order in [6].…”

“…However, no mathematical relationships have been established between window parameters and FRFT order in [6]. It has been shown in [6] that when FRFT order is decreased from 1 to 0, the MSLL and SLFOR increase while HMLW decreases.…”

“…However, no mathematical relationships have been established between window parameters and FRFT order in [6]. It has been shown in [6] that when FRFT order is decreased from 1 to 0, the MSLL and SLFOR increase while HMLW decreases. Same methodology has been used earlier in [7] to tune the Transition Bandwidth (TBW) of Kaiser Window [2] and PC6 window [8] based FIR filters using FRFT.…”

Spectrum shaping analysis using tunable parameter of fractional based Bartlett window

“…In [10] fractional Kaiser and PC6 window function is used to show that main lobe width of the window function is dependent on a tunable parameter by which it can be controlled. In [11], Dirichlet and generalized Hamming window functions are solved in the fractional domains. Taking the work of [11] one step forward we have solved Bartlett window function in fractional Fourier domain.…”

“…In [11], Dirichlet and generalized Hamming window functions are solved in the fractional domains. Taking the work of [11] one step forward we have solved Bartlett window function in fractional Fourier domain. We have shown that the main lobe width of the central lobe is dependent on a tunable parameter α, which is also called the angle of the FRFT and is related to the order of the FRFT i.e.…”