Spectral Analysis of Generalized Triangular and Welch Window Functions using Fractional Fourier Transform.

The paper presents a new closed-form expression for the fractional Fourier transform of generalized Triangular and Welch window functions. Fractional Fourier Transform (FrFT) is a parameterized transform having an adjustable transform parameter which makes it more flexible and superior over ordinary Fourier transform in several applications. It is an important tool used in signal processing for spectral analysis. The analysis of generalized Triangular andWelch window functions in fractional Fourier domain establishes a direct relationship between their FrFTs and fractional angle. Based on the mathematical model obtained, it is observed that adjustable spectral parameters of these functions can be obtained by modifying the fractional angle. The various values of spectral parameters such as half main-lobe width, side lobe fall-off rate and maximum side-lobe level with change in order of fractional Fourier transform are also obtained for these functions. [ABSTRACT FROM AUTHOR]

U radu je prikazan novi izraz za zatvoreni oblik frakcijske Fourierove transformacije poop´cene trokutaste i Welchove prozorske funkcije. Frakcijska Fourierova transformacija (FrFT) parametrizirana je transformacija s podesivim parametrom transformacije koja je u odreženim primjenama fleksibilnija i superiornija u odnosu na uobiˇcajenu Fourierovu transformaciju. Istiˇce se kao važan alat u obradi signala i spektralnoj analizi. Analiza poop´cene trokutaste i Welchove prozorske funkcije u podruˇcju frkacijske Fourierove transformacije uspostavlja izravni odnos izmežu FrFT-a i frakcijskog kuta. Koriste´ci dobiveni matematiˇcki model, uoˇceno je da se podesivi spektralni parametri ovih funkcija mogu izvesti mijenjanjem frakcijskog kuta. Razliˇcite vrijednosti spektralnih parametara, kao što su polovica širine spektralnog vrha, stopa snižavanja amplituda viših harmonika ili najve´ca amplituda viših harmonika, odnosno njihova ovisnost u odnosu na red frakcijske Fourierove transformacije, takožer se mogu odrediti upotrebom ovih funkcija. [ABSTRACT FROM AUTHOR]

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