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