Original scientific paper
https://doi.org/10.7305/automatika.2016.07.718
Spectral Analysis of Generalized Triangular and Welch Window Functions using Fractional Fourier Transform
Pooja Mohindru
; Department of Electronics and Communication Engineering, University College of Engineering, Punjabi University, Urban Estate Phase II, IN-147002, Patiala, Punjab, India
Rajesh Khanna
; Thapar University,, Department of Electronics and Communication Engineering, Punjab, India
S. S. Bhatia
; School of Mathematics and Computer Applications, Thapar University, Nabha Road, IN-147004, Patiala, Punjab, India
Abstract
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.
Keywords
Fractional Fourier transform; Generalized triangular function; Spectral analysis; Welch window; Window function
Hrčak ID:
165518
URI
Publication date:
1.9.2016.
Visits: 1.788 *