New tuning model for rectangular windowed FIR filter using fractional Fourier transform

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• 作者：Pooja Mohindru (1)
  Rajesh Khanna (2)
  S. S. Bhatia (3)
  
  1. E.C.E. Department ; University College of Engineering ; Punjabi University ; Patiala ; Punjab ; India
  2. Department of Electronics and Communication Engineering ; Thapar University ; Patiala ; 147004 ; Punjab ; India
  3. School of Mathematics and Computer Applications ; Thapar University ; Patiala ; 147004 ; Punjab ; India
  
• 关键词：Window function ; Variable digital filter ; Fractional Fourier transform (FrFT) ; Rectangular window
• 刊名：Signal, Image and Video Processing
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：9
• 期：4
• 页码：761-767
• 全文大小：651 KB
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• 刊物类别：Engineering
• 刊物主题：Signal,Image and Speech Processing
  Image Processing and Computer Vision
  Computer Imaging, Vision, Pattern Recognition and Graphics
  Multimedia Information Systems
  
• 出版者：Springer London
• ISSN：1863-1711

文摘

In this paper, new mathematical model is developed for computing the rectangular windowed low-pass FIR filter transfer function where the rotation angle of fractional Fourier transform is used as a free parameter. By changing the rotation angle in the range from \(0\) to \(\pi /2\) , the transition bandwidth and the stop-band attenuation can be tuned. The closed-form expression derived establishes a direct relationship between magnitude response of the filter and fractional angle of the transform. It is shown that sharp transition bandwidth followed with an increase in the stop-band attenuation can be achieved with the rectangular window for small values of the rotation angle. Digital filters with variable frequency responses can be obtained directly by raising the filter length. This involves recomputation of impulse response coefficients and redesigning of a new filter from the existing one. More number of data registers, multipliers and filter coefficients will be needed, which adds to computational burden. Using proposed fractional Fourier transformation technique, the response characteristics of FIR filter can be tuned during operation by changing only one parameter, while keeping coefficients of the fixed FIR filter unchanged.