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      Kesirli fourier dönüşümünün zaman bölgesinde sonlu farklar yöntemine uygulanması

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      Author(s)
      Sayın, I.
      Arıkan F.
      Arıkan, Orhan
      Date
      2010-04
      Source Title
      SIU 2010 - IEEE 18th Signal Processing and Communications Applications Conference
      Publisher
      IEEE
      Pages
      728 - 731
      Language
      Turkish
      Type
      Conference Paper
      Item Usage Stats
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      Abstract
      Bilgisayarların hız ve belleklerinin gelişmesi ile birlikte elektromanyetik problemlerin çözümünde saysal yöntemler sıkça kullanılmaya başlanmış ve bu konuda çok sayda araştırma yapılmıştır. Saysal Elektromanyetik yöntemleri genel olarak zaman ve frekans tabanlı yöntemler olarak sınıflandırılabilir. Zaman tabanlı yöntemler geçici tepkilerin ve geniş bantlı problemlerin incelenmesinde kullanışlı olurken, frekans tabanlı yöntemler durağan hal tepkilerin ve dar bantlı problemlerin incelenmesinde en iyi çözümü vermektedir. Her iki yaklaşımın da avantajlarını ön plana çıkarabilecek bir yöntem geliştirilebileceği düşünülmektedir. Uzayda ve/veya zamanda Kesirli Fourier Dönüşümü uygulanarak bazı durumlarda hesaplama karmaşıklığı azaltılabilir. Kesirli Fourier Dönüşümü, sürekli Fourier Dönüşümünün genelleştirilmiş halidir. Son yıllarda bu konu üzerinde çeşitli çalışmalar yapılmakta ve uygulama alanları genişlemektedir. Genel olarak, sinyal işleme ve gürültü süzme gibi alanlarda kullanılmaktadır. Bu çalmada Kesirli Fourier Dönüşümü, ilk kez Maxwell denklemlerine zaman bölgesinde uygulanmış ve elde edilen diferansiyel denklemler sonlu farklar yaklaşımı ile ayrık hale getirilmiştir. Elde edilen ayrık sonlu fark denklemlerinin çözümü için öneriler sunulmuştur.
       
      With the improvement in the computer speed and memory, Numerical Methods are frequently used in the solution of electromagnetic problems. Numerical Methods can be classified as the frequency domain and the time domain based methods. While the time domain methods are suitable for modeling of the transient response and wideband problems, the frequency domain methods are suitable for modeling of the steady state response and narrow band problems. A numerical method that has the advantages of both time and frequency domain approaches can be developed. Applying Fractional Fourier Transform in space and/or time can reduce the computational complexity for some cases. The Fractional Fourier Transform is a generalization of the continuous Fourier Transform. In last decades, there are several studies and applications concerning this transform. Generally, it is used in signal processing and noise filtering. In this study, Fractional Fourier Transform is applied to the Maxwell's Equations for the first time in literature. Finite difference equations are obtained by the application of finite difference approximation to the differential equations. ©2010 IEEE.
      Keywords
      Computer speed
      Electromagnetic problems
      Finite difference approximations
      Finite difference equations
      Fourier
      Fractional Fourier transforms
      Frequency domains
      Frequency-domain methods
      Maxwell's equations
      Narrow bands
      Noise filtering
      Steady-state response
      Time and frequency domains
      Time domain
      Time-domain methods
      Transient response
      Wide-band
      Computational complexity
      Difference equations
      Finite difference time domain method
      Frequency domain analysis
      Maxwell equations
      Numerical methods
      Signal processing
      Fourier transforms
      Permalink
      http://hdl.handle.net/11693/28475
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/SIU.2010.5653954
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      • Department of Electrical and Electronics Engineering 3702
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