Browsing by Keywords "Fractional Fourier transforms"
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Digital computation of the fractional Fourier transform
(Institute of Electrical and Electronics Engineers, 199609)An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with timebandwidth product N, the presented algorithm computes the fractional transform in O(NlogN) time. A ... 
Digital Fourier optics
(Optical Society of America, 19960310)Analog Fourier optical processing systems can perform important classes of signal processing operations in parallel, but suffer from limited accuracy. Digital–optical equivalents of such systems could be built that share ... 
Fast and accurate algorithm for the computation of complex linear canonical transforms
(Optical Society of America, 20100805)A fast and accurate algorithm is developed for the numerical computation of the family of complex linear canonical transforms (CLCTs), which represent the inputoutput relationship of complex quadraticphase systems. ... 
Fast computation of the ambiguity function and the Wigner distribution on arbitrary line segments
(IEEE, 2001)By using the fractional Fourier transformation of the timedomain signals, closedform expressions for the projections of their auto or cross ambiguity functions are derived. Based on a similar formulation for the projections ... 
Fractional Fourier domains
(Elsevier BV, 199509)It is customary to define the timefrequency plane such that time and frequency are mutually orthogonal coordinates. Representations of a signal in these domains are related by the Fourier transform. We consider a continuum ... 
The fractional fourier transform
(IEEE, 2001)A brief introduction to the fractional Fourier transform and its properties is given. Its relation to phasespace representations (time or spacefrequency representations) and the concept of fractional Fourier domains are ... 
Fractional Fourier transforms and their optical implementation. II
(Optical Society of America, 1993)The derivation of a linear transform kernel for fractional Fourier transforms is presented. Discussed in direct relation to fractal Fourier transforms are spatial resolution and the spacebandwidth product for propagation ... 
Fundamental structure of Fresnel diffraction: Longitudinal uniformity with respect to fractional Fourier order
(Optical Society of America, 20111224)Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. Transverse samples can be taken on these surfaces with ... 
Generalization of timefrequency signal representations to joint fractional Fourier domains
(IEEE, 200509)The 2D signal representations of variables rather than time and frequency have been proposed based on either Hermitian or unitary operators. As an alternative to the theoretical derivations based on operators, we propose ... 
Generalized filtering configurations with applications in digital and optical signal and image processing
(Bilkent University, 1999)In this thesis, we first give a brief summary of the fractional Fourier transform which is the generalization of the ordinary Fourier transform, discuss its importance in optical and digital signal processing and its ... 
Image processing with the fractional Fourier transform: synthesis, compression and perspective projections
(Bilkent University, 2000)In this work, first we give a summary of the fractional Fourier transform including its definition, important properties, generalization to twodimensions and its discrete counterpart. After that, we repeat the concept ... 
Kesirli fourier dönüşümü genliklerinden karmaşık sinyallerin geri kazanımı
(IEEE, 200404)Bu makalede kesirli Fourier dönüşümü genlikleri kullanılarak karmaşık sinyallerin evrelerinin bulunması üzerinde durulmuştur. Bu aynı zamanda optik eksende enine boyuna rastgele iki yerde yapılan genlik ölçümlerinden evre ... 
Kesirli fourier dönüşümünün zaman bölgesinde sonlu farklar yöntemine uygulanması
(IEEE, 201004)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 ... 
Linear algebraic analysis of fractional Fourier domain interpolation
(IEEE, 2009)In this work, we present a novel linear algebraic approach to certain signal interpolation problems involving the fractional Fourier transform. These problems arise in wave propagation, but the proposed approach to these ... 
Linear canonical transforms, degrees of freedom, and sampling in optical signals and systems
(IEEE, 2014)We study the degrees of freedom of optical systems and signals based on spacefrequency (phasespace) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the spacefrequency ... 
A new approach to timefrequency localized signal design
(IEEE, 2002)A novel approach is presented for the design of signals in Wigner Domain. In this method, the desired signal features in the timefrequency domain are specified in two stages. First the user specifies the spine curve around ... 
Nonorthogonal domains in phase space of quantum optics and their relation to fractional Fourier transforms
(Elsevier BV * NorthHolland, 19951015)It is customary to define a phase space such that position and momentum are mutually orthogonal coordinates. Associated with these coordinates, or domains, are the position and momentum operators. Representations of the ... 
Nonseperable twodimensional fractional Fourier transform
(Optical Society of America, 1998)Previous generalizations of the fractional Fourier transform to two dimensions assumed separable kernels. We present a nonseparable definition for the twodimensional fractional Fourier transform that includes the separable ... 
Relationships among ray optical, Gaussian beam, and fractional Fourier transform descriptions of firstorder optical systems
(Elsevier BV * NorthHolland, 19971101)Although wave optics is the standard method of analyzing systems composed of a sequence of lenses separated by arbitrary distances, it is often easier and more intuitive to ascertain the function and properties of such ... 
Repeated fractional Fourier domain filtering is equivalent to repeated time and frequency domain filtering
(Elsevier BV, 199610)Any system consisting of a sequence of multiplicative filters inserted between several fractional Fourier transform stages, is equivalent to a system composed of an appropriately chosen sequence of multiplicative filters ...