The fourier transform and its applications / Ronald N Bracewell
Por: Bracewell, Ronald N [Autor].
Tipo de material: LibroEditor: New York McGraw-Hill 2000Descripción: 616 p.ISBN: 0073039381.Tema(s): TRANSFORMACION DE FOURIER | TRANSFORMATIONS MATEMATICAS | ANALISIS HARMONICO | ESTADISTICA | LITERATURA EN IDIOMA INGLESClasificación CDD: 515 Resumen: GROUNDWORK. The Fourier transform and Fourier’s integral theorem. Conditions for the existence of Fourier transform. Transforms in the limit. CONVOLUTION. Examples of convolution. Serial products. Convolution by computer. NOTATION FOR SOME USEFUL FUNCTIONS. Rectangle function of unit height and base, II. Triangle function of unit height and area. Heaviside´s unit step function. THE IMPULSE SYMBOL. The sifting property. The sampling or replicating symbol III. The even and odd impulse pairs II. THE BASIC THEOREMS. A few transforms for illustration. Similarity theorem. Addition theorem. OBTAINING TRANSFORM. Integration in closed form. Numerical Fourier transformation. The slow Fourier transform program. THE TWO DOMAINS. Definite integral. The first moment. Centroid. WAVEFORMS, SPECTRA, FILTERS, AND LINEARITY. Electrical waveforms and spectra. Filters. Generality of linear filter theory. SAMPLING AND SERIES. Sampling theorem. Interpolation. Rectangular filtering in frequency domain. THE DISCRETE FOURIER TRANSFORM AND THE FFT. The discrete transform formula. Cyclic convolution. Examples of discrete Fourier transforms. THE DISCRETE HARTLEY TRANSFORM. A strictly reciprocal real transform. Notation and example. The discrete Hartley transform. RELATIVES OF THE FOURIER TRANSFORM. The two-dimensional Fourier transform. Two-dimensional convolution. The hankel transform. THE LAPLACE TRANSFORM. Convergence of the Laplace integral. Theorems for the Laplace transform. Transient-response problems. ATENNAS AND OPTICS. One-dimensional apertures. Analogy with waveforms and spectra. Beam width and aperture width. APPLICATIONS IN STATISTICS. Distribution of a sum. Consequences of the convolution relation. The characteristic function. RANDOM WAVEFORMS AND NOISE. Discrete representation by random digits. Effect on autocorrelation. Effect on spectrum. HEAT CONDUCTION AND DIFFUSION. One-dimensional diffusion. Gaussian diffusion from a point. Diffusion of a spatial sinusoid. DYNAMIC POWER SPECTRA. The concept of dynamic spectrum. The dynamic spectrograph. Equivalence theorem.Tipo de ítem | Ubicación actual | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras | Reserva de ejemplares |
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GROUNDWORK. The Fourier transform and Fourier’s integral theorem. Conditions for the existence of Fourier transform. Transforms in the limit. CONVOLUTION. Examples of convolution. Serial products. Convolution by computer. NOTATION FOR SOME USEFUL FUNCTIONS. Rectangle function of unit height and base, II. Triangle function of unit height and area. Heaviside´s unit step function. THE IMPULSE SYMBOL. The sifting property. The sampling or replicating symbol III. The even and odd impulse pairs II. THE BASIC THEOREMS. A few transforms for illustration. Similarity theorem. Addition theorem. OBTAINING TRANSFORM. Integration in closed form. Numerical Fourier transformation. The slow Fourier transform program. THE TWO DOMAINS. Definite integral. The first moment. Centroid. WAVEFORMS, SPECTRA, FILTERS, AND LINEARITY. Electrical waveforms and spectra. Filters. Generality of linear filter theory. SAMPLING AND SERIES. Sampling theorem. Interpolation. Rectangular filtering in frequency domain. THE DISCRETE FOURIER TRANSFORM AND THE FFT. The discrete transform formula. Cyclic convolution. Examples of discrete Fourier transforms. THE DISCRETE HARTLEY TRANSFORM. A strictly reciprocal real transform. Notation and example. The discrete Hartley transform. RELATIVES OF THE FOURIER TRANSFORM. The two-dimensional Fourier transform. Two-dimensional convolution. The hankel transform. THE LAPLACE TRANSFORM. Convergence of the Laplace integral. Theorems for the Laplace transform. Transient-response problems. ATENNAS AND OPTICS. One-dimensional apertures. Analogy with waveforms and spectra. Beam width and aperture width. APPLICATIONS IN STATISTICS. Distribution of a sum. Consequences of the convolution relation. The characteristic function. RANDOM WAVEFORMS AND NOISE. Discrete representation by random digits. Effect on autocorrelation. Effect on spectrum. HEAT CONDUCTION AND DIFFUSION. One-dimensional diffusion. Gaussian diffusion from a point. Diffusion of a spatial sinusoid. DYNAMIC POWER SPECTRA. The concept of dynamic spectrum. The dynamic spectrograph. Equivalence theorem.
Bracewell, Ronald N 2000 2000
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