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Weaver H.J. — Applications of discrete and continous Fourier analysis
Weaver H.J. — Applications of discrete and continous Fourier analysis

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Название: Applications of discrete and continous Fourier analysis

Автор: Weaver H.J.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1983

Количество страниц: 384

Добавлена в каталог: 21.03.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Airy pattern      228
Algorithm      257
Aliasing      114
Almost band-limited function      119
Almost time-limited function      119
Amplitude      9—10
Aperture function      206 228
Aperture function, circular      208
Aperture function, rectangular      209
Associative law, for convolution      68
Associative law, for two-dimensional convolution      85
Autocorrelation      73
Autocorrelation graph      355
Autocorrelation, and random signals      355 360 362
Autocorrelation, two dimensional      86
Average      328 339
Average, of random signal      360
Band Pass Filter      178—181
Band-limited function      115
Bandwidth      115
Bar chart      246 249
Bar chart, Fourier transform of      249
Bounded support      118
Central limit theorem      350 354
Central tendency      328
Circ function      84
Circ function, Fourier transform of      85
Circular aperature function      208
Circular frequency      9
Circular lens      228
Coefficient of heat capacity      297
Coherent optical system      237
Coherent optical system, resolution of      246
Comb function      131 231 253
Comb function, Fourier transform of      131 253
Commutative law, for convolution      68—69
Commutative law, for two-dimensional convolution      85
Complementary probability      333
Complex exponential function, orthogonality of      41
Complex function, Fourier scries of      44
Complex number      19
Complex number, conjugate of      23
Complex number, exponential form      25
Complex number, imaginary unit element      21
Complex number, modulus of      3
Complex number, polar form      23
Complex number, properties of      19—20 21 26
Complex number, rectangular form      23
Complex number, unit element      21
Complex number, zero element      21
Computer calculated Fourier series      127
Computer calculated Fourier transform      120
Concept of frequency content      10
Conditional probability      334
Conjugate system      364
Constant (step) function      77
Constant (step) function, Fourier transform of      77
Contrast ratio      247
Convolution      68
Convolution theorem      72
Convolution theorem, two-dimensional      86
Convolution, and probability distributions      352—354
Convolution, graphical interpretation      70
Convolution, in two dimensions      85
Convolution, of delta or impulse function      78
Convolution, of Gaussian functions      74
Convolution, of two pulse functions      71—72
Cooley — Tukey algorithm      102
Correlation, statistical      341—346
Cosine function, definition      2
Cosine function, definition, orthogonality of      33
Cosine function, definition, Taylor series expansion of      25
Crosscorrelation      73
Crosscorrelation, of random signal      362
Cubic interpolation      288
Cumulative frequency distribution      325
Cumulative probability density function      339
Degree measure of an angle      6
Delta function      75
Delta function, as unit element under convolution      78
Delta function, Fourier transform of      77
Derivative      9
Derivative algorithms      264—272
Derivative, Fourier transform of      66
Derivative, of Fourier transform      66
Derivative, of trigonometric functions      6
Diffraction equations      202
Diffraction equations, small angle approximation      204
Digital filter      258
Dirac function      75
Dirac function, as unit element under convolution      78
Dirac function, Fourier transform of      77
Direct Fourier transform      55
Dirichlet conditions      32
Discrete Fourier Transform      91 92
Discrete Fourier transform, first shifting theorem      96
Discrete Fourier transform, linearity of      95
Discrete Fourier transform, negative indices of      94
Discrete Fourier transform, of discrete Fourier transform      97
Discrete Fourier transform, of first forward difference      98
Discrete Fourier transform, of odd/even sequences      99
Discrete Fourier transform, of real/imaginary sequences      100
Discrete Fourier transform, periodicity of      93
Discrete Fourier transform, reciprocity of      92
Discrete Fourier transform, second shifting theorem      96
Discrete Fourier transform, simultaneous calculation of 3 real sequences      100
Discrete Fourier transform, symmetry relations of      99
Distributive law, for convolution      69
Distributive law, two-dimensional convolution      85
Duhamel integral      68
d’Alembert’s solution      185
Eigenfunction      154
Eigenfunction, of digital filter      260
Electrical capacitor/resistor/inductor      170—172
Ensemble      360
Ergodicity principle      368
Euler’s equations      25
Even function      47
Even sequences      99
Expected value      335 360 363
Exponential form of complex number      25
Exponential function      60
Exponential function, Fourier transofrm of      61
Exponential function, Taylor series expansion of      25
Factorial form      275
Factorial form, first forward difference of      275
Far field region      207—208
Fast Fourier transform, Cooley Tukey      102
Fast Fourier transform, mixed radix      106
Feedback system      152
Finite difference calculus      275—278
Finite Fourier cosine transform      297 299
Finite Fourier cosine transform, of second derivative      299
Finite Fourier sine transform      297 298
Finite Fourier sine transform, of second derivative      298
First central difference      269
First central difference, transfer function of      269
First forward difference      97 264
First forward difference, of discrete Fourier transform      98
First forward difference, transfer function of      265
First shifting theorem, for discrete Fourier transform      96
First shifting theorem, for Fourier series      43
First shifting theorem, for Fourier transform      62
First shifting theorem, for two-dimensional Fourier transform      81
Forward difference of factorial form      275
Fourier series      33
Fourier Series, first shifting theorem      43
Fourier series, linearity of      43
Fourier Series, of complex function      40 44
Fourier Series, of monchromatic functions      52
Fourier Series, of odd/even functions      49
Fourier Series, of pulse function      130
Fourier Series, of triangle function      37
Fourier series, properties of      42
Fourier Series, second shifting theorem      46—47
Fourier Series, truncated      233
Fourier Series, via digital computer      127
Fourier transform      55
Fourier transform, derivative of      66
Fourier transform, first shifting theorem      62
Fourier transform, frequency content      58
Fourier transform, linearity of      62
Fourier transform, of circ function      85
Fourier transform, of comb function      130 253
Fourier transform, of constant (step) function      77
Fourier transform, of delta or impulse function      77
Fourier transform, of exponential function      61
Fourier transform, of Fourier transform      65
Fourier transform, of Gaussian function      67
Fourier transform, of pulse function      59
Fourier transform, of rectangle function      82
Fourier transform, of separable function      82
Fourier transform, of shifted pulse function      64
Fourier transform, of sine function      65 121
Fourier transform, of the derivative      66
Fourier transform, properties of      62
Fourier transform, scale change      65
Fourier transform, scaled      207
Fourier transform, second shifting theorem      64
Fourier transform, summetry relations      75
Fourier transform, two dimensional      80—81
Fourier transform, via digital computer      120
Fourier — Bessel transform      84
Fraunhofer diffraction equation      207
Free space transfer function      212
frequency      9
Frequency content      16
Frequency content, concept of      10
Frequency content, Fourier series      32
Frequency content, Fourier transform      58
Frequency distribution, statistical      325
Frequency domain plot      18 26—27 59
Fresnel diffraction equation, as Fourier transform      206
Fresnel diffraction equation, first form      203
Fresnel diffraction equation, Fourier transform of first form      215
Fresnel diffraction equation, Fourier transform of second form      212 214
Fresnel diffraction equation, second form      206
Gaussian function      67 208
Gaussian function, and windowing      136
Gaussian function, convolution of      74
Gaussian function, Fourier transform of      67
Gaussian function, self-reciporicity of      67
Geometrical optics imaging equation      221 224
Gibb’s effect      34 39 134 136 307
Grad, measure of an angle      6
Hannkel transform      84
Heat equation      295
Heat equation, two-dimensional      297
Heat flow in infinite one-dimensional body      316
Heaviside operator      151
Helmholtz equation      183 185
High pass filter      177
High pass filter, transfer function of      178
Huygen — Fresnel principle      199
Image      220
Image, out of focus      226
Image, virtual      222
Imaginary function      75
Imaginary sequences      100
Imaging equation of geometrical optics      221 224
Impulse function      75
Impulse function, as unit clement under convolution      78
Impulse function, Fourier transform of      77
Impulse response      152
Impulse response, and transfer function      156
Impulse response, of optical system      229
Incoherent image      240
Incoherent optical system      237
Incoherent optical system, resolution of      247
Independent events      333
Integration algorithms      276—286
Interpolation algorithms      286—289
Invariance      150
Invariance, of otical system      230
Invariance, of recursive algorithm      274
Inverse clement of a complex number      22
Inverse discrete Fourier transform      92
Inverse Fourier transform      55
Joint probability      333—335
Kirchoff s law      174
Laplace equation      310
Law of Large Numbers      332
Lawrence Livermore National Laboratory      135
Line pairs, optical      246
Linear correlation analysis      343
Linear interpolation      286
Linearity, of discrete Fourier transform      95
Linearity, of Fourier series      43
Linearity, of Fourier transform      62
Linearity, of optical system      229
Linearity, of recursive algorithm      274
Linearity, of system      150
Linearity, of two-dimensional Fourier transform      81
Lorentzian function      176
Low pass filter      175
Low pass filter, impulse response of      177
Low pass filter, synthesis of      291—292
Low pass filter, transfer function of      174
Mass-spring-damper system      164
Maxwell’s equations      196
Mean deviation      328
Mean of an angle      6
Mean of continuous probability distribution      340
Mean of function      347
Mechanical spring-damper      162
Mechanical system      159
Mechanical/electrical systems, differential equations of      159
Mechanical/electrical systems, transfer function of      160
Mixed radix fast transforms      106
Modulation transfer function (MTF)      239
Modulus of complex number      23
Monochromatic function, Fourier series of      52
Monochromatic light      198
Mutually exclusive event      333
Near field region      209
Negative indices of the discrete Fourier transform      94
Newton’s theorem      276—278
Nonrecursive filter, sythcscs of      290—293
Nonrecursive smoothing algorithms      261—263
nth forward difference      265
nth moment of a function      347
nth order sequence      90
nth order sequence, multiplication by a constant      91
nth order sequence, product of      90
nth order sequence, sum of      90
Nyquist rate      117
Odd function      47
Odd sequences      99
One-dimensional heat flow, ends at different constant temp      302
One-dimensional heat flow, ends at specified variable temp      306
One-dimensional heat flow, ends at zero temp      299
One-dimensional heat flow, ends insulated      309
Optical line pairs      231 240
Optical spectrum      196
Optical system resolution      242
Optical Transfer Function (OTF)      239
Orthogonality, of comlex exponential      41
Orthogonality, of trigonometric functions      33
Out of focus image      22
Parameter, statistical      324
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