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