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| Авторизация |
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| Поиск по указателям |
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| Weaver H.J. — Applications of discrete and continous Fourier analysis |
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| Предметный указатель |
Parseval's energy formula 74
Parseval's energy formula, two-dimensional 86
Pearson’s r coefficient 343 358
Period 10
Periodic function 34
Periodicity of discrete Fourier transform 93
Phase 10
Point source of light 213 227
Point spread function 229 231 242
Polar form of complcx number 23
Population 324
Population space 331
Power spectrum 367
probability 331
Probability density function 337
probability distribution 335
Product of nth order sequences 90
Product theorem 73
Product theorem, two-dimensional 86
Protracted function 34
Pulse function 59
Pulse function, as a window 135
Pulse function, Fourier series of 60 130
Pulse function, Fourier transform of 59
Quantization 115
Radial frequency 10
Radial symmetric function 83—84
Radian, measure of an angle 6
Random function 335 359
Raw data 324
Rayleigh resolution criterion 243
Real function 75
Real sequences 100
Real world sampling theorem 119
Reciprocity of the discrete Fourier transform 92
Rectangle function 82
Rectangle function, Fourier transform of 82
Rectangular aperture 209—210
Rectangular form of complex number 23
Recursive algorithms 272—274
Recursive algorithms, transfer function of 273
Resolution, of coherent optical system 246
Resolution, of incoherent optical system 247
Resolution, of optical systems 242
Sample, statistical 324
Sampling a function 113
Sampling rate 113 115 117 118
Sampling theorem 117
Sampling theorem, real world 119
Sampling theory, optical illustraton 251
Sampling via the comb function 132
Scalar wave equation 182
Scale change, two-dimensional Fourier transform 81
Scaled Fourier transform 207
Second central difference 270
Second central difference, transfer function of 271
Second forward difference 265
Second forward difference, transfer function of 267
Second shifting theorem, Fourier series 46—47
Second shifting theorem, Fourier transform 64
Second shifting theorem, of discrete Fourier transform 96
Second shifting theorem, two-dimensional Fourier transform 81
Separable function 82
Separable function, Fourier transform of 82
simple harmonic motion 6
Simpson’s  rule 282
Simpson’s  rule 284
Sinc function 2
Sinc function, Fourier transform of 65 121
Sine function 2
Sine function, orthogonality of 33
Sine function, Taylor series expansion of 25
Sinusoidal motion 6
Smoothing algorithms 261—263
Space-limited function 118
Spatial filtering 248
Spatial transfer function, of infinite string 184
Standard deviation 329
Stastics, definition 323
Stationary system 150 366
| Statistical variable 324
Sum of nth order sequences 90
Super — Gaussian function 136
Symmetry relations, of discrete Fourier transform 99
Synthesis of nonrecursivc filters 290—293
system 150
System, conjugate of 364
System, feedback 152
System, impulse response 152
System, linearity of 150
System, mechanical 159
System, stationary 366
Taylor series, of exponential function 25
Taylor series, of trigonometric functions 25
thermal conductivity 295
Thin lens 217—221
Thin lens, imaging properities of 223
Time-limited function 118
Transfer function, and impulse response 156
Transfer function, free space 212
Transfer function, general mechanical/electrical system 160
Transfer function, low pass filter 174
Transfer function, mass-spring-damper system 164
Transfer function, of capacitor 172
Transfer function, of cubic interpolation 289
Transfer function, of first forward difference 265
Transfer function, of hi pass filter 178
Transfer function, of inductor 171—172
Transfer function, of infinite string, spatial 184
Transfer function, of infinite string, temporal 185
Transfer function, of linear interpolation 288
Transfer function, of mechanical damper 162
Transfer function, of mechanical spring 162
Transfer function, of optical system 231
Transfer function, of recursive algorithms 273
Transfer function, of resistor 170—171
Transfer function, of second central difference 271
Transfer function, of second forward difference 267
Transfer function, of Simpson’s rule 283
Transfer function, of Simpson’s rule 284
Transfer function, of smoothing by five’s digital filter 262
Transfer function, of smoothing by three’s digital filter 261
Transfer function, of trapezoidal rule 280
Transfer function, R — L — C circuit 172—174
Transfer function, system 154
Transverse vibration of infinite string 182
Transverse vibrations of finite spring 188—193
Trapezoidal rule 280
Triangle function 37
Trionometric functions 2
Trionometric functions, derivative of 6
Trionometric functions, Taylor series expansion of 25
Truncated Fourier series 233
Two-dimensional, autocorrelation 86
Two-dimensional, convolution 85
Two-dimensional, convolution theorem 86
Two-dimensional, Fourier transform 80
Two-dimensional, Fourier transform, first shifting theorem 81
Two-dimensional, Fourier transform, linearity of 81
Two-dimensional, Fourier transform, of Fourier trasform 81
Two-dimensional, Fourier transform, scale change 81
Two-dimensional, Fourier transform, second shifting theorem 81
Two-dimensional, Parseval’s energy formula 86
Two-dimensional, product theorem 86
Two-dimensional, steady state heat flow 310
Two-dimensional, transient heat flow 314
Unit element, complex number 21
Variance 339
Variance, continuous probability distribution 340
Variance, of function 347
Virtual images 222
Wave Equation, D’Alembert’s Solution 185
Wave equation, D’Alembert’s solution, three-dimensional 198 375
wave number 10
Wavelength, general definition 10
Weighting kernal 91
Weighting kernal, properties of 93
Window, super — Gaussian 140
Windowing 115
z-score 331
Zero element, complex number 21
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