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| Ïîèñê ïî óêàçàòåëÿì |
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| Brandwood D. — Fourier Transforms in Radar and Signal Processing |
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| Ïðåäìåòíûé óêàçàòåëü |
 -function 6 15—17 67 150
-function in time-domain 16
-function properties 15
-function, defined 15
-function, envelope 180
-function, illustrated 16
-function, position of 16
-function, scaled 16—17
Aliasing, defined 94
Aliasing, no 95
Amplitude distortion 158
Amplitude equalization 134—135
Amplitude error 127
Amplitude of side-lobe peak magnitudes 172
Amplitude of sine function 172
Amplitude sensitivity 159
Analog-to-digital converters (ADCs) 82
Analytic signals 7
Analytic signals, low IF, sampling 81—84
Analytic signals, use advantage 7
Aperture distribution 162 169
Aperture distribution function 164—165
Aperture distribution, inverse Fourier transform 163
Aperture distribution, linear array 182
Aperture distribution, rect function 163
Aperture distribution, shading 67
Aperture distribution, tapering 167
Aperture distribution, weighting 167
Apertures, continuous 167 187
Apertures, discrete 187
Apertures, phase shift 162
Apertures, sampled 164
Array beamforming 161—188
Array beamforming, basic principles 162—164
Array beamforming, introduction 161—162
Array beamforming, nonuniform linear arrays 180—187
Array beamforming, summary 187—188
Array beamforming, uniform linear arrays 164—180
Arrays, factor 163 180
Arrays, linear 164—187
Arrays, nonuniform linear 180—187
Arrays, rectangular planar 162
Arrays, reflector-backed 178 179
Arrays, uniform linear 164—180
Asymmetrical trapezoidal pulse 44—47. See also Pulses; Pulse spectra
Asymmetrical trapezoidal pulse, illustrated 45
Asymmetrical trapezoidal pulse, rising edge 44
Asymmetrical trapezoidal pulse, spectra illustrations 46
Asymmetrical trapezoidal pulse, spectrum examples 45—47
Autocorrelation functions by Wiener — Khinchine theorem 111
Autocorrelation functions of waveforms 26 110
Autocorrelation functions, power spectra and 111—113
Back lobe 176
Beam patterns for ULA with additional shading 171
Beam patterns, constant-level side-lobe 173. See also Array beamforming
Beam patterns, Fourier transform relationship 161
Beam patterns, low side-lobe 167—174
Beam patterns, reflection symmetry 164
Beam patterns, slope 169
Beam patterns, stretching 165
Beam patterns, two-dimensional 162
Beam patterns, uniform linear array 166
Beam patterns, uniform linear array (raised cosine shading) 168
Beam patterns, weights relationship with 162
Broadband array radar, array steering 138
Broadband array radar, equalization for 135—138
Comb function 18 92
Comb function, defined 18
Comb function, expanding 95
Comb function, illustrated 18
Constant functions 5 6
Contour integration 37
Convolution 18—21
Convolution notation 18
Convolution of rect functions 20 150
Convolution of sine functions 150
Convolution with nonsymmetric function 20
Delay amplitude 135
Delay compensation 155
Delay equalization 139
Delay errors 135
Delay mismatch 130
Delay, weights for 96
Delayed waveform time series 89—123
Difference beam slope 148
Difference beam slope, bandwidth 158
Difference beam slope, expanded larger filter response 157
Difference beam slope, expanded small filter response 157
Difference beam slope, larger filter response 157
Difference beam slope, small filter response 157
Difference beam, equalization 147—158
Difference beam, gain response against frequency offset 156
Difference beam, pattern 147
Difference beam, response 154
Difference beam, with narrowband weights 154
Directional beams 164—167. See also Uniform linear arrays
Directional beams, beam patterns 166
Directional beams, beam steering 165
Directional beams, repetitions 187
Directional beams, variations 187—188
Doppler shift 61 62
Element response, with reflector 177
Equalization 125—160
Equalization delay 139
Equalization for broadband array radar 135—138
Equalization in communications channel 127
Equalization of linear amplitude distortion 138
Equalization parameters, varying 144 145
Equalization, amplitude, example 134—135
Equalization, basic approach 126—130
Equalization, difference beam 147—158
Equalization, effective 159
Equalization, filter parameters 143
Equalization, introduction 125—126
Equalization, sum beam 138—147
Equalization, summary 158—159
Equalization, tap filters 146
Equalizing filters 128
Error power 109—110
Error power, levels 114
Error power, minimizing 128
Error power, normalizing 129
Error(s) amplitude 127
Error(s) delay 135
Error(s) waveform 109
Error(s), squared 129 134—135
Falling edge, of trapezoid 150 151
Filter model 50
FIR filter 127
FIR filter for interpolation 91 109
FIR filter, coefficients 119 121
FIR filter, Gaussian 120
FIR filter, length 121
FIR filter, tap weights 121
FIR filter, weights for interpolation 94
Fourier series 32
Fourier series, coefficients, finding 5
Fourier series, concept 4
Fourier series, representation 32
Fourier transforms as limiting case of Fourier series 5
Fourier transforms of constant functions 6
Fourier transforms of power spectrum 111 150
Fourier transforms of rect function 13
Fourier transforms, complex 7
Fourier transforms, defined 1
Fourier transforms, generalized functions and 4—6
Fourier transforms, inverse 12—13 33 135
Fourier transforms, notation 12—13
Fourier transforms, pairs 22
Fourier transforms, rules 21
| Fourier transforms, rules-and-pairs method 1—4 11—27
Frequency distortion, compensation 126
Frequency distortion, forms 125
Frequency distortion, frequency axis as 143
Frequency distortion, sum beam response with 144
Frequency offset, difference beam gain response against 156
Functions, -function 6 15—17 67 150
Functions, autocorrelation 26 110 111—113
Functions, comb 18 92 95
Functions, constant 5
Functions, convolution of 18—21
Functions, diagrams 11
Functions, generalized 4—6
Functions, interpolating 77 95
Functions, nonsymmetric 20
Functions, ramp 130—131 150
Functions, rect 13—15 125
Functions, rep 17—18
Functions, repeated, overlapping 169
Functions, sine 3 13—15 125
Functions, sketches 4
Functions, snc 132—134
Functions, spectral power density 126
Functions, step 15—17
Functions, transformed 3—4
Functions, trapezoidal 100
Functions, trigonometric 5
Functions, weighting 169 174
Gain pattern 182
Gaussian clutter 114—120
Gaussian clutter, defined 114
Gaussian clutter, efficient waveform generation 119—120
Gaussian clutter, waveform, direct generation of 116—119
Gaussian spectrum 112—113
Generalized functions, defined 6
Generalized functions, Fourier transform and 4—6
Grating lobes 164
Hamming weighting 104
High IF sampling 84—85
Hilbert sampling 65 74—75 85.
Hilbert sampling, approximation to 75
Hilbert sampling, theorem 75
Hilbert transform 7 74 75 85 86—88
Hilbert transform, phase shift and 87—88
Hilbert transform, wideband phase shift and 88
Impulse responses 51
Impulse responses, exponential 52
Impulse responses, rect 52
Impulse responses, smoothing 53
Interpolating function 95
Interpolating function as product of sine functions 99
Interpolating function in uniform sampling 77
Interpolation for delayed waveform time series 89—123
Interpolation, efficient clutter waveform generation with 119—120
Interpolation, factor 93
Interpolation, FIR filter 91 109
Interpolation, FIR, weights 98
Interpolation, least squared error 107—114
Interpolation, performance 96
Interpolation, resampling and 120—121
Interpolation, spectrum independent 90—107
Interpolation, summary 122—123
Interpolation, worst case for 93
Inverse Fourier transform 12—13 33 135.
Inverse Fourier transform of aperture distribution 163
Inverse Fourier transform, performing 74
Least squared error interpolation 107—114. See also Interpolation
Least squared error interpolation, error power levels 114
Least squared error interpolation, FIR filter for 109
Least squared error interpolation, method of minimum residual error power 107—111
Least squared error interpolation, power spectra and autocorrelation functions 111—113
Low IF analytic signal sampling 81—84
Low side-lobe patterns 167—174
Maximum sampling rate 71
Minimum sampling rate 69—71
Minimum sampling rate, modified form 94
Minimum sampling rate, spectrum independent interpolation 90—93
Mismatch powers for rectangular spectrum 116
Mismatch powers for two power spectra 115
Modified quadrature sampling 80—81. See also Quadrature sampling
Modified quadrature sampling, defined 80
Modified quadrature sampling, relative sampling rates 81
Monopulse measurement 138
Narrowband waveforms 24
Narrowband waveforms, Hilbert transformer and 74
Narrowband waveforms, spectra 25
Narrowband, defined 137
Narrowband, steering 147
Newton's approximation method 170
Nonuniform linear arrays 180—187 188.
Nonuniform linear arrays problem 180—181
Nonuniform linear arrays, sector pattern 184
Nonuniform linear arrays, steered, sector patterns 186
Organization, this book 8—9
Oversampling 93—97
Oversampling, benefit 146
Oversampling, factor 114
Oversampling, filter weights with 101 103
Oversampling, flat waveform 97
Oversampling, optimum rectangular gate 96
Oversampling, rate 140 146
Oversampling, rate, increasing 146
Oversampling, tap weight with 108
Pairs 35—37. See also Rules and pairs method
Pairs for Fourier transforms 22
Pairs, defined 22
Pairs, derivation example 23
Pairs, derivations 35—37
Pairs, P11 37
Pairs, P1a 35
Pairs, P1b 35
Pairs, P2a 35
Pairs, P2b 36
Pairs, P3a 36
Pairs, P3b 36
Pairs, P4 36
Pairs, P5 36—37
Pairs, P6—10 37
Parseval's theorem 3 24—26
Planar arrays 162
Poisson's formula 3
Pulse Doppler radar 61—62
Pulse repetition frequency (PRF) 59 114
Pulse spectra 39—63
Pulse spectra, asymmetrical trapezoidal 44—47
Pulse spectra, general rounded trapezoidal 53—58
Pulse spectra, introduction 39—40
Pulse spectra, pulse Doppler radar waveform 61—62
Pulse spectra, raised cosine 47—49
Pulse spectra, regular RF train 58—59
Pulse spectra, rounded 49—53
Pulse spectra, summary 62—63
Pulse spectra, symmetrical trapezoidal 40—41
Pulse spectra, symmetrical triangular 41—44
Pulses, asymmetrical trapezoidal 44—47
Pulses, general rounded trapezoidal 53—58
Pulses, raised cosine 47—49
Pulses, rectangular 49
Pulses, regular RF train 58—59
Pulses, rounded 49—53
Pulses, symmetrical trapezoidal 40—41
Pulses, symmetrical triangular 41—44
Pulses, unit height trapezoidal 56
Quadrature sampling 65 75—81.
Quadrature sampling, basic analysis 75—78
Quadrature sampling, general sampling rate 78—81
Quadrature sampling, illustrated 76
Quadrature sampling, modified 80—81
Quadrature sampling, relative sampling rates 78 80 81
Quadrature sampling, theorem 81
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