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| Brandwood D. — Fourier Transforms in Radar and Signal Processing |
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| Предметный указатель |
Radar sum beam 126
Raised cosine gate 102—105. See also Spectral gates
Raised cosine gate, defined 102—104
Raised cosine gate, filter weights with oversampling and 106
Raised cosine gate, illustrated 104
Raised cosine gate, results and comparison 107
Raised cosine pulse 47—49. See also Pulses; Pulse spectra
Raised cosine pulse, defined 47
Raised cosine pulse, illustrated 47
Raised cosine pulse, spectrum 47—49
Raised cosine pulse, spectrum (log scale) 49
Raised cosine spectrum 112
Ramp functions 53—55
Ramp functions, corners 55
Ramp functions, defined 53
ramp functions, illustrated 131
ramp functions, polynomial 131
ramp functions, product of 150 152
Ramp functions, pulse separation into 56
ramp functions, rect function narrower than 152
ramp functions, scaled 152
ramp functions, sum of 158
ramp functions, transforms of 158
Rect function 13—15 125
rect function for aperture distribution 163
rect function, convolution 20 150
rect function, defined 13
rect function, Fourier transform of 13
rect function, illustrated 13
rect function, impulse response 52
rect function, narrower than ramp function 152
rect function, product of 152
rect function, zero 130
Rectangular spectrum 111
Rectangular spectrum, minimum sampling rate 111
Rectangular spectrum, mismatch power for 116
Regular RF pulse train 58—59. See also Pulses; Pulse spectra
Regular RF pulse train, illustrated 58
Regular RF pulse train, spectrum 59
Regularly gated carrier 59—61
Regularly gated carrier, defined 59—60
Regularly gated carrier, illustrated 60
Regularly gated carrier, spectrum 60
Relative sampling rates 73 78.
Relative sampling rates, lines of 80
Relative sampling rates, modified quadrature sampling 81
Rep operator 17—18
Rep operator, defined 17
Rep operator, illustrated 18
Resampling 120—121
Resampling, defined 120
Resampling, illustrated 120
Rounded pulses 49—53. See also Pulses; Pulse spectra
Rounded pulses, rectangular 51
Rounded pulses, rounding form 51
Rounded pulses, trapezoidal 53—58
Rules 29—34
Rules and pairs method 1—4 11—27.
Rules and pairs method, illustrations 24—27
Rules and pairs method, introduction 11—12
Rules and pairs method, narrowband waveforms and 24
Rules and pairs method, notation 12—21
Rules and pairs method, origin 2—3
Rules and pairs method, outline 3—4
Rules and pairs method, Parseval's theorem and 24—26
Rules and pairs method, regular linear arrays and 187
Rules and pairs method, uses 2
Rules and pairs method, Wiener — Khinchine relation and 26—27
Rules for Fourier transforms 21
Rules, defined 21—22
Rules, derivation example 22—23
Rules, derivations 29—34
Rules, R1 29
Rules, R10a 34
Rules, R10b 34
Rules, R2 29
Rules, R3 29
Rules, R4 29
Rules, R5 30
Rules, R6a 30
Rules, R6b 30
Rules, R7a 31
Rules, R7b 31
Rules, R8a 31—32
Rules, R8b 32—33
Rules, R9a 33
Rules, R9b 34
Sampling rates 69—73
Sampling rates, allowed, relative to bandwidth 80
Sampling rates, delay and 78
Sampling rates, general 71—73 78—81
Sampling rates, increasing 79
Sampling rates, maximum 72
Sampling rates, minimum 69—71 83 89 94
Sampling rates, overlapping and 83
Sampling rates, relative 73 78
Sampling rates, ripple effect at 135
Sampling theorems 3
Sampling theorems, Hilbert 75
Sampling theorems, quadrature 81
Sampling theorems, uniform 73
Sampling theorems, wideband 69
Sampling theorems, Woodward's proof of 4
Sampling, basic technique 66—67
Sampling, high IF 84—85
Sampling, Hilbert 65 74—75 85
Sampling, low IF analytic signal 81—84
Sampling, quadrature 65 75—81
Sampling, summary 85—86
Sampling, theory 65—86
Sampling, uniform 65 69—73
Sampling, wideband 65 67—69
Schwarz, Laurent 6
Sector beams 174—180
Sector beams with phase variation across beam 181
Sector beams, sixty-degree 175
Sector beams, splitting 180
Sector beams, steered 178 179
| Side-lobes, constant-level 173
Side-lobes, low, patterns 167—174
Side-lobes, peak magnitudes 172
Side-lobes, ripples 176
Signal processing, analytic signal 7
Signal processing, complex waveforms / spectra in 7—8
Simulated Gaussian clutter 114—120
Sine functions 3 13—15 125
Sine functions properties 14 27—28
Sine functions, amplitudes 172
Sine functions, convolution 150
Sine functions, derivatives of 158 170
Sine functions, envelope 174
Sine functions, illustrated 14
Sine functions, interpolating function as product of 99
Sine functions, product of 41
Sine functions, useful facts 15
Sine-angle coordinate 147
Snc functions 132—134
Snc functions, illustrated 133
Snc functions, snc1 132
Snc functions, snc2 132
Spectral gates 97—105
Spectral gates, rectangular with raised cosine rounding 102—105
Spectral gates, rectangular with trapezoidal rounding 100—102
Spectral gates, results and comparisons 105—107
Spectral gates, tap weight variation with oversampling rate for 108
Spectral gates, trapezoidal 97—100
Spectral gating condition 93—97
Spectral power density function 126 127—128
Spectrum independent interpolation 90—107. See also Interpolation
Spectrum independent interpolation, minimum sampling rate solution 90—93
Spectrum independent interpolation, oversampling and spectral gating condition 93—97
Spectrum independent interpolation, results and comparisons 105—107
Spectrum independent interpolation, spectral gates 97—105
Squared error function 129
Squared error function, total 182
Squared error function, unweighted 134—135
Squint 139
Steered sector beam 178 179
Step function 15—17
Step function, defined 17
Step function, illustrated 17
Sum beam equalization 138—147
Sum beam equalization, array response with 141
Sum beam equalization, benefit 139
Sum beam equalization, defined 139
Sum beam, defined 138
Sum beam, delay compensation and 126
Sum beam, frequency response (effect of bandwidth) 142
Sum beam, frequency response (variation of equalization parameters) 145
Sum beam, gain with frequency sensitive elements 160
Sum beam, response with frequency offset 144
Sum beam, steering 138—139
Symmetrical trapezoidal pulse 40—41. See also Pulses; Pulse spectra
Symmetrical trapezoidal pulse, analysis 40
Symmetrical trapezoidal pulse, illustrated 40
Symmetrical trapezoidal pulse, linear form 42
Symmetrical trapezoidal pulse, logarithmic form 42
Symmetrical trapezoidal pulse, spectrum 40—41
Symmetrical triangular pulse 41—44. See also Pulses; Pulse spectra
Symmetrical triangular pulse, defined 41
Symmetrical triangular pulse, illustrated 43
Symmetrical triangular pulse, spectrum 43—44
Transforms, diagrams 11. See also Fourier transforms
Transforms, Hilbert 7 74 75 85 86—88
Transforms, inverse 87
Transforms, of ramp functions 158
Trapezoidal gate 97—100. See also Spectral gates
Trapezoidal gate, defined 97—99
Trapezoidal gate, filter weights with oversampling and 101
Trapezoidal gate, illustrated 98
Trapezoidal gate, results and comparison 105
Trapezoidal pulses, asymmetrical 44—47
Trapezoidal pulses, convolving 50
Trapezoidal pulses, symmetrical 40—41
Trapezoidal rounding gate 100–102. See also Spectral gates
Trapezoidal rounding gate, defined 100—102
Trapezoidal rounding gate, filter weights with oversampling and 103
Trapezoidal rounding gate, illustrated 102
Trapezoidal rounding gate, results and comparison 105
Trapezoidal spectrum 113 150
Triangular spectrum 112
Uniform linear arrays 164—167. See also Array beamforming
Uniform linear arrays, beam patterns 166
Uniform linear arrays, beam patterns (raised cosine shading) 168
Uniform linear arrays, directional beams 164—167
Uniform linear arrays, low side-lobe patterns 167—174
Uniform linear arrays, rules-and-pairs method and 187
Uniform linear arrays, sector beams 174—180
Uniform sampling 65 69—73.
Uniform sampling, general sampling rate and 71—73
Uniform sampling, minimum sampling rate and 69—71
Uniform sampling, theorem 73
Waveforms, autocorrelation function of 26 110
Waveforms, boxcar 69
Waveforms, error 109
Waveforms, flat, oversampling 97
Waveforms, gated repeated 68
Waveforms, generation 116—120
Waveforms, local oscillator (LO) 83
Waveforms, narrowband 24 25 74
Waveforms, wideband 67—68
Weighted squared error match 127
Weighting functions 169 174
Weights for oversampled factors 97
Weights, beam patterns relationship 162
Weights, filter, with oversampling 101 103
Weights, FIR filter 94
Weights, FIR interpolation 98
Weights, narrowband 140 154
Weights, tap 105
Wideband 137
Wideband sampling 65 67—69.
Wideband sampling, defined 67—68
Wideband sampling, theorem 65 69
Wiener — Khinchine relation 26—27 111
Woodward, P.M. 2—3 65
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