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Brandwood D. Ч Fourier Transforms in Radar and Signal Processing
Brandwood D. Ч Fourier Transforms in Radar and Signal Processing

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Ќазвание: Fourier Transforms in Radar and Signal Processing

јвтор: Brandwood D.


Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. Now you can solve many of these problems with the integration-free approach to carrying out Fourier transforms (and Fourier series) presented in this book.
By building upon Woodward's well known "Rules and Pairs" method and related concepts and procedures, this book establishes a unified system that makes implicit the integration required for performing Fourier transforms on a wide variety of functions. It details how complex functions can be broken down to their constituent parts for analysis. You can now concentrate on functional relationships instead of getting bogged down in the details of integration. This approach to implementing Fourier transforms is illustrated with many specific examples from digital signal processing as well as radar and antenna operation.

язык: en

–убрика: ћатематика/„исленные методы/¬ейвлеты, обработка сигналов/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2003

 оличество страниц: 216

ƒобавлена в каталог: 27.02.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
$\delta$-function      6 15Ч17 67 150
$\delta$-function in time-domain      16
$\delta$-function properties      15
$\delta$-function, defined      15
$\delta$-function, envelope      180
$\delta$-function, illustrated      16
$\delta$-function, position of      16
$\delta$-function, scaled      16Ч17
Aliasing, defined      94
Aliasing, no      95
Amplitude distortion      158
Amplitude equalization      134Ч135
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      81Ч84
Analytic signals, use advantage      7
Aperture distribution      162 169
Aperture distribution function      164Ч165
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      161Ч188
Array beamforming, basic principles      162Ч164
Array beamforming, introduction      161Ч162
Array beamforming, nonuniform linear arrays      180Ч187
Array beamforming, summary      187Ч188
Array beamforming, uniform linear arrays      164Ч180
Arrays, factor      163 180
Arrays, linear      164Ч187
Arrays, nonuniform linear      180Ч187
Arrays, rectangular planar      162
Arrays, reflector-backed      178 179
Arrays, uniform linear      164Ч180
Asymmetrical trapezoidal pulse      44Ч47. 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      45Ч47
Autocorrelation functions by Wiener Ч Khinchine theorem      111
Autocorrelation functions of waveforms      26 110
Autocorrelation functions, power spectra and      111Ч113
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      167Ч174
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      135Ч138
Comb function      18 92
Comb function, defined      18
Comb function, expanding      95
Comb function, illustrated      18
Constant functions      5 6
Contour integration      37
Convolution      18Ч21
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      89Ч123
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      147Ч158
Difference beam, gain response against frequency offset      156
Difference beam, pattern      147
Difference beam, response      154
Difference beam, with narrowband weights      154
Directional beams      164Ч167. See also Uniform linear arrays
Directional beams, beam patterns      166
Directional beams, beam steering      165
Directional beams, repetitions      187
Directional beams, variations      187Ч188
Doppler shift      61 62
Element response, with reflector      177
Equalization      125Ч160
Equalization delay      139
Equalization for broadband array radar      135Ч138
Equalization in communications channel      127
Equalization of linear amplitude distortion      138
Equalization parameters, varying      144 145
Equalization, amplitude, example      134Ч135
Equalization, basic approach      126Ч130
Equalization, difference beam      147Ч158
Equalization, effective      159
Equalization, filter parameters      143
Equalization, introduction      125Ч126
Equalization, sum beam      138Ч147
Equalization, summary      158Ч159
Equalization, tap filters      146
Equalizing filters      128
Error power      109Ч110
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 134Ч135
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      4Ч6
Fourier transforms, inverse      12Ч13 33 135
Fourier transforms, notation      12Ч13
Fourier transforms, pairs      22
Fourier transforms, rules      21
Fourier transforms, rules-and-pairs method      1Ч4 11Ч27
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, $\delta$-function      6 15Ч17 67 150
Functions, autocorrelation      26 110 111Ч113
Functions, comb      18 92 95
Functions, constant      5
Functions, convolution of      18Ч21
Functions, diagrams      11
Functions, generalized      4Ч6
Functions, interpolating      77 95
Functions, nonsymmetric      20
Functions, ramp      130Ч131 150
Functions, rect      13Ч15 125
Functions, rep      17Ч18
Functions, repeated, overlapping      169
Functions, sine      3 13Ч15 125
Functions, sketches      4
Functions, snc      132Ч134
Functions, spectral power density      126
Functions, step      15Ч17
Functions, transformed      3Ч4
Functions, trapezoidal      100
Functions, trigonometric      5
Functions, weighting      169 174
Gain pattern      182
Gaussian clutter      114Ч120
Gaussian clutter, defined      114
Gaussian clutter, efficient waveform generation      119Ч120
Gaussian clutter, waveform, direct generation of      116Ч119
Gaussian spectrum      112Ч113
Generalized functions, defined      6
Generalized functions, Fourier transform and      4Ч6
Grating lobes      164
Hamming weighting      104
High IF sampling      84Ч85
Hilbert sampling      65 74Ч75 85.
Hilbert sampling, approximation to      75
Hilbert sampling, theorem      75
Hilbert transform      7 74 75 85 86Ч88
Hilbert transform, phase shift and      87Ч88
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      89Ч123
Interpolation, efficient clutter waveform generation with      119Ч120
Interpolation, factor      93
Interpolation, FIR filter      91 109
Interpolation, FIR, weights      98
Interpolation, least squared error      107Ч114
Interpolation, performance      96
Interpolation, resampling and      120Ч121
Interpolation, spectrum independent      90Ч107
Interpolation, summary      122Ч123
Interpolation, worst case for      93
Inverse Fourier transform      12Ч13 33 135.
Inverse Fourier transform of aperture distribution      163
Inverse Fourier transform, performing      74
Least squared error interpolation      107Ч114. 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      107Ч111
Least squared error interpolation, power spectra and autocorrelation functions      111Ч113
Low IF analytic signal sampling      81Ч84
Low side-lobe patterns      167Ч174
Maximum sampling rate      71
Minimum sampling rate      69Ч71
Minimum sampling rate, modified form      94
Minimum sampling rate, spectrum independent interpolation      90Ч93
Mismatch powers for rectangular spectrum      116
Mismatch powers for two power spectra      115
Modified quadrature sampling      80Ч81. 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      180Ч187 188.
Nonuniform linear arrays problem      180Ч181
Nonuniform linear arrays, sector pattern      184
Nonuniform linear arrays, steered, sector patterns      186
Organization, this book      8Ч9
Oversampling      93Ч97
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      35Ч37. See also Rules and pairs method
Pairs for Fourier transforms      22
Pairs, defined      22
Pairs, derivation example      23
Pairs, derivations      35Ч37
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      36Ч37
Pairs, P6Ч10      37
Parseval's theorem      3 24Ч26
Planar arrays      162
Poisson's formula      3
Pulse Doppler radar      61Ч62
Pulse repetition frequency (PRF)      59 114
Pulse spectra      39Ч63
Pulse spectra, asymmetrical trapezoidal      44Ч47
Pulse spectra, general rounded trapezoidal      53Ч58
Pulse spectra, introduction      39Ч40
Pulse spectra, pulse Doppler radar waveform      61Ч62
Pulse spectra, raised cosine      47Ч49
Pulse spectra, regular RF train      58Ч59
Pulse spectra, rounded      49Ч53
Pulse spectra, summary      62Ч63
Pulse spectra, symmetrical trapezoidal      40Ч41
Pulse spectra, symmetrical triangular      41Ч44
Pulses, asymmetrical trapezoidal      44Ч47
Pulses, general rounded trapezoidal      53Ч58
Pulses, raised cosine      47Ч49
Pulses, rectangular      49
Pulses, regular RF train      58Ч59
Pulses, rounded      49Ч53
Pulses, symmetrical trapezoidal      40Ч41
Pulses, symmetrical triangular      41Ч44
Pulses, unit height trapezoidal      56
Quadrature sampling      65 75Ч81.
Quadrature sampling, basic analysis      75Ч78
Quadrature sampling, general sampling rate      78Ч81
Quadrature sampling, illustrated      76
Quadrature sampling, modified      80Ч81
Quadrature sampling, relative sampling rates      78 80 81
Quadrature sampling, theorem      81
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