LIST OF ILLUSTRATIONS

Figures

1.1 A sinc (t) function.
1.2 A linear system.
1.3 Graphical representations of a function in terms of pulses.
1.4 A time-invariant linear system.
1.5 A periodic signal gp(t).
1.6 Fourier series coefficients of a periodic pulse.
1.7 A single pulse g(t) and its Fourier transform G(ω).
1.8 A single-pulse frequency spectrum G(ω) and its inverse Fourier transform g(t).
1.9 A periodic impulse train and its Fourier transform.
1.10 Fourier transform of a periodic pulse train.
1.11 Graphical representations of the sampling theory.
1.12 Interpolation filters.
1.13 Original and half-sample-shifted digital signals.
1.14 Frequency spectra of a digitized bandpass signal.
1.15 Downsampling with a FIR filter.
1.16 Interpolation with zero insertion and FIR LPF.
1.17 Fractional rate interpolation with M = 2.5.
1.18 Interpolation on evenly spaced data.
1.19 Generation of unevenly spaced data index.
1.20 Relationship between evenly and unevenly spaced data.
1.21 Interpolation on unevenly spaced data.
2.1 A periodic sequence.
2.2 Linear convolution.
2.3 Circular convolution.
2.4 Linearized circular convolution.
2.5 Convolution using overlap-and-add method.
2.6 Convolution using overlap-and-save method.
2.7 Hanning window with different sampling frequencies.
2.8 A 32-point Hanning window.
2.9 Hanning window with time-domain zero padding.
2.10 Hanning window with frequency-domain zero padding.
2.11 DFT with sliding (overlapping).
2.12 Hamming and Blackman window functions.
2.13 Three-stage computation of an 8-point DFT.
2.14 An 8-point FFT with decimation-in-time algorithm.
2.15 First stage of the decimation-in-frequency FFT algorithm.
2.16 The 8-piont decimation-in-frequency FFT algorithm.
2.17 Input block (a) and end effects in DFT (b) and DCT (c).
2.18 Graphical representations of DFT.
2.19 Example of resampling.
3.1 Potentials generated by current/charge distribution.
3.2 Radiation from a point radiator.
3.3 Far-field approximation of z-oriented dipole.
3.4 Radiation pattern of a half-wavelength dipole.
3.5 A 10-element linear array.
3.6 Normalized linear antenna array factor for N = 10.
3.7 Normalized linear antenna array factor for N = 10, d = λ/2.
3.8 Field pattern in rectangular format for N = 6.
3.9 Field pattern in polar format for N = 6.
3.10 Graphical representation of a solid angle.
3.11 Antenna radiation pattern approximated as a rectangular area.
3.12 Antenna radiation pattern approximated as an elliptical area.
3.13 Polarized fields.
3.14 Popular antennas: (a) circular loop antenna; (b) linear polarized horn antenna; (c) parabolic antenna.
3.15 Printed patch antenna.
3.16 Configuration of a 4-dipole linear array.
3.17 Half-wavelength dipole-based 2D antenna array.
4.1 Transmitter and receiver pulse trains.
4.2 Pulse repetition period and range ambiguity.
4.3 Range resolution.
4.4 Block diagram of a radar system.
4.5 Key elements of radar range equation.
4.6 Surface clutter and volume clutter.
4.7 Wave propagation for stationary source and stationary receiver.
4.8 Wave propagation for moving source and stationary receiver.
4.9 Wave propagation for stationary source and moving receiver.
4.10 Wave propagation for moving source and moving receiver.
4.11 Doppler radar with separate source and receiver.
4.12 Example of Doppler frequency.
4.13 Rectangular pulse and its frequency spectrum.
4.14 Ambiguity function of a rectangular pulse in 3D view.
4.15 Cross-sectional view of Fig. 4.14 with τ = 0 (a) and τ = 0.5Tp (b).
4.16 Cross-sectional view of Fig. 4.14 with fD = 0 (a) and fD = 2.5/Tp (b).
4.17 A 3-dB contour of ambiguity function of a rectangular pulse in 3D view.
5.1 Transmitter block diagram of a pulse-modulated radar system.
5.2 Time- and frequency-domain waveforms of pulse-modulated radar signal.
5.3 Time- and frequency-domain waveforms of two video pulses.
5.4 Block diagram of Doppler frequency extraction.
5.5 Block diagram of an offset carrier demodulation.
5.6 Block diagram of a pulse–Doppler radar system.
5.7 Time-domain waveform (a) and time–frequency relation (b) of a pulsed LFM signal.
5.8 Time- and frequency-domain waveforms of a pulsed symmetric LFM signal.
5.9 Time- and frequency-domain waveforms of a pulsed nonsymmetric LFM signal.
5.10 Block diagram of a PLFM radar system.
5.11 Block diagram of a CWLFM radar system.
5.12 Time–Frequency relationship of a CWLFM radar signal.
5.13 Waveforms of (a) a CWSFM radar signal and (b) a pulsed SFM radar signal.
5.14 Time–frequency relationship of (a) CWSFM radar signal and (b) a PSFM radar signal.
5.15 Block diagram of a stepped frequency modulation radar.
5.16 In-phase–quadrature-phase (I–Q) demodulator.
5.17 DFT-based processing of chirp signal.
5.18 Waveforms of Tx signal and matched filter function.
5.19 Waveforms of Tx signal and Rx signal.
5.20 Frequency spectrum of Tx signal.
5.21 Frequency spectrum of matched filter (MF) function.
5.22 Frequency spectrum of Rx signal.
5.23 Comparison of pulse compression based on convolution and DFT.
5.24 Waveforms of Tx signal and MF function.
5.25 Frequency spectra of Tx signal and MF function.
5.26 Time- and frequency-domain waveforms of Rx signal.
5.27 Comparison of pulse compression based on convolution and DFT.
5.28 Time–frequency relationship of Tx, reference, and echo signals.
5.29 Block diagram of dechirp processing.
5.30 Time–frequency relationship of Tx and echo signals from two stationary targets.
5.31 Time–frequency relationship of Tx and echo signals from two moving targets.
5.32 Baseband echo response from PSFM signal.
5.33 A single-target range profile based on PSFM signal.
5.34 Stepped frequency pulse train and echoes returned in one pulse period.
5.35 A multiple-target range profile based on PSFM.
6.1 Configurations of (a) a stripmap SAR and (b) a scan SAR.
6.2 Imaging radar for (a) a spotlight SAR and (b) an interferometric SAR.
6.3 Geometry of stripmap imaging radar.
6.4 Geometry of (a) a broadside SAR and (b) a squint SAR.
6.5 (a) Imaging radar and (b) radar pulse and received echo.
6.6 (a) Single channel radar range data; (b) M × N radar imaging data array.
6.7 Configuration of a broadside SAR system.
6.8 A simplified broadside SAR system.
6.9 Echo signal from the point target before (a) and after (b) range compression.
6.10 Broadside SAR with multiple targets.
6.11 Slant range R(u) versus radar position u for three targets at equal (a) and different (b) ranges.
6.12 Broadside SAR with single point target.
6.13 (a) Radiation pattern from a typical antenna array; (b) real part of a LFM signal.
6.14 (a) 3-dB beamwidth of a radiation pattern from a typical antenna array;
(b) real part of amplitude-weighted LFM signal.
6.15 Doppler frequency and multiple targets
6.16 Doppler frequency versus slant range for single target.
6.17 Doppler frequency versus slant range for multiple targets.
6.18 Geometry of a forward-looking radar system with nonzero squint angle.
6.19 Small θq Doppler frequency versus slow time s (a) and slant range r (b).
6.20 Low θq Doppler frequency versus slow time s (a) and slant range r (b).
6.21 Comparison of Doppler frequencies for different SAR systems.
6.22 (a) Multiple-target squint SAR system; (b) plot of Doppler frequency fD versus radar displacement u.
6.23 A simplified single-target squint SAR system.
6.24 Single-target trajectory in squint SAR system.
6.25 Geometric distortions of radar image.
6.26 The resolution cell of a side-looking radar.
7.1 Geometry of a range imaging radar.
7.2 An ideal target function.
7.3 Matched filtering for range imaging.
7.4 A reconstructed target function f(x).
7.5 (a) A typical cross-range radar imaging system; (b) a simplified system.
7.6 Relationship between radar beams and targets.
7.7 Relationship between received signal and reference signal.
7.8 Computation of spatial frequency band limitation.
7.9 Matched filtering for cross-range imaging.
7.10 A squint mode cross-range imaging system.
7.11 Relationship between targets and squint radar beam.
7.12 Computation of spatial frequency band limitation for squint radar.
7.13 I–Q radar signal generation.
7.14 Doppler frequency spectra of a broadside SAR.
7.15 Doppler frequency spectra of a squint SAR.
8.1 Major tasks of SAR radar image processing.
8.2 System model of radar image generation.
8.3 A simplified broadside SAR system for radar image generation.
8.4 A simplified squint SAR system for radar image generation.
8.5 Single-target broadside SAR system for radar image generation.
8.6 Received signal array from Fig. 8.5.
8.7 A simplified and digitized received signal array from Fig. 8.6.
8.8 Waveforms of the real and imaginary parts of a baseband symmetric LFM signal.
8.9 Waveforms of received baseband signal from Fig. 8.5.
8.10 Received signal arrays from Fig. 8.3.
8.11 A simplified and digitized signal array from Fig. 8.10.
8.12 Waveforms of the individual received signal from Fig. 8.10.
8.13 Waveforms of the received signals from Fig. 8.10.
8.14 System model of a single-target squint SAR.
8.15 A received signal array from Fig. 8.14.
8.16 A digitized signal array from Fig. 8.15.
8.17 Waveforms of a received baseband signal from Fig. 8.14.
8.18 System model of a three-target squint SAR.
8.19 The received signal arrays from Fig. 8.18.
8.20 The digitized signal arrays from Fig. 8.19.
8.21 Waveforms of the individual received signal from Fig. 8.18.
8.22 Waveforms of the received signals from Fig. 8.18.
8.23 Flow diagram of the range–Doppler algorithm.
8.24 (a) An M × N 2D data array; (b) mth row of 2D data array.
8.25 Operation of a corner turn.
8.26 A range-compressed signal array in range–Doppler frequency domain.
8.27 A range-compressed signal array after fractional interpolation.
8.28 A range-compressed signal array after sample shift.
8.29 Waveforms of transmitter baseband signal, range reference function, and azimuth reference function.
8.30 Frequency spectra of range and azimuth matched filters.
8.31 3D view of a range-compressed signal array based on Fig. 8.5.
8.32 2D view of a range-compressed signal array based on Fig. 8.31.
8.33 3D view of a range–Doppler frequency spectrum based on Fig. 8.31.
8.34 2D view of a range–Doppler frequency spectrum based on Fig. 8.33.
8.35 3D view of a reconstructed single-target function based on Fig. 8.33.
8.36 Cross-sectional view of a reconstructed single-target function based on Fig. 8.35.
8.37 3D view of a range-compressed signal array based on Fig. 8.3.
8.38 2D view of a range-compressed signal array based on Fig. 8.37.
8.39 3D view of a range–Doppler frequency spectrum based on Fig. 8.37.
8.40 2D view of a range–Doppler frequency spectrum based on Fig. 8.39.
8.41 3D view of a reconstructed target function based on Fig. 8.39.
8.42 Cross-sectional view of Fig. 8.41 at range samples 181 and 211.
8.43 Cross-sectional view of Fig. 8.41 at azimuth lines 563, 818, and 939.
8.44 Waveforms of the real and imaginary parts of azimuth reference function.
8.45 Frequency spectrum of azimuth reference function.
8.46 3D view of a range-compressed signal based on Fig. 8.14.
8.47 2D view of a range-compressed signal from Fig. 8.14.
8.48 3D view of a spatial Fourier transformed signal from Fig. 8.46.
8.49 2D view of a spatial Fourier-transformed signal from Fig. 8.46.
8.50 3D view of Fig. 8.46 after range cell migration correction.
8.51 2D view of Fig. 8.46 after range cell migration correction.
8.52 3D view of a reconstructed target function from Fig. 8.14.
8.53 Cross-sectional view of Fig. 8.52 at range sample 181 and azimuth line 571, respectively.
8.54 3D view of a range-compressed signal from Fig. 8.18.
8.55 2D view of a range-compressed signal from Fig. 8.18.
8.56 3D view of spatial Fourier-transformed signal from Fig. 8.54.
8.57 2D view of a spatial Fourier-transformed signal from Fig. 8.54.
8.58 3D view of Fig. 8.56 after range cell migration correction.
8.59 2D view of Fig. 8.56 after range cell migration correction.
8.60 3D view of a reconstructed target function from Fig. 8.18.
8.61 Cross-sectional view of Fig. 8.60 at range samples 181 and 211.
8.62 Cross-sectional view of Fig. 8.60 at azimuth lines 571, 786, and 947.
9.1 Data distribution before (a) and after (b) transformation.
9.2 Data distribution before (images) and after (•) interpolation.
9.3 Block diagram of the Stolt interpolation algorithm.
9.4 System model of a six-target broadside SAR.
9.5 Received signal array based on Fig. 9.4.
9.6 Waveforms of the real part of individual echo signal based on Fig. 9.4.
9.7 Waveforms of received signal based on Fig. 9.4.
9.8 3D view of s1c(t, ωD) in range–Doppler frequency domain.
9.9 2D view of s1c(t, ωD) in range–Doppler frequency domain.
9.10 3D view of the roughly compressed six-target function.
9.11 Side view, from the range direction, of Fig. 9.10.
9.12 Side view, from the azimuth direction, of Fig. 9.10.
9.13 3D view of refocused six-target function.
9.14 Side view, from the range direction, of Fig. 9.13.
9.15 Side view, from the azimuth direction, of Fig. 9.13.
9.16 System model of a 6-target squint SAR.
9.17 Received signal array derived from Fig. 9.16.
9.18 Waveforms of the real part of individual echo signal from Fig. 9.16.
9.19 Waveforms of received signal from Fig. 9.16.
9.20 3D view of s1c(t, ωD) in range–Doppler frequency domain.
9.21 2D view of s1c(t, ωD) in range–Doppler frequency domain.
9.22 Synthesized 1D azimuth reference function for squint SAR system.
9.23 3D view of roughly compressed target function.
9.24 Side view, from the range direction, of Fig. 9.23.
9.25 Side view, from the azimuth direction, of Fig. 9.23.
9.26 3D view of refocused target function.
9.27 Side view, from the range direction, of Fig. 9.26.
9.28 Side view, from the azimuth direction, of Fig. 9.26.
9.29 3D view of Haz(t, ωD).
9.30 2D view of Haz(t, ωD).
9.31 3D view of reconstructed target function.
9.32 Side view, from the range direction, of Fig. 9.31.
9.33 Side view, from the azimuth direction, of Fig. 9.31.
9.34 Waveforms of the real and imaginary parts of a received satellite baseband signal. (With permission from MDA Geospatial Services.)
9.35 Image of a received satellite signal after range compression.
9.36 Image of a range-compressed signal in range–Doppler frequency domain.
9.37 Radar image after bulk compression.
9.38 Radar image after differential azimuth compression.
9.39 Radar image processed by range–Doppler algorithm.
9.40 Radar image processed by Stolt interpolation technique.
9.41 Radar image processed by range–Doppler algorithm.

Table

1.1 16 sets of 8-tap interpolation filters
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