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 () 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. |