Chirp Fourier Transform Research Articles

An Effective Clutter Suppression Approach Based on Null-Space Technique for the Space-Borne Multichannel in Azimuth High-Resolution and Wide-Swath SAR System

In this article, an effective clutter suppression algorithm is presented for the space-borne azimuth multiantenna high-resolution and wide-swath (HRWS) synthetic aperture radar (SAR) system, which is based on the null-space technique. First, the echo of bistatic geosynchronous-low earth orbit (GEO-LEO) azimuth multiantenna HRWS SAR-ground moving target indication (GMTI) system is utilized to deduce the coarse-focused image of moving targets and clutter, where the Chirp Fourier transform (CFT) in azimuth is involved. Then, the matrix form can be utilized to describe the coarse-focused image of the multiantenna SAR system and the corresponding covariance matrix can be estimated. After that, the null-space is constructed using the covariance matrix corresponding to clutter, where at least a redundant channel freedom is required. Since the null-space vector is orthogonal to signal-space vector, it can be used to suppress the clutter. As an equivalent phase is brought by the slant velocity, the moving targets’ echo can be preserved during clutter suppression. Then, the optimization and suboptimization vectors for clutter suppression are introduced. It is worth noting that the proposed clutter suppression algorithm is robust for the antenna mismatch, that is, the antenna mismatch in phase and the corresponding position error. Finally, the theoretical investigations are validated using some simulation experiments, where the experiments for bistatic GEO-LEO and single-platform azimuth multiantenna HRWS SAR-GMTI system are both included. In addition, the real measured single-platform azimuth multiantenna HRWS SAR data experiments are also performed.

A novel hypersonic vehicle-borne multichannel SAR-GMTI scheme based on adaptive sum and difference beams within eigenspace

This paper investigates a novel ground moving target indication (GMTI) scheme for a hypersonic vehicle-borne multichannel synthetic aperture radar (MC-SAR) system with Doppler ambiguity. First, after the range compression and azimuth chirp Fourier transform (CFT), by applying the eigenspace-based adaptive sum and difference beams (EASDB) on the coarse-focused images, the high-precision cross-track velocity (CTV) can be retrieved. Then, utilizing the high-precision CTV to construct an accurate moving target steering vector to extract the moving target energy. With the proposed CFT-two-step method, we have avoided cumbersome CTV search, and simplified the process of range walk correction, resulting in lower computational complexity. Compared to the CFT-center and CFT-two-step methods, the proposed scheme obtains the accurate two-dimension motion parameters of a moving target, and has better performance and robustness in the detection, focusing, and location, preserving the moving target envelope and achieving higher signal-to-clutter-and-noise ratio (SCNR). Finally, using the processing results of simulation and real measured MC-SAR data, we verify the effectiveness and feasibility of our proposed scheme.

Inverse synthetic aperture radar imaging method of complex maneuvering target based on instantaneous autocorrelation function – chirp Fourier transform

As the maneuverability of aerial targets increases, in the process of using traditional imaging algorithms to image complex maneuvering targets, the results obtained will inevitably appear defocus and blurring. In order to achieve high-resolution imaging of complex maneuvering targets, the inverse synthetic aperture radar (ISAR) imaging method for complex maneuvering targets based on instantaneous autocorrelation function-chirp Fourier transform (IAF-CFT) is proposed in this work. The method first uses IAF to reduce the order of echo, and then chirp Fourier Transform is used to estimate the echo parameters. Finally, the CLEAN technology is adopted to reconstruct the echo and get the result of ISAR imaging. The simulation results prove the effectiveness of this method.

Investigation on Estimator of Chirp Rate and Initial Frequency of LFM Signals Based on Modified Discrete Chirp Fourier Transform

An accurate estimator of chirp rate and initial frequency of the linear frequency modulation (LFM) signals based on modified discrete chirp Fourier transform (MDCFT) is investigated in this study. The proposed algorithm consists of two banks, namely coarse search and fine search. The coarse search returns a coarse estimate of the parameter by addressing the maximum MDCFT coefficient of a LFM signal. The coarse estimate is refined by fine search algorithms, including spectrum slices and iterative interpolation methods. Compared to conventional fine search approaches, spectrum slices and iterative interpolation methods are always more efficient because they utilize more prior information about the MDCFT results, thus requiring fewer extra computations. Finally, computer simulations are conducted to evaluate the performance of our algorithms by comparison with the Cramer–Rao lower bound. The proposed estimator shows robust performance for various values of the signal parameters with the addition in the additive white Gaussian noise.

Efficient angular chirp-Fourier transform and its application to high-speed target detection

In this paper, a new class of efficient angular chirp-Fourier transform (EACFT) algorithms are proposed to realize the fast detection and parameter estimation of chirp signal. The angular chirp-Fourier transform (ACFT) is first introduced to overcome the disadvantages of chirp-Fourier transform (CFT) and fractional Fourier transform (FRFT). Similar to FRFT, ACFT is also a time-frequency rotation operator. We derive the analytic relations between the length of time-frequency line and the width of spectral support (WSS) in the ACFT domain. Exploiting the time-frequency rotation property of ACFT, the EACFT is then proposed to detect the chirp signal and estimate its parameters. The EACFT can achieve high estimation accuracy only with two selected rotation angles instead of traditional traversal search, which largely reduces the computational cost. Based on the concept of EACFT, robust methods, i.e., morphology filtering-EACFT (MF-EACFT) and spectrum smoothing-EACFT (SS-EACFT), are further proposed to improve the applicability of EACFT in the low signal-to-noise ratio (SNR) and multi-component circumstances, respectively. Finally, the application of EACFT to the high-speed maneuvering target detection is developed. A new fast detection algorithm based on adjacent cross correlation function (ACCF) and SS-MF-EACFT is presented. Theoretical analysis and simulated experiments demonstrate the effectiveness of the proposed method.

Clutter suppression and ground moving target imaging approach for hypersonic vehicle borne multichannel radar based on two-step focusing method

In this paper, a novel clutter suppression and ground moving target imaging approach is proposed for hypersonic vehicle (HSV) borne multichannel (MC) synthetic aperture radar (SAR) system. Compared with the traditional MC SAR ground moving target indication (GMTI) methods, the proposed algorithm can suppress clutter and decrease the moving target energy loss based on the improved MC clutter suppression method in the chirp Fourier transform (CFT) domain. Moreover, the moving target can be accurately focused by compensating the range curvature and the third order phase item. In addition, the motion parameters can be estimated precisely and the moving target can be focused accurately. Finally, the effectiveness of the proposed method is validated by the simulation examples.

A Novel Inverse Synthetic Aperture Radar Imaging Method for Maneuvering Targets Based on Modified Chirp Fourier Transform

When inverse synthetic aperture radar (ISAR) imaging maneuvers targets, the azimuth echo of the target scattering point causes a Doppler frequency time-varying problem, which leads to the blurring and defocusing of the imaging results. Traditional imaging methods struggle to meet the imaging requirements for maneuvering targets due to a poor imaging effect or low efficiency. Given these challenges, a modified chirp Fourier transform (MCFT) imaging method is proposed in this paper, based on the specific relationship between the target rotation parameters and the radar echo signal parameters. Firstly, discrete chirp Fourier transform is used to quickly estimate the target’s coarse rotation ratio. Then, the minimum entropy function and gradient descent method are used to calculate the target’s accurate rotation ratio. Finally, the azimuth focusing image is accomplished by performing MCFT once on the azimuth echo signal using the accurate rotation ratio. This method avoids estimating and separating the sub-echo components one-by-one, considerably improves the imaging speed, and guarantees the best imaging quality by applying the global minimum entropy principle. The experimental results show that the proposed method effectively achieves the two-dimensional, high-quality, and fast imaging of maneuvering targets.

Spectral analysis for GNSS coordinate time series using chirp Fourier transform

Spectral analysis for global navigation satellite system (GNSS) coordinate time series provides a principal tool to understand the intrinsic mechanism that affects tectonic movements. Spectral analysis methods such as the fast Fourier transform, Lomb–Scargle spectrum, evolutionary power spectrum, wavelet power spectrum, etc. are used to find periodic characteristics in time series. Among spectral analysis methods, the chirp Fourier transform (CFT) with less stringent requirements is tested with synthetic and actual GNSS coordinate time series, which proves the accuracy and efficiency of the method. With the length of series only limited to even numbers, CFT provides a convenient tool for windowed spectral analysis. The results of ideal synthetic data prove CFT accurate and efficient, while the results of actual data show that CFT is usable to derive periodic information from GNSS coordinate time series.

Novel method for parameter estimation of Newton’s rings based on CFRFT and ER-WCA

Newton’s rings is one of the important optical signals, it can be used to measure the curvature radius of optical lens. Owing to the photoelectronic digitized realization and newly established mathematical model of Newton’s rings, the measuring of curvature radius can be changed to parameter estimation of Newton’s rings. Therefore, some modern signal processing tools have been successfully applied to parameter estimation of Newton’s rings, such as Fourier transform (FT), chirp-Fourier transform (CFT) and fractional Fourier transform (FRFT). Nowadays, it has been one of the latest developments in optical signal processing field. In this paper, a novel method for parameter estimation of Newton’s rings is proposed based on concise fractional Fourier transform (CFRFT) and evaporation rate based water cycle algorithm (ER-WCA). A pretreatment technology is further proposed to solve uneven illumination of actual Newton’s rings. The experimental results show that the efficiency of proposed method is much higher than that of FRFT-based method. It can also be seen from the experimental results that the proposed pretreatment technology can increase the accuracy.

Instantaneous Rotating Speed Estimation Using Adaptive Short-time Chirp-Fourier Transform and Its Applications

Instantaneous Rotating Speed Estimation Using Adaptive Short-time Chirp-Fourier Transform and Its Applications

ISAR Imaging of Targets With Complex Motion Based on Discrete Chirp Fourier Transform for Cubic Chirps

In inverse synthetic aperture radar (ISAR) imaging of targets with complex motion such as the high maneuvering airplanes and fluctuating ships with oceanic waves, the azimuth echo signals can be modeled with cubic chirps after translational motion compensation, and then, the azimuth focusing quality will be deteriorated by the time-varying chirp rate. In this paper, a parameter estimation method of cubic chirps is proposed based on the discrete chirp Fourier transform (DCFT), which is generated from DCFT for quadratic chirps. Several properties of DCFT for cubic chirps are derived, and we show that the modified DCFT (MDCFT) is more appropriate to deal with the practical applications (e.g., ISAR imaging) than the original DCFT. Therefore, we put forward the imaging algorithm based on MDCFT, and then, simulation results confirm the validity of the proposed algorithm.

Study on time-varying velocity measurement with self-mixing laser diode based on Discrete Chirp-Fourier Transform

Laser's optical output power and frequency are modulated when the optical beam is back-scattered into the active cavity of the laser. By signal processing, the Doppler frequency can be acquired, and the target's velocity can be calculated. Based on these properties, an interferometry velocity sensor can be designed. When target move in time-varying velocity mode, it is difficult to extract the target's velocity. Time-varying velocity measurement by self-mixing laser diode is explored. A mathematics model was proposed for the time-varying velocity (invariable acceleration) measurement by self-mixing laser diode. Based on this model, a Discrete Chirp-Fourier Transform (DCFT) method was applied, DCFT is analogous to DFT. We show that when the signal length N is prime, the magnitudes of all the side lobes are 1, whereas the magnitudes of the main lobe is , And the coordinates of the main lobe shows the target's velocity and acceleration information. The simulation results prove the validity of the algorithm even in the situation of low SNR when N is prime.

Performance analysis and measurement of a saw‐based group demodulator for on‐board processing in communications satellites

AbstractFuture satellites for ‘thin route’, mobile and portable services will require group demodulators on board the satellite to take advantage of the cost benefits offered with regenerative architectures. The demodulators will translate FDMA up‐links into TDM down‐links. This paper describes the measured performance of a 24‐channel multi‐carrier (64 kb/s QPSK for each carrier) group demodulator which uses SAW chirp Fourier transform (CFT) processing. The recovered data are combined into a single TDM bit stream at the standard T1 rate of 1.544 Mb/s. The 40 dB side‐lobe suppression obtained in the CFT has resulted in less than 0.35 dB combined interference degradation achieved with all channels active. The added degradation over Olympus with a saturated up‐link amplifier is less than 1 dB.

Saw‐based chirp fourier transform and its application to analogue on‐board signal processing

AbstractThis paper reports on the work done at ELAB‐RUNIT on surface acoustic wave (SAW) on‐board signal processing. The main processing is done by the analogue chirp Fourier transformer (CFT) and its inverse (ICFT). In a CFT, the input signal is transformed from an FDMA format to a TDM format and at the same time filtered by a filter bank. By multiplying and convolving the signal with chirp waveforms, the CFT is implemented by one bandpass cover filter and one chirp filter. The paper demonstrates that SAW reflector array compressors (RAC) built by ELAB‐RUNIT have suitable chirp responses and adequate precision for digital satellite communication. Two applications are described. An on‐board multicarrier demodulator (MCD) for 9·6 kb/s QPSK carriers and a processor for filtering, routeing and beam steering (FROBE) for flexible transparent repeaters. For MCDs the use of SAW CFTs leads to a power consumption for demultiplexing and A/D conversion of 15 mW per carrier with room for improvements. For transparent paylods, the FROBE leads to more flexibility and narrower guardbands than can be obtained by other analogue processors.

Investigation of chirp interference on RAC demodulation

Recently, many satellite systems have started to employ reflective-array compressors (RAC) to demodulate efficiently their M-FSK communication signals. Because the RAC's time delay varies with temperature, pilot-tones are usually introduced as the operational reference. In this letter, the basic chirp Fourier transform (CFT) is briefly reviewed. Then, an investigation into possible pilot-tone interference caused by various chirp signals with the RAC's dispersive delay properties is presented and discussed.

Fast Field Program (FFP) for Surface Duct Propagation

The FFP is a numerical method, due to H. W. Marsh, of evaluating accurately and efficiently the solution of the acoustics wave equation. Presented here is a form of the FFP, due to W. S. Liggett, in which by proper choice of an integration contour the wave solution is expressed as a sum of residues plus a branch cut integral. By appropriate approximation, these can be evaluated using the FFT or Chirp Fourier Transform algorithms. A general numerical integration scheme, which allows arbitrary sound-velocity profiles that need not be approximated by analytic functions nor divided into layers, and which permits propagation loss computation as a function of both range and depth, is used to evaluate the kernel of the FFT. Although the FFP is more generally applicable, to illustrate the procedure, the propagation loss is computed for a surface duct case with no bottom returns. Our results are compared to those in the literature for this case, which were found by normal mode and ray trace computations and from empirical data. [This research was supported by the Office of Naval Research.]