Discrete Chirp Fourier Transform Research Articles

Two-Step Frequency Estimation of GNSS Signal in High-Dynamic Environment

To improve frequency accuracy which is affected by two parameters in high-dynamic acquisition, we propose a two-step frequency estimation method based on the mean frequency (MF) model for high-dynamic parameters estimation. The first step is based on the discrete chirp-Fourier transform (DCFT) for coarse MF estimation, where the MF accuracy and frequency search step are derived. In the second step, the maximum likelihood estimation process (MLEP) is adopted for fine MF estimation. Compared with state-of-art methods, it is verified that the two-step method can improve the detection probability in coarse MF estimation and improve the MF accuracy with low computational burdens under conditions with a moderate signal-to-noise ratio (SNR).

A recognition algorithm of VGPO jamming based on discrete chirp-Fourier transform

This paper addresses the recognition problem of velocity gate pull-off (VGPO) jamming from the target echo signal for the velocity-based tracking system. The discrete chirp-Fourier transform (DCFT) is studied in this paper to jointly estimate the chirp rates and frequencies of the target and jamming signals. Firstly, the scaling characteristic of the DCFT algorithm is explored. Then, we focus on the quantitative effect of the VGPO jamming signal by analyzing the jointly estimated results in each pulse. The quantitative effect indicates that, as long as the estimated frequency is unchanged, the relationship between the estimated chirp rate and the pulse numbers is similar to the relationship between the frequency offset of VGPO jamming and the time. Finally, by utilizing the joint estimated results in each pulse repetition interval and calculating the mean square to variance ratio (MSVR) of the normalized estimated chirp rate, the VGPO jamming can be recognized. Simulation results show that the jamming signal and the target echo become distinguishable with the proposed feature. Comparing to the existing works, the proposed method can correctly recognize the jamming signal with lower jamming-to-noise ratio (JNR) 5 dB with less data needed, which means it can work effectively in the early stage of interference implementation and shows great potential in practical applications.

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.

Multicomponent Chirp Signal Detection Based on Discrete Chirp-Fourier Transform

This paper investigates the signal detection of multiple chirps based on the discrete chirp-Fourier transform (DCFT). The detection method based on signal energy is proposed and the detection performance is analyzed. Firstly, the relationship of signal energy in both the time and DCFT domain is analyzed. An important property is presented, that is, the total energy of the signal in the time domain is equal to the sum of energy along the direction of constant frequency in the DCFT domain. The detection decision threshold of the multicomponent chirp signal is derived in ideal noiseless environment. Secondly, by analyzing the characters of the additive independent identical distribution Gaussian white noise in the DCFT domain, the modified detection decision threshold of the multicomponent chirp signal is determined in noisy environment. Finally, the simulation results show the effectiveness of the proposed method.

A block zero-padding method based on DCFT for L1 parameter estimations in weak signal and high dynamic environments

Weak L1 signal acquisition in a high dynamic environment primarily faces a challenge: the integration peak is negatively influenced by the possible bit sign reversal every 20 ms and the frequency error. The block accumulating semi-coherent integration of correlations (BASIC) is a state-of-the-art method, but calculating the inter-block conjugate products restricts BASIC in a low signal-to-noise ratio (SNR) acquisition. We propose a block zero-padding method based on a discrete chirp-Fourier transform (DCFT) for parameter estimations in weak signal and high dynamic environments. Compared with the conventional receiver architecture that uses closed-loop acquisition and tracking, it is more suitable for open-loop acquisition. The proposed method combines DCFT and block zero-padding. In this way, the post-correlation signal is coherently post-integrated with the bit sequence stripped off, and the high dynamic parameters are precisely estimated using the threshold set based on a false alarm probability. In addition, the detection performance of the proposed method is analyzed. Simulation results show that compared with the BASIC method, the proposed method can precisely detect the high dynamic parameters in lower SNR when the length of the received signal is fixed.

Discrete chirp‐Fourier transform‐based acquisition algorithm for weak global positioning system L5 signals in high dynamic environments

For the acquisition of weak global positioning system L5 signals in high dynamic environments, coherent integration time is necessarily extended for signal-to-noise ratio improvement. However, the incidental problems, such as high-rate sign transitions, tiered codes and particularly the concurrence of Doppler shift and Doppler rate, will bring challenges to the acquisition. This study proposes a novel acquisition algorithm based on the discrete chirp-Fourier transform (DCFT) to solve the problems above. The 1 ms complex correlation is modelled as a chirp signal to account for high dynamics effect. Then the DCFT is introduced to simultaneously estimate the Doppler shift and Doppler rate residuals. In this way, the 1 ms complex correlations are coherently post-integrated and a high processing gain can be obtained when both the primary and secondary code phases are aligned. Furthermore, the false alarm and detection probabilities are derived to statistically characterise the acquisition performance. Simulation results demonstrate that the proposed algorithm is tolerant of high dynamics and robust to noise. Specifically, it can acquire the L5 signal with up to 20 g acceleration and only 25 dB Hz carrier-to-noise ratio, which is impossible for the conventional fast Fourier transform scheme.

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.

Discrete chirp Fourier transform based analysis of reconstructed interference fields in digital holographic interferometry

In digital holographic interferometry, the information on the measurand is encoded in the phase of the reconstructed interference fields. This letter introduces a new method for the analysis of the reconstructed interference fields using discrete chirp Fourier transform (DCFT). In the proposed method, the interference phase to be estimated is modelled as a piecewise polynomial signal. Each row of the reconstructed interference field is subsequently divided into several segments, and a parametric estimation of the phase using DCFT is performed in each segment. We show that the phase estimated in this manner is accurate and continuous, thereby enabling us to bypass the commonly followed practices of filtering and 2-D phase unwrapping. Simulation and experimental results substantiate the effectiveness of the proposed method.

A novel approach for characterizing the nonlinear phase steps of the PZT in interferometry

We propose a novel approach to estimate the phase distribution in the presence of nonlinear response of the PZT. The proposed method is an outcome of two different concepts based on the discrete chirp Fourier transform (DCFT) and the maximum-likelihood estimator for the estimation of nonlinear phase step. The robustness of the proposed method is tested for various magnitudes of nonlinearity and harmonics. Comparison of our proposed method with the bench marking algorithm by Hibino et al.'s six and nine sample algorithm in the presence of noise shows that our method is highly efficient.

Estimation of FM signal parameters in impulse noise environments

A simple algorithm based on discrete chirp Fourier transform (DCFT) is used for the chirp signal parameters estimation in impulse noise environments. A modification of the DCFT is introduced in order to produce accurate estimates in this case. This modification, called the robust DCFT, produces highly accurate results in impulse noise environments, while for the Gaussian noise it is only slightly worse than the standard one. Generalization to the parametric estimation of polynomial phase signals is given. It is based on the robust form of the integrated generalized ambiguity function (IGAF). We applied the IGAF-based procedure on the signal filtered by using the robust filter designed in the frequency domain.

Comments on discrete chirp-Fourier transform and its application to chirp rate estimation [with reply

This comment points out that the sample rate of the discrete chirp-Fourier transform (DCFT) proposed by Xia (see ibid., vol.48, p. 3122-33, 2000) is not sufficient to avoid severe picket-fence effect and causes some restrictions for its practical applications. By increasing the sample rate and modifying the DCFT definition, a new robust DCFT is proposed. Xia (see ibid., vol.50, no.12, p.3116, 2002) replies by first correcting an error on the analog-to-discrete parameter conversions of a chirp signal. Xia also add that when the chirp rate detection resolution is increased, it is more robust to the chirp rate error. On the other- hand, what is sacrificed by doing so is that the magnitudes of the sidelobes of the transform are increased, which may limit its capability of detecting chirps in a multicomponent or low SNR signal. Therefore, which DCFT needs to be used has to depend on the practical application.

Discrete chirp-Fourier transform and its application to chirp rate estimation

The discrete Fourier transform (DFT) has found tremendous applications in almost all fields, mainly because it can be used to match the multiple frequencies of a stationary signal with multiple harmonics. In many applications, wideband and nonstationary signals, however, often occur. One of the typical examples of such signals is chirp-type signals that are usually encountered in radar signal processing, such as synthetic aperture radar (SAR) and inverse SAR imaging. Due to the motion of a target, the radar return signals are usually chirps, and their chirp rates include the information about the target, such as the location and the velocity. In this paper, we study discrete chirp-Fourier transform (DCFT), which is analogous to the DFT. Besides the multiple frequency matching similar to the DFT, the DCFT can be used to match the multiple chirp rates in a chirp-type signal with multiple chirp components. We show that when the signal length N is prime, the magnitudes of all the sidelobes of the DCFT of a quadratic chirp signal are 1, whereas the magnitude of the mainlobe of the DCFT is /spl radic/N. With this result, an upper bound for the number of the detectable chirp components using the DCFT is provided in terms of signal length and signal and noise powers. We also show that the N-point DCFT performs optimally when N is a prime.