Parameter Estimation Of Chirp Signals Research Articles

Chirp Signal Denoising Based on Convolution Neural Network

Many classic chirp signal processing algorithms may show significant performance degradation when the signal-to-noise ratio (SNR) is low. To address this problem, this paper proposes a pre-filtering method in time-domain based on deep learning. Different from traditional signal filtering methods, the proposed denoising convolutional neural network (DCNN) is trained to recover the pure signal from the noisy signal as much as possible. Following denoising, we use two classic chirp signal parameter estimation algorithms to estimate the parameters of the DCNN output. The simulation results show that, compared with no DCNN processing, the parameter estimation accuracy is significantly improved. This is mainly due to the powerful pure signal extraction ability of DCNN, which can significantly improve the SNR and the accuracy of signal parameter estimation.

Parameter estimation for chirp signals using the spectrum phase

In this study, the authors propose for the parameter estimation of chirp signals at low signal-to-noise ratios using the spectrum phase instead of the traditional temporal phase. First, the spectrum phase expression of chirp signals is derived, which demonstrates that the spectrum phase can be approximated as a quadratic function of the frequency. However, the spectrum phase is a wrapped phase modulo 2π, like the temporal phase. To obtain the unwrapped spectrum phase, the authors develop a robust phase unwrapping method and then perform linear regression on the unwrapped spectrum phase to obtain the estimates of the parameters. Finally, the estimates are refined by the O'Shea refinement strategy to reduce bias. The simulation results show that the proposed technique has a lower signal-to-noise ratio threshold and is less complex than the existing methods.

Performance of Chirp Parameter Estimation in the Fractional Fourier Domains and an Algorithm for Fast Chirp-Rate Estimation

This article addresses the problem of fast and accurate chirp signal parameter estimation in fractional Fourier domains. By employing a perturbation analysis, it is shown that the fractional Fourier transform can be used as an effective tool to yield an asymptotically minimum-variance unbiased estimator of the chirp parameters. Furthermore, it is shown that the asymptotic performance of the fractional-Fourier-transform-based chirp-rate estimator depends only on the actual chirp rate, not the initial frequency. Consequently, the chirp-rate estimation can be done in only one-dimensional search space, which greatly reduces the computational cost. In order to validate theoretical outcomes, we propose a fast and powerful method for the estimation of chirp rates in the fractional Fourier domains based on the golden section search. Extensive computer simulations confirm the theoretical results by demonstrating that the estimation performance of the chirp rate achieves the Cramer–Rao lower bound for both single- and multicomponent chirps. Consequently, we assert that the proposed method of chirp parameter estimation in the fractional Fourier domains is the minimum-variance unbiased estimator, requiring minimal computational cost.

ADMM–Net: A Deep Learning Approach for Parameter Estimation of Chirp Signals Under Sub-Nyquist Sampling

Parameter estimation of chirp signals plays an important role in the field of radar countermeasures. Compressed sensing (CS) based sub-Nyquist sampling and parameter estimation methods alleviates the pressure on hardware systems to acquire and process chirp signals with large time-bandwidths. In this paper, a framework based on the fractional Fourier transform (FrFT) and alternating direction method of multipliers network (ADMM-Net) is proposed to realize chirp signal parameter estimation under sub-Nyquist sampling. The whole framework is composed of multiple parallel ADMM-Nets, where each ADMM-Net is defined over a data flow graph, which is derived from the iterative procedures of the ADMM algorithm for optimizing a CS-based $p$ -order FrFT spectral estimation model. The chirp rate and central frequency of chirp signals are obtained through a two-dimensional search on the spectrum image output by the network group. Experiments demonstrate that the proposed ADMM-Net-based method can achieve higher estimation accuracy and computational efficiency at lower signal-to-noise ratios and sampling ratios than traditional CS methods. We also demonstrate that the proposed ADMM-Net-based framework has strong generalization ability for multi-component chirp signals. Furthermore, we further generalize ADMM-Net to GADMM-Net, in which the activation function is data-driven instead of model-driven. Experiments demonstrate that GADMM-Net significantly improves on the basic ADMM-Net and achieves higher spectral resolution with faster computation speed.

On approximate least squares estimators of parameters of one-dimensional chirp signal

ABSTRACTChirp signals are quite common in many natural and man-made systems such as audio signals, sonar, and radar. Estimation of the unknown parameters of a signal is a fundamental problem in statistical signal processing. Recently, Kundu and Nandi [Parameter estimation of chirp signals in presence of stationary noise. Stat Sin. 2008;75:187–201] studied the asymptotic properties of least squares estimators (LSEs) of the unknown parameters of a simple chirp signal model under the assumption of stationary noise. In this paper, we propose periodogram-type estimators called the approximate least squares estimators (ALSEs) to estimate the unknown parameters and study the asymptotic properties of these estimators under the same error assumptions. It is observed that the ALSEs are strongly consistent and asymptotically equivalent to the LSEs. Similar to the periodogram estimators, these estimators can also be used as initial guesses to find the LSEs of the unknown parameters. We perform some numerical simulations to see the performance of the proposed estimators and compare them with the LSEs and the estimators proposed by Lahiri et al. [Efficient algorithm for estimating the parameters of two dimensional chirp signal. Sankhya B. 2013;75(1):65–89]. We have analysed two real data sets for illustrative purposes.

Parameter estimation of chirp signals based on fractional Fourier transform

The purpose of this project is to implement the fractional Fourier transform (FrFT) on chirp signals and realize the detection and parameter estimation of different chirp signals. In the application of FrFT, pre-estimated method is proposed in this paper to improve the speed of peak searching in the parameter estimation, and suitable dimensional normalization method is selected. So that, a faster and more effective pre-estimation searching method is proposed, and the parameters such as the frequency modulation slope, center frequency, and amplitude can be estimated at the same time. From the simulation results, the estimation of parameters for multi-components chirp signals can be actualized based on FrFt, and the mixed signals can be identified successfully.

Universal FRFT-based algorithm for parameter estimation of chirp signals

The realization of the parameter estimation of chirp signals using the fractional Fourier transform (FRFT) is based on the assumption that the sampling duration of practical observed signals would be equal to the time duration of chirp signals contained in the former. However, in many actual circumstances, this assumption seems unreasonable. On the basis of analyzing the practical signal form, this paper derives the estimation error of the existing parameter estimation method and then proposes a novel and universal parameter estimation algorithm. Furthermore, the proposed algorithm is developed which allows the estimation of the practical observed Gaussian windowed chirp signal. Simulation results show that the new algorithm works well.

Speech recovery based on the linear canonical transform

As is well known, speech signal processing is one of the hottest signal processing directions. There are exist lots of speech signal models, such as speech sinusoidal model, straight speech model, AM–FM model, gaussian mixture model and so on. This paper investigates AM–FM speech model by the linear canonical transform (LCT). The LCT can be considered as a generalization of traditional Fourier transform and fractional Fourier transform, and proved to be one of the powerful tools for non-stationary signal processing. This has opened up the possibility of a new range of potentially promising and useful applications based on the LCT. Firstly, two novel recovery methods of speech based on the AM–FM model are presented in this paper: one depends on the LCT domain filtering; the other one is based on the chirp signal parameter estimation to restore the speech signal in LCT domain. Then, experiments results are presented to verify the performance of the proposed methods. Finally, the summarization and the conclusion of the paper is given.

Fractional Power Spectrum

In this paper, by investigating the definitions of the fractional power spectrum and the fractional correlation for the deterministic process, we consider the case associated with the random process in an explicit manner. The fractional power spectral relations for the fractional Fourier domain filter are derived, and the expression for the fractional power spectrum in terms of the fractional correlation is obtained. In addition, the definitions and the properties of the fractional white noise and the chirp-stationary process are presented. Simulation results verify the theoretical derivations and demonstrate the potential applications, such as detection and parameter estimation of chirp signals, fractional power spectral estimation and system identification in the fractional Fourier domain.

Parameter estimation of chirp signals

The problem of the parameter estimation of chirp signals is addressed. Several closely related estimators are proposed whose main characteristics are simplicity, accuracy, and ease of online or offline implementation. For moderately high signal-to-noise ratios they are unbiased and attain the Cramer-Rao bound. Monte Carlo simulations verify the expected performance of the estimators. It should be easy to extend this approach to signals having polynomials of any degree in the exponent. All the derivations will be done under the assumption that the signal-to-noise ratio is sufficiently high. >