Frequency estimation of a two dimensional (2-D) multi-component sinusoidal signal in the presence of additive white Gaussian noise (AWGN) is a significant problem in various disciplines such as signal processing, radar/sonar, and wireless communications. This letter presents a novel, fast and accurate DFT-based algorithm for the frequency estimation of 2-D multi-component sinusoidal signals. We show that the proposed method attains the Cramér-Rao bound (CRB) when the parameters DFT-shift, iteration number, and minimum DFT frequency separations are chosen appropriately. Comprehensive numerical simulation results show that our algorithm almost reaches the CRB limit after a certain signal-to-noise ratio (SNR) threshold value.

Parameter estimation of multiple sinusoids is one of the fundamental problems of signal processing having numerous application areas, including wireless communications and array signal processing. This article proposes an iterative, fast, and efficient algorithm to estimate the frequencies and amplitudes of multiple sinusoids in noisy environments. The proposed approach interpolates on the q-shifted DFT coefficients of multiple sinusoids. We theoretically demonstrate that the performance of the proposed algorithm depends on DFT-shift, number of iterations and minimum DFT frequency separation parameters. Further, mean square error of the proposed algorithm achieves the Cramér-Rao lower bound when these parameters are selected appropriately. We also propose solid bounds regarding how these parameters can be selected for optimum overall performance. The total computational cost of the proposed algorithm is in the order ofO(K NlogN), where K is the number of sinusoidal components and N is the signal length. We provide comprehensive numerical simulations that confirm the correctness of our theoretical deductions.

Estimating the frequencies of a multi-component sinusoidal signal is a fundamental problem in signal processing that has very wide and diverse application areas. Most of these applications require very fast and accurate estimation of the sinusoidal frequencies. This letter presents a fast, accurate, simple, and powerful DFT-based algorithm that estimates the frequencies of sums of multiple exponential sinusoidal signals. We show that the presented algorithm requires much less computational cost compared to conventional parametric and non-parametric methods. The simulation results show that the proposed method nearly reaches the Crámer-Rao lower limit after a certain SNR threshold.

Automatic modulation classification has significant commercial and military applications and is one of the most challenging problems of the cognitive radio. To demodulate a captured signal, it is necessary to know the parameters of the signals and the preliminary information about the type of modulation. However, in most cases, the signal has no prior knowledge of the modulation type. Even more, there may not be a modulation pool available for possible modulation types. Cyclostationary-based features can be employed to blindly identify the unknown modulation type. In this study, a detailed theoretical analysis of the first order cyclostationarity was performed on FSK and AM signals, which are known to be first-order cyclostationary. Theoretical relationship between the threshold and the constant false alarm rate detector is derived for the first order cyclostationarity test. Theoretical analyses are validated by simulation results.

Fast and accurate frequency estimation of a complex sinusoidal plays an important role in many applications, including communications, radar, and sonar. This paper presents two methods for the frequency estimation of a complex sinusoidal in noisy environments. The proposed methods interpolate on shifted DFT coefficients to acquire the frequency estimates iteratively. The first method interpolates on the q-shifted DFT coefficients of the signal, whose optimum iteration number is found to be a logarithmic function of the signal length. Furthermore, we also show that by appropriately selecting the value of the shift q, the proposed method becomes asymptotically efficient. In the second method, we use hybrid half-shifted and q-shifted DFT interpolators together, which converges in only two iterations. It is shown that both of the estimators are asymptotically unbiased with their mean square errors performing on the Crámer-Rao lower bound. Theoretical results are validated by extensive computer simulations.

In this letter, a method for finding the compact fractional Fourier domains is presented. As a measure of compactness, we take the ℓ1-norm. It is proposed that there exists at least one fractional Fourier domain in which ℓ1-norm of the transformed signal is minimum. A coarse-to-fine grid search strategy is adopted to find the optimum fractional Fourier transform angle that makes ℓ1-norm minimum with low computational cost. Extensive simulsation results validate the proposed method.