Space is becoming increasingly congested and contested, which calls for effective means to conduct effective monitoring of high-value space assets, especially in Space Situational Awareness (SSA) missions, while there are imperfections in existing methods and corresponding algorithms. To overcome such a problem, this letter proposes an algorithm for accurate Connected Element Interferometry (CEI) in SSA based on more interpolation information and iterations. Simulation results show that: (i) after iterations, the estimated asymptotic variance of the proposed method can basically achieve uniform convergence, and the ratio of it to ACRB is 1.00235 in δ0 ∈ [-0.5, 0.5], which is closer to 1 than the current best AM algorithms; (ii) In the interval of SNR ∈ [-14dB, 0dB], the estimation error of the proposed algorithm decreases significantly, which is basically comparable to CRLB (maintains at 1.236 times). The research of this letter could play a significant role in effective monitoring and high-precision tracking and measurement with significant space targets during futuristic SSA missions.

The narrow bandwidth limitation of 300-3400Hz on the public switching telephone network results in speech quality deterioration. In this paper, we propose an artificial bandwidth extension approach that reconstructs the missing lower bandwidth of 50-300Hz using sinusoidal synthesis based on the first formant location. Sinusoidal synthesis generates sinusoidal waves with a harmonic structure. The proposed method detects the fundamental frequency using an autocorrelation method based on YIN algorithm, where a threshold processing avoids the false fundamental frequency detection on unvoiced sounds. The amplitude of the sinusoidal waves is calculated in the time domain from the weighted energy of 300-600Hz. In this case, since the first formant location corresponds to the first peak of the spectral envelope, we reconstruct the harmonic structure to avoid attenuating and overemphasizing by increasing the weight when the first formant location is lower, and vice versa. Consequently, the subjective and objective evaluations show that the proposed method reduces the speech quality difference between the original speech signal and the bandwidth extended speech signal.

The windowed interpolation DFT methods have been utilized to estimate the parameters of a single frequency and multi-frequency signal. Nevertheless, they do not work well for the real-valued sinusoids with closely spaced positive- and negative- frequency. In this paper, we describe a novel three-point windowed interpolation DFT method for frequency measurement of real-valued sinusoid signal. The exact representation of the windowed DFT with maximum sidelobe decay window (MSDW) is constructed. The spectral superposition of positive- and negative-frequency is considered and calculated to improve the estimation performance. The simulation results match with the theoretical values well. In addition, computer simulations demonstrate that the proposed algorithm provides high estimation accuracy and good noise suppression capability.

An extended harmonic disturbance observer is designed for speed (or position) sensorless current control of DC motor subject to a biased sinusoidal disturbance and parameter uncertainties. The proposed method does not require the information on the mechanical part of the motor equation. Theoretical analysis via the singular perturbation theory is performed to verify that the feedforward compensation using the estimation can improve the robust transient performance of the closed-loop system. A stability condition is derived against parameter uncertainties. Comparative experimental results validate the robustness of the proposed method against the uncertainties.

This paper presents an implementation of a digital chaotic signal generator based on compound one-dimensional sinusoidal maps. The proposed chaotic map not only offers high chaoticity measured from a positive lyapunov exponent but also provides diverse bifurcation structures with robust chaos over most regions of parameter spaces. Implementation on FPGA realizes small number of components and offers a highly random chaotic sequence with no autocorrelation. The proposed chaotic signal generator offers a potential alternative in random test pattern generation or in secured data communication applications.

Blind source separation (BSS) techniques are required for various signal decomposing issues. Independent component analysis (ICA), assuming only a statistical independence among stochastic source signals, is one of the most useful BSS tools because it does not need a priori information on each source. However, there are many requirements for decomposing multiple deterministic signals such as complex sinusoidal signals with different frequencies. These requirements may include pulse compression or clutter rejection. It has been theoretically shown that an ICA algorithm based on maximizing non-Gaussianity successfully decomposes such deterministic signals. However, this ICA algorithm does not maintain a sufficient separation performance when the frequency difference of the sinusoidal waves becomes less than a nominal frequency resolution. To solve this problem, this paper proposes a super-resolution algorithm for complex sinusoidal signals by extending the maximum likelihood ICA, where the probability density function (PDF) of a complex sinusoidal signal is exploited as a priori knowledge, in which the PDF of the signal amplitude is approximated as a Gaussian distribution with an extremely small standard deviation. Furthermore, we introduce an optimization process for this standard deviation to avoid divergence in updating the reconstruction matrix. Numerical simulations verify that our proposed algorithm remarkably enhances the separation performance compared to the conventional one, and accomplishes a super-resolution separation even in noisy situations.

For an adaptive system identification filter with a stochastic input signal, a coefficient vector updated with an NLMS algorithm converges in the sense of ensemble average and the expected convergence vector has been revealed. When the input signal is periodic, the convergence of the adaptive filter coefficients has also been proved. However, its convergence vector has not been revealed. In this paper, we derive the convergence vector of adaptive filter coefficients updated with the NLMS algorithm in system identification for deterministic sinusoidal inputs. Firstly, we derive the convergence vector when a disturbance does not exist. We show that the derived convergence vector depends only on the initial vector and the sinusoidal frequencies, and it is independent of the step-size for adaptation, sinusoidal amplitudes, and phases. Next, we derive the expected convergence vector when the disturbance exists. Simulation results support the validity of the derived convergence vectors.

In this letter, an improved statistical simulation model with a new parameter computation method is proposed for Rayleigh fading channels. Compared with the existing simulators, the proposed model yields much higher simulation efficiency, while it can still obtain adequate approximations of the desired statistical properties.

In the near future, decentralized network systems consisting of a huge number of sensor nodes are expected to play an important role. In such a network, each node should control itself by means of a local interaction algorithm. Although such local interaction algorithms improve system reliability, how to design a local interaction algorithm has become an issue. In this paper, we describe a local interaction algorithm in a partial differential equation (or PDE) and propose a new design method whereby a PDE is derived from the solution we desire. The solution is considered as a pattern of nodes' control values over the network each of which is used to control the node's behavior. As a result, nodes collectively provide network functions such as clustering, collision and congestion avoidance. In this paper, we focus on a periodic pattern comprising sinusoidal waves and derive the PDE whose solution exhibits such a pattern by exploiting the Fourier method.

A new frequency estimator for a single real-valued sinusoid signal in white noise is proposed. The new estimator uses the Pisarenko Harmonic Decomposer (PHD) estimator to get a coarse frequency estimate and then makes use of multiple correlation lags to obtain an adjustment term. For the limited-length single sinusoid, its correlation has the same frequency as itself but with a non-zero phase. We propose to use Taylor series to expand the correlation at the PHD coarse estimated frequency with amplitude and phase of the correlation into consideration. Simulation results show that this new method improves the estimation performance of the PHD estimator. Moreover, when compared with other existing estimator, the mean square frequency error of the proposed method is closer to the Cramer-Rao Lower Bound (CRLB) for certain SNR range.

An algorithm for estimating sinusoidal parameters is presented. In this paper, it is assumed that an observed signal is a single sinusoidal signal contaminated by white Gaussian noise. Based on this assumption, the sinusoidal parameters can be found by minimizing a cost function using the mean squared error (MSE) between the observed signal and a sinusoidal signal with arbitrary sinusoidal parameters. Because the cost function is nonlinear and not convex, it has undesirable local minima. To solve the minimization problem, we propose to use the roots of an algebraic equation. The algebraic equation is derived straightforwardly from the cost function. We show that the global solution is formulated by using the roots of the algebraic equation.

ICA (Independent Component Analysis) has a remarkable capability of separating mixtures of stochastic random signals. However, we often face problems of separating mixtures of deterministic signals, especially sinusoidal signals, in some applications such as radar systems and communication systems. One may ask if ICA is effective for deterministic signals. In this paper, we analyze the basic performance of ICA in separating mixtures of complex sinusoidal signals, which utilizes the fourth order cumulant as a criterion of independency of signals. We theoretically show that ICA can separate mixtures of deterministic sinusoidal signals. Then, we conduct computer simulations and radio experiments with a linear array antenna to confirm the theoretical result. We will show that ICA is successful in separating mixtures of sinusoidal signals with frequency difference less than FFT resolution and with DOA (Direction of Arrival) difference less than Rayleigh criterion.

The noise performances under AWGN channel of the IF-derivative and the quadrature differential FM discriminators, which are widely utilized in modern low power wireless radios, are analyzed and compared. The analysis relies upon the time-domain multi-sinusoidal representation of the noise that facilitates accurate and closed-form analytical SNR characteristics. Derivation of the SNR equations is detailed and discussion based on the analysis results is given to provide insights into the discriminators' performance limitation where it is demonstrated that the differential scheme is considerably more advantageous. Simulated SNR characteristics of practical continuous-phase frequency shift keying (CPFSK) systems using both the FM discriminators are presented as analysis verification.

This letter proposes a low-complexity scheme for estimating the frequency of a complex sinusoid in flat fading channels. The proposed estimator yields an estimation performance that is comparable to the existing autocorrelation-based frequency estimator, while retaining the same frequency range. Its implementation complexity is much lower than the conventional scheme, thus this allows for fast estimation in real time.

Two discrete-time Wirtinger-type inequalities relating the power of a finite-length signal to that of its circularly-convolved version are developed. The usual boundary conditions that accompany the existing Wirtinger-type inequalities are relaxed in the proposed inequalities and the equalizing sinusoidal signal is free to have an arbitrary phase angle. A measure of this sinusoidal signal's power, when corrupted with additive noise, is proposed. The application of the proposed measure, calculated as a ratio, in the evaluation of the power of a sinusoid of arbitrary phase with the angular frequency π/N, where N is the signal length, is thoroughly studied and analyzed under additive noise of arbitrary statistical characteristic. The ratio can be used to gauge the power of sinusoids of frequency π/N with a small amount of computation by referring to a ratio-versus-SNR curve and using it to make an estimation of the noise-corrupted sinusoid's SNR. The case of additive white noise is also analyzed. A sample permutation scheme followed by sign modulation is proposed for enlarging the class of target sinusoids to those with frequencies M π/N, where M and N are mutually prime positive integers. Tandem application of the proposed scheme and ratio offers a simple method to gauge the power of sinusoids buried in noise. The generalization of the inequalities to convolution kernels of higher orders as well as the simplification of the proposed inequalities have also been studied.

In this paper, a recursive Gauss-Newton (RGN) algorithm is first developed for adaptive tracking of the amplitude, frequency and phase of a real sinusoid signal in additive white noise. The derived algorithm is then simplified for computational complexity reduction as well as improved with the use of multiple forgetting factor (MFF) technique to provide a flexible way of keeping track of the parameters with different rates. The effectiveness of the simplified MFF-RGN scheme in sinusoidal parameter tracking is demonstrated via computer simulations.

A new sinusoidal modeling approach for the analysis-by-synthesis (AbS) of parameters that characterize a linear combination of damped sinusoids is proposed. In addition to the typical sinusoidal parameters, two different damping factors, which represent the time-varying nature of speech, were used to efficiently reduce the modeling error. Even though the proposed model does not employ the overlap-adding synthesis or smoothly interpolative synthesis scheme, it shows substantially better modeling performance in the synthesis of voiced and transient segments.

By utilizing the second and fourth order linear prediction errors, a novel estimator for a single noisy sinusoid is devised. The frequency estimate is obtained from a solving a cubic equation and a simple root selection procedure is provided. Asymptotical variance of the estimated frequency is derived and confirmed by computer simulations. It is demonstrated that the proposed estimator is superior to the reformed Pisarenko harmonic decomposer, which is the improved version of Pisarenko harmonic decomposer.

This paper discusses the on-line frequency identification problem for a measured sinusoidal signal by using the adaptive method and filter theory. The proposed method is based on an identity between the sinusoidal signal and its second order derivative. For a set of chosen parameters, the proposed method is robust to the initial phase, the amplitude, and the frequency in a wide range. The convergence rate can be adjusted by the chosen parameters. The estimation error mainly depends on the frequency of the sinusoid, the measurement noise and a key design parameter.

Sinusoidal representation has been widely applied to speech modification, low bit rate speech and audio coding. Usually, speech signal is analyzed and synthesized using the overlap-add algorithm or the peak-picking algorithm. But the overlap-add algorithm is well known for high computational complexity and the peak-picking algorithm cannot track the transient and syllabic variation well. In this letter, both algorithms are applied to speech analysis/synthesis. Peaks are picked in the curve of power spectral density for speech signal; the frequencies corresponding to these peaks are arranged according to the descending orders of their corresponding power spectral densities. These frequencies are regarded as the candidate frequencies to determine the corresponding amplitudes and initial phases according to the least mean square error criterion. The summation of the extracted sinusoidal components is used to successively approach the original speech signal. The results show that the proposed algorithm can track the transient and syllabic variation and can attain the good synthesized speech signal with low computational complexity.