The bias eliminated least squares (BELS) method,which is known as efficient for unknown parameter estimation of transfer function in the correlated noise case,has been developed and applied effectively to the closed-loop system identification. In this paper,under the general settings,the realizations of the BELS method as a weighted instrumental variables (WIV) method in both direct and indirect closed-loop system identification are established through constructing an appropriate weighting matrix in the WIV method. The constructed structures are similar in both cases,which reveals that all the proof procedures of the two realizations are the same. Thus,the unified realizations of the BELS as the WIV method for the closed-loop system identification can be built. A simulation example is given to validate our theoretical analysis.
An important and hard problem in signal processing is the estimation of parameters in the presence of observation noise. In this paper, adaptive finite impulse response (FIR) filtering with noisy input-output data is considered and two developed bias compensation least squares (BCLS) methods are proposed. By introducing two auxiliary estimators, the forward output predictor and the backward output predictor are constructed respectively. By exploiting the statistical properties of the cross-correlation function between the least squares (LS) error and the forward/backward prediction error, the estimate of the input noise variance is obtained; the effect of the bias can thereafter be removed. Simulation results are presented to illustrate the good performances of the proposed algorithms.
The sampling rate conversion is always used in order to decrease computational amount and storage load in a system. The fractional Fourier transform (FRFT) is a powerful tool for the analysis of nonstationary signals, especially, chirp-like signal. Thus, it has become an active area in the signal processing community, with many applications of radar, communication, electronic warfare, and information security. Therefore, it is necessary for us to generalize the theorem for Fourier domain analysis of decimation and interpolation. Firstly, this paper defines the digital fre- quency in the fractional Fourier domain (FRFD) through the sampling theorems with FRFT. Secondly, FRFD analysis of decimation and interpolation is proposed in this paper with digital frequency in FRFD followed by the studies of interpolation filter and decimation filter in FRFD. Using these results, FRFD analysis of the sam- pling rate conversion by a rational factor is illustrated. The noble identities of decimation and interpolation in FRFD are then deduced using previous results and the fractional convolution theorem. The proposed theorems in this study are the bases for the generalizations of the multirate signal processing in FRFD, which can advance the filter banks theorems in FRFD. Finally, the theorems introduced in this paper are validated by simulations.
Feature extraction of symmetrical triangular linear frequency modulation continu ous wave (LFMCW) signal is studied. Combined with its peculiar characteristics, a novel algorithm based on Wigner-Hough transform (WHT) is presented for the de tection and parameter estimation of this type of waveform. The initial frequency and chirp rate of each segment of this wave are estimated, and the peak-value searching steps in the parameter space is given. Compared with Wigner-Ville dis tribution (WVD), Pseudo-Wigner-Ville distribution (PWD) and Smoothed-Peseudo -Wigner-Ville distribution (SPWD), WHT has proven itself to be the best method for feature extraction of symmetrical triangular LFMCW signal. In the end, Mont e-Carlo simulations under different SNRs are carried out, with validating resul ts on this method.
Reconstruction of a continuous time signal from its periodic nonuniform samples and multi-channel samples is fundamental for multi-channel parallel A/D and MIMO systems. In this paper,with a filterbank interpretation of sampling schemes,the efficient interpolation and reconstruction methods for periodic nonuniform sampling and multi-channel sampling in the fractional Fourier domain are presented. Firstly,the interpolation and sampling identities in the fractional Fourier domain are derived by the properties of the fractional Fourier transform. Then,the particularly efficient filterbank implementations for the periodic nonuniform sampling and the multi-channel sampling in the fractional Fourier domain are introduced. At last,the relationship between the multi-channel sampling and the filterbank in the fractional Fourier domain is investigated,which shows that any perfect reconstruction filterbank can lead to new sampling and reconstruction strategies.
Passive radar is one of the current research focuses. The implementation of the Chinese standard digital television terrestrial broadcasting (DTTB) creates a new opportunity for passive radar. DTTB system contains single-carrier and multicarrier application modes. In this paper, ambiguity functions of the DTTB signals in the single-carrier and multicarrier application modes are analyzed. Ambiguity function of the DTTB signal contains one main peak and many side peaks. The relative positions and amplitudes of the side peaks are derived and the reasons for the occurrence of the side peaks are obtained. The side peaks identification (SPI) algorithm is proposed for avoiding the false alarms caused by the side peaks. Experimental results show that the SPI algorithm can indentify all the side peaks without the power loss. This research provides the foundation for designing the DTTB based passive radar.
Oversampling is widely used in practical applications of digital signal processing. As the fractional Fourier transform has been developed and applied in signal processing fields, it is necessary to consider the oversampling theorem in the fractional Fourier domain. In this paper, the oversampling theorem in the fractional Fourier domain is analyzed. The fractional Fourier spectral relation between the original oversampled sequence and its subsequences is derived first, and then the expression for exact reconstruction of the missing samples in terms of the subsequences is obtained. Moreover, by taking a chirp signal as an example, it is shown that, reconstruction of the missing samples in the oversampled signal is suitable in the fractional Fourier domain for the signal whose time-frequency distribution has the minimum support in the fractional Fourier domain.
The fractional Fourier transform(FRFT) has multiplicity,which is intrinsic in frac-tional operator.A new source for the multiplicity of the weight-type fractional Fou-rier transform(WFRFT) is proposed,which can generalize the weight coefficients of WFRFT to contain two vector parameters M,N ∈ZM.Therefore a generalized frac-tional Fourier transform can be defined,which is denoted by the multiple-parameter fractional Fourier transform(MPFRFT).It enlarges the multiplicity of the FRFT,which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases,but also introduces new fractional Fourier transforms.It provides a unified framework for the FRFT,and the method is also available for fractionalizing other linear operators.In addition,numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.
