A modification of the conventional Lagrange interpolator is proposed in this paper, that allows one to approximate a band-limited signal from its own nonuniform samples with high accuracy. The modification consists in applying the Lagrange method to the signal, but pre-multiplied by a fixed function, and then solving for the desired signal value. Its efficiency lies in the fact that the fixed function is independent of the sampling instants. It is shown in this paper that the function can be selected so that the interpolation error decreases exponentially with the number of samples, for the case in which the sampling instants have a maximum deviation from a uniform grid. This paper includes a low-complexity recursive implementation of the method. Its accuracy is validated in the numerical examples by comparison with several interpolators in the literature, and by deriving upper and lower bounds for its maximum error.

A variable fractional delay (VFD) filter is presented that constitutes an efficient alternative to the usual Farrow structure. The filter is constructed by multiplying the signal to interpolate by a window with proper truncation properties, and then applying the sampling theorem. The resulting interpolator involves less arithmetic operations than the existing variants of the Farrow structure. Besides, if its coefficients are numerically optimized, its performance is close to that of the FIR equi-ripple filter. The final part of the correspondence includes a description of the VFD filter implementation corresponding to this interpolator.

We present a technique to compute the Spectral and (Unitary) Root MUSIC estimations from the roots of a real polynomial in the problem of estimating the angles of arrival to a Uniform Linear Array (ULA). The computed estimations are the actual MUSIC or (Unitary) Root MUSIC estimations, but the need for a one-dimensional (1-D) search in Spectral MUSIC is eliminated, and the number of polynomial coefficients to compute in (Unitary) Root MUSIC is halved. Besides, the proposed technique makes it possible to perform the polynomial rooting step in these methods through real arithmetic.

In the problem of estimating the angles of arrival to a uniform linear array, we present an efficient method to compute Maximum Likelihood (ML) estimations, based on the Modified Variable Projection (MVP) algorithm. In contrast to methods like Iterative Quadratical Maximum Likelihood (IQML) or the Iterative Method of Direction Estimation (IMODE), it is not based on a polynomial parameterization but on directly exploiting the Vandermonde structure through analytical tools like the Fast Fourier Transform (FFT), the geometric series summation formula, and Horner's synthetic division. The computational burden of the proposed method is significantly smaller than the burden of IMODE and of the Relaxation (RELAX) algorithm. Besides, it is shown that the computation of the ML estimation can be divided in a preliminary step in which a few FFTs are computed and an iterative step with a complexity that is independent of the array size.

Phase quality is a key element in the analysis of the deformation of the Earth's surface carried out with differential synthetic aperture radar interferometry. Various decorrelation sources may degrade the surface deformation estimates, and thus, phase filters are needed for this kind of application. The well-known Goldstein filter is the most widely used due to its simple implementation and computational efficiency. In the past years, improved filters have been proposed, which are based on this filter but introduce variations in the data processing. The effectiveness of these filters mostly depends on the size of the filtering window, the weight of the smoothed spectrum, and the kernel used to filter the spectrum. In this paper, we evaluate the performance of four of these filters and present a new method that outperforms all of them. The proposed filter is based on an iterative method in which the original phase is denoised progressively with adaptive filtering windows of different sizes. The effectiveness of the filter is controlled by the interferometric coherence, a direct indicator of the phase quality. Moreover, we introduce some modifications regarding the processing of the power spectrum. Specifically, we propose to smooth the original phase using a new filter which is based on a Chebyshev interpolation scheme. The performance of the new filter has been tested on both simulated and real interferograms, acquired by RADARSAT-2 and the Uninhabited Aerial Vehicle Synthetic Aperture Radar, which mapped two different geological events that caused surface deformation.

This paper presents a method to interpolate a periodic band-limited signal from its samples lying at nonuniform positions in a regular grid, which is based on the FFT and has the same complexity order as this last algorithm. This kind of interpolation is usually termed “the missing samples problem” in the literature, and there exists a wide variety of iterative and direct methods for its solution. The one presented in this paper is a direct method that exploits the properties of the so-called erasure polynomial and provides a significant improvement on the most efficient method in the literature, which seems to be the burst error recovery (BER) technique of Marvasti's The paper includes numerical assessments of the method's stability and complexity.