An efficient filtering structure for Lagrange interpolation

A novel filtering structure with linear complexity is proposed for Lagrange interpolation. The structure is similar to the Farrow structure in principle, but it is more efficient and has the additional feature of being order updatable on-the-fly. The main application for the proposed structure is the implementation of fractional delay filters to mitigate the symbol synchronization errors in digital communications. Some other applications are time-delay estimation, echo cancellation, acoustic modeling, and arbitrary sampling rate conversion.


Exact Relation Between Continuous and Discrete Linear Canonical Transforms
Öktem, Sevinç Figen (Institute of Electrical and Electronics Engineers (IEEE), 2009-08-01)
Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. The Fourier and fractional Fourier transforms are special cases of LCTs. We present the exact relation between continuous and discrete LCTs (which generalizes the corresponding relation for Fourier transforms), and also express it in terms of a new definition of the discrete LCT (DLCT), which is independent of the sampling interval. This p...
Türker, Burhan Lemi (Springer Science and Business Media LLC, 1992-01-01)
A novel method, based on the topology of the cardinal vertex, is described to find an upper bound for the largest eigenvalue of a graph.
On higher order approximations for hermite-gaussian functions and discrete fractional Fourier transforms
Candan, Çağatay (Institute of Electrical and Electronics Engineers (IEEE), 2007-10-01)
Discrete equivalents of Hermite-Gaussian functions play a critical role in the definition of a discrete fractional Fourier transform. The discrete equivalents are typically calculated through the eigendecomposition of a commutator matrix. In this letter, we first characterize the space of DFT-commuting matrices and then construct matrices approximating the Hermite-Gaussian generating differential equation and use the matrices to accurately generate the discrete equivalents of Hermite-Gaussians.
On the Eigenstructure of DFT Matrices
Candan, Çağatay (Institute of Electrical and Electronics Engineers (IEEE), 2011-03-01)
The discrete Fourier transform (DFT) not only enables fast implementation of the discrete convolution operation, which is critical for the efficient processing of analog signals through digital means, but it also represents a rich and beautiful analytical structure that is interesting on its own. A typical senior-level digital signal processing (DSP) course involves a fairly detailed treatment of DFT and a list of related topics, such as circular shift, correlation, convolution operations, and the connectio...
Robust adaptive unscented Kalman filter for attitude estimation of pico satellites
Hacızade, Cengiz; Söken, Halil Ersin (Wiley, 2014-02-01)
Unscented Kalman filter (UKF) is a filtering algorithm that gives sufficiently good estimation results for the estimation problems of nonlinear systems even when high nonlinearity is in question. However, in case of system uncertainty or measurement malfunctions, the UKF becomes inaccurate and diverges by time. This study introduces a fault-tolerant attitude estimation algorithm for pico satellites. The algorithm uses a robust adaptive UKF, which performs correction for the process noise covariance (Q-adapt...
Citation Formats
Ç. Candan, “An efficient filtering structure for Lagrange interpolation,” IEEE SIGNAL PROCESSING LETTERS, pp. 17–19, 2007, Accessed: 00, 2020. [Online]. Available: