Linear Prolate Functions for Signal Extrapolation with Time Shift

Generalized Prolate Spheroidal Functions

Generalized Prolate Spheroidal Functions (GPSF) are the eigenfunctions of the truncated Fourier transform, restricted to D-dimensional balls in the spatial domain and frequency domain. Despite their useful properties in many applications, GPSFs are often replaced by crude approximations. The purpose of this paper is to review the elements of computing GPSFs and associated eigenvalues. This pape...

Digital Binary Phase-shift Keyed Signal Detector

We have developed the effective algorithm for detecting digital binary phase-shift keyed signals. This algorithm requires a small number of arithmetic operations over the signal period. It can be relatively easy implemented based on the modern programmable logic devices. It also provides high interference immunity by identifying signal presence when signal-to-noise ratio is much less that its w...

A Fast Algorithm for Selective Signal Extrapolation with Arbitrary Basis Functions

Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by generating a model of the signal to be extrapolated as weighted superposition of basis functions. Unfortunately, this algorithm is computationally very expensive...

Extrapolation of Transient Electromagnetic Response Using Approximate Prolate Series

A novel technique for extrapolation of transient response using early-time and low-frequency data is proposed in this paper. An improved extrapolation scheme using approximate prolate series is presented to obtain a transient electromagnetic response. The approximate prolate series, which has an approximately band-limited and sub-domain nature, is a better choice for extrapolating the timedomai...

On Functions of Linear Shift Register Sequences