A New Matrix Method for Reconstruction of Band-Limited Periodic Signals from the Sets of Integrated Values

Predrag PETROVIC  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.6   pp.1446-1454
Publication Date: 2008/06/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.6.1446
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
signal reconstruction,  band-limited signals,  analytical solutions,  integrated values,  

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Summary: 
This paper presents a new method for reconstruction of trigonometric polynomials, a specific class of bandlimited signals, from a number of integrated values of input signals. It is applied in signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. The proposed method of processing can be used for precise rms measurements of periodic signal (or power and energy) based on the presented signal reconstruction. Based on the value of the integral of the original input (analogue) signal, with a known frequency spectrum but unknown amplitudes and phases, a reconstruction of its basic parameters is done by the means of derived analytical and summarized expressions. Subsequent calculation of all relevant indicators related to the monitoring and processing of ac voltage and current signals is provided in this manner. Computer simulation demonstrating the precision of these algorithms. We investigate the errors related to the signal reconstruction, and provide an error bound around the reconstructed time domain waveform.