Perfect pulse-compression coding via ARMA algorithms and unimodular transfer functions

Lassi Roininen; Markku S. Lehtinen

doi:10.3934/ipi.2013.7.649

Article Contents

2013, Volume 7, Issue 2: 649-661. Doi: 10.3934/ipi.2013.7.649

This issue Previous Article Constructing continuous stationary covariances as limits of the second-order stochastic difference equations Next Article

Perfect pulse-compression coding via ARMA algorithms and unimodular transfer functions

Lassi Roininen^1, and
Markku S. Lehtinen^1,

1.
University of Oulu, Sodankylä Geophysical Observatory, Tähteläntie 62, FI-99600 Sodankylä

Received: November 30, 2011

Revised: February 28, 2013

Published: April 2013

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Abstract

We propose a method to construct perfect pulse-compression codes with autoregressive moving average algorithms. We first show the relation between the study of coding and decoding techniques in radar engineering and the study of unimodular polynomials with constrained coefficients. Then we extend the study to unimodular Fourier series and unimodular rational functions. We use the Fourier series and rational functions as transfer functions in the autoregressive moving average algorithms. We show that by a suitable choice of the coefficients, the autoregressive moving average algorithms are realisable, stable and causal. We show examples of some almost perfect codes, i.e. numerically truncated perfect codes. We end by proposing perfect code design principles for practical radar engineering purposes.

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Mathematics Subject Classification: Primary: 68P30; Secondary: 94A12, 93E11, 93E03.

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