Abstract

Traditional Finite Rate of Innovation (FRI) theory has considered the problem of sampling continuous-time signals. This framework can be naturally extended to the case where the input is a discrete-time signal. Here we present a novel approach which uses both the traditional FRI sampling scheme, based on the annihilating filter method, and the fact that in this new setup the null space of the problem to be solved is finite dimensional. In the noiseless scenario, we show that this new approach is able to perfectly recover the original signal at the critical sampling rate. We also present simulation results in the noisy scenario where this new approach improves performances in terms of the mean squared error (MSE) of the reconstructed signal when compared to the canonical FRI algorithms and compressed sensing (CS).

Highlights

  • Finite Rate of Innovation (FRI) sampling theory [1,2,3,4] has shown that it is possible to sample and reconstruct classes of non-bandlimited signals

  • In this paper we present a novel method that is based on the annihilating filter that is used in the traditional FRI framework, but we take advantage of the fact that in this new context the null space has finite dimension

  • We show simulation results where the new finite dimensional FRI method outperforms traditional FRI and compressed sensing (CS)

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Summary

INTRODUCTION

FRI sampling theory [1,2,3,4] has shown that it is possible to sample and reconstruct classes of non-bandlimited signals. Authors in [5] present the use of polynomial or exponential reproducing kernels with the advantage of achieving perfect reconstruction with compact support kernels This framework has recently been extended to arbitrary sampling kernels with the penalty of not achieving perfect reconstruction [6]. The reconstruction is based on estimating exponentials from a sequence of samples, which is a classical problem in spectral estimation [7, 8] This framewok can be naturally extended to discrete-time signals. In this paper we present a novel method that is based on the annihilating filter that is used in the traditional FRI framework, but we take advantage of the fact that in this new context the null space has finite dimension.

TRADITIONAL FRI IN DISCRETE-TIME
FINITE DIMENSIONAL FRI
Perfect reconstruction in the noiseless scenario
Noisy case
SIMULATION RESULTS
CONCLUSIONS

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