FHSS signal sparsification in the Hermite transform domain

2016 ◽  
Author(s):  
Milos Brajovic ◽  
Andjela Draganic ◽  
Irena Orovic ◽  
Srdjan Stankovic
Keyword(s):  
Transform Domain ◽  
Hermite Transform

scholarly journals Compressive Sensing in Signal Processing: Algorithms and Transform Domain Formulations

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Irena Orović ◽  
Vladan Papić ◽  
Cornel Ioana ◽  
Xiumei Li ◽  
Srdjan Stanković
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Compressive Sensing ◽  
Signal Reconstruction ◽  
Signal Acquisition ◽  
Transform Domain ◽  
Hermite Transform ◽  
Time Frequency ◽  
Reconstruction Methods ◽  
Fourier Transform Domain

Compressive sensing has emerged as an area that opens new perspectives in signal acquisition and processing. It appears as an alternative to the traditional sampling theory, endeavoring to reduce the required number of samples for successful signal reconstruction. In practice, compressive sensing aims to provide saving in sensing resources, transmission, and storage capacities and to facilitate signal processing in the circumstances when certain data are unavailable. To that end, compressive sensing relies on the mathematical algorithms solving the problem of data reconstruction from a greatly reduced number of measurements by exploring the properties of sparsity and incoherence. Therefore, this concept includes the optimization procedures aiming to provide the sparsest solution in a suitable representation domain. This work, therefore, offers a survey of the compressive sensing idea and prerequisites, together with the commonly used reconstruction methods. Moreover, the compressive sensing problem formulation is considered in signal processing applications assuming some of the commonly used transformation domains, namely, the Fourier transform domain, the polynomial Fourier transform domain, Hermite transform domain, and combined time-frequency domain.

Representation of uniformly sampled signals in the Hermite transform domain

2016 ◽  
Author(s):  
Milos Brajovic ◽  
Irena Orovic ◽  
Milos Dakovic ◽  
Srdan Stankovic
Keyword(s):  
Transform Domain ◽  
Hermite Transform

scholarly journals Compressive Sensing Approach in the Hermite Transform Domain

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Srdjan Stanković ◽  
Ljubiša Stanković ◽  
Irena Orović
Keyword(s):  
Compressive Sensing ◽  
Signal Reconstruction ◽  
Transform Domain ◽  
Numerical Examples ◽  
Hermite Transform ◽  
Sensing Applications ◽  
Random Samples ◽  
Significant Interest ◽  
Small Set ◽  
Short Time

Compressive sensing has attracted significant interest of researchers providing an alternative way to sample and reconstruct the signals. This approach allows us to recover the entire signal from just a small set of random samples, whenever the signal is sparse in certain transform domain. Therefore, exploring the possibilities of using different transform basis is an important task, needed to extend the field of compressive sensing applications. In this paper, a compressive sensing approach based on the Hermite transform is proposed. The Hermite transform by itself provides compressed signal representation based on a smaller number of Hermite coefficients compared to the signal length. Here, it is shown that, for a wide class of signals characterized by sparsity in the Hermite domain, accurate signal reconstruction can be achieved even if incomplete set of measurements is used. Advantages of the proposed method are demonstrated on numerical examples. The presented concept is generalized for the short-time Hermite transform and combined transform.

scholarly journals Sparse representation of FHSS signals in the Hermite transform domain

2017 ◽  
Vol 9 (2) ◽  
pp. 92-97 ◽  
Author(s):  
Milos Brajovic ◽  
Andjela Draganic ◽  
Irena Orovic ◽  
Srdjan Stankovic
Keyword(s):  
Sparse Representation ◽  
Transform Domain ◽  
Hermite Transform

Compressive sensing of signals sparse in 2D Hermite transform domain

2016 ◽  
Author(s):  
Milos Brajovic ◽  
Irena Orovic ◽  
Milos Dakovic ◽  
Srdan Stankovic
Keyword(s):  
Compressive Sensing ◽  
Transform Domain ◽  
Hermite Transform

Gradient‐based signal reconstruction algorithm in Hermite transform domain

2016 ◽  
Vol 52 (1) ◽  
pp. 41-43 ◽  
Author(s):  
M. Brajović ◽  
I. Orović ◽  
M. Daković ◽  
S. Stanković
Keyword(s):  
Signal Reconstruction ◽  
Reconstruction Algorithm ◽  
Transform Domain ◽  
Hermite Transform ◽  
Gradient Based
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