Polynomial Fourier domain as a domain of signal sparsity

Stanković, Srdjan; Orović, Irena; Stanković, Ljubiša

doi:10.1016/j.sigpro.2016.07.015

Cited by 29 publications

(9 citation statements)

References 48 publications

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“…In this section, we consider the possibility of CS reconstruction of polynomial phase signals [28]. Observe the multicomponent polynomial phase signal vector s, with elements s(n):…”

Section: Cs In the Polynomial Fourier Transform Domainmentioning

confidence: 99%

Compressive Sensing in Signal Processing: Algorithms and Transform Domain Formulations

Orović

Papić

Ioana

et al. 2016

Mathematical Problems in Engineering

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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.

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“…In this section, we consider the possibility of CS reconstruction of polynomial phase signals [28]. Observe the multicomponent polynomial phase signal vector s, with elements s(n):…”

Section: Cs In the Polynomial Fourier Transform Domainmentioning

confidence: 99%

Compressive Sensing in Signal Processing: Algorithms and Transform Domain Formulations

Orović

Papić

Ioana

et al. 2016

Mathematical Problems in Engineering

Self Cite

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“…For efficient signal reconstruction, it is important to separate those (N-K) coefficients belonging to the noise component from signal components. To separate signals from noise, we need to define the probability ( ( )) that noise samples in the frequency domain are below a threshold T. The probability that all (N-K) samples corresponding to noise value, which are below T, is given in [43].…”

Section: Effect Of Compressive Sensing On Snrmentioning

confidence: 99%

Compressive sensing based maximum-minimum subband energy detection for cognitive radios

Dagne

Fante

Desta

2020

Heliyon

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To satisfy the growing spectrum demands of emerging wireless applications, cognitive radios have been considered as a viable option. It enables dynamic spectrum access opportunistically using wideband spectrum sensing (WSS) methods to discover the temporarily free frequency bands. WSS requires a high-speed analog-to-digital converter (ADC), which has high power consumption and hardware complexity. Improving the power consumption and hardware complexity of the ADC is one of the existing challenges in energy-constrained applications. To alleviate this problem, we propose compressive sensing (CS) in maximum-minimum subband energy detection method to sense the wideband spectrum by utilizing the sparse nature of spectrum occupancy with the minimal possible number of measurements. The CS method uses Fourier Transform and chaotic sequence in designing the measurement matrix to achieve both determinacy and randomness. The Bayesian method is used to reconstruct the signal from the available measurements. From the reconstructed signal, the maximum-minimum subband energy detection (ED) method is used to decide whether the primary user (PU) is absent or present in a particular frequency band. The simulation results show that the proposed CS-based maximum-minimum subband energy detection approach improves the probability of detection by 7.5% compared to the conventional maximum-minimum subband energy detection method of spectrum sensing. The proposed spectrum sensing method is simple and robust to noise uncertainty and signal strength variations.

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“…As a result, the i th signal component is demodulated and becomes a sinusoid in the polynomial Fourier transform domain [105]. The polynomial Fourier transform representation is not strictly sparse as in the case of a single polynomial phase signal, but the i th component will be dominant in the polynomial Fourier transform spectrum.…”

Section: Time-frequency Based Compressive Sensingmentioning

confidence: 99%

“…It means that the demodulation vector d should be also calculated only for N a available instants. Now, the measurement vector y can be defined as follows [105]: y=s(na)d(na)=x(na) where n a denotes available sample positions.…”

Section: Time-frequency Based Compressive Sensingmentioning

confidence: 99%

Compressive sensing meets time–frequency: An overview of recent advances in time–frequency processing of sparse signals

Sejdić

Orović

Stanković

2018

Digital Signal Processing

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Compressive sensing is a framework for acquiring sparse signals at sub-Nyquist rates. Once compressively acquired, many signals need to be processed using advanced techniques such as time-frequency representations. Hence, we overview recent advances dealing with time-frequency processing of sparse signals acquired using compressive sensing approaches. The paper is geared towards signal processing practitioners and we emphasize practical aspects of these algorithms. First, we briefly review the idea of compressive sensing. Second, we review two major approaches for compressive sensing in the time-frequency domain. Thirdly, compressive sensing based time-frequency representations are reviewed followed by descriptions of compressive sensing approaches based on the polynomial Fourier transform and the short-time Fourier transform. Lastly, we provide brief conclusions along with several future directions for this field.

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Polynomial Fourier domain as a domain of signal sparsity

Cited by 29 publications

References 48 publications

Compressive Sensing in Signal Processing: Algorithms and Transform Domain Formulations

Compressive Sensing in Signal Processing: Algorithms and Transform Domain Formulations

Compressive sensing based maximum-minimum subband energy detection for cognitive radios

Compressive sensing meets time–frequency: An overview of recent advances in time–frequency processing of sparse signals

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