A simple algorithm for generating discrete prolate spheroidal sequences

Gruenbacher, Don; Hummels, D.R.

doi:10.1109/78.330397

Cited by 44 publications

(17 citation statements)

References 7 publications

(4 reference statements)

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“…In this section we present Discrete Prolate Spheroidal Sequences -DPSS and how they can form a sparsifying basis. DPSS are useful for projecting digital filters, also in pulse shaping, secure communications and in phase amplitude modulation (PAM) [14].…”

Section: Discrete Prolate Spheroidal Sequencesmentioning

confidence: 99%

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The Use of Discrete Prolate Spheroidal Sequences and Trig Prolates to Compressed Sensing

Assis¹,

Gurjão²

2016

Anais De XXXIV Simpósio Brasileiro De Telecomunicações

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Compressed sensing may offer the possibility to acquire certain signals at a rate below Nyquist with guaranteed perfect recovery of these signals. In the present article, we investigate the utilization of Discrete Prolate Spheroidal Sequences as a sparsifying basis for multiband signals, from where compressed sensing may be applied. We also compare their use with the use of trig prolates, a similar and simpler to compute basis, in the context of compressed sensing. Using CoSaMP as the reconstruction algorithm we demonstrate the infeasibility of trig prolates as a basis for perfect recovery.

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Section: Discrete Prolate Spheroidal Sequencesmentioning

confidence: 99%

“…Sampling time is supposedly T s = 1 Bnyq and the number of possible bands is J = Bnyq B band = 256. For each k value considered, D = kJ and Ψ N ×D is the basis defined in (14). The half digital bandwidth parameter is set to W = B band Ts 2 = 1…”

Section: Simulationsmentioning

confidence: 99%

The Use of Discrete Prolate Spheroidal Sequences and Trig Prolates to Compressed Sensing

Assis¹,

Gurjão²

2016

Anais De XXXIV Simpósio Brasileiro De Telecomunicações

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“…Finding in a direct way U such that M has equal diagonal entries is unfeasible. Thus, we resort to an iterative procedure to equalize by pairs diagonal entries of M. This is achieved by updating U by means of Givens rotations [19]. In the following, we shall note D = diag (d 1 , ..., d L ) and R (a,b) (θ) will represent the Givens rotation with angle θ in the subspace of dimension 2 with entry (a, b).…”

Section: Energy Balancing Algorithmmentioning

confidence: 99%

Orthogonal signals with jointly balanced spectra: Application to cdma transmissions

Chonavel

2011

J Wireless Com Network

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This paper presents a technique for generating orthogonal bases of signals with jointly optimized spectra, in the sense that they are made as close as possible. To this end, we propose a new criterion, the minimization of which leads to signals with close energy inside a set of prescribed subbands. Starting with the case of a single subband, we illustrate it by building orthogonal signals with maximum energy concentration in time and in frequency, with the same energy rate outside a fixed frequency interval or a fixed time interval, by resorting to Slepian sequences or Slepian functions, respectively. Then, we present spectrum balancing in a set of frequency intervals. We apply this method to Slepian sequences and Slepian functions, as well as to Walsh-Hadamard codes. On these examples, we point out a number of nice properties of the so-built orthogonal families that are of interest for signaling applications.

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“…Equation (20)) is numerically problematic, especially for large sequence lengths. A numerically stable method can be found in Reference [11]. The CT counterpart of DPSSs and DPSWFs are extensively studied in References [12][13][14][15].…”

Section: Introduction To Discrete Prolate Spheroidal Wave Functions Amentioning

confidence: 99%

Causal discrete‐time system approximation of non‐bandlimited continuous‐time systems by means of discrete prolate spheroidal wave functions

Tzschoppe

Huber

2008

Trans Emerging Tel Tech

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SUMMARYIn general, linear time-invariant (LTI) continuous-time (CT) systems can be implemented by means of LTI discrete-time (DT) systems, at least for a certain frequency band. If a causal CT system is not bandlimited, the equivalent DT system may has be to non-causal for perfectly implementing the CT system within a certain frequency band. This paper studies the question to which degree a causal DT system can approximate the CT system. By reducing the approximation frequency band, the approximation accuracy can be increased-at the expense of a higher energy of the impulse response of the DT system. It turns out, that there exists a strict trade-off between approximation accuracy, measured in the squared integral error, and energy of the impulse response of the DT system. The theoretically optimal trade-off can be achieved by approximations based on a weighted linear combination of the discrete prolate spheroidal wave functions (DPSWFs). The results are not limited to the case of approximating a CT system by means of a causal DT system, but they generally hold for the approximation of an arbitrary spectrum by means of a spectrum of an indexlimited time sequence.

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A simple algorithm for generating discrete prolate spheroidal sequences

Cited by 44 publications

References 7 publications

The Use of Discrete Prolate Spheroidal Sequences and Trig Prolates to Compressed Sensing

The Use of Discrete Prolate Spheroidal Sequences and Trig Prolates to Compressed Sensing

Orthogonal signals with jointly balanced spectra: Application to cdma transmissions

Causal discrete‐time system approximation of non‐bandlimited continuous‐time systems by means of discrete prolate spheroidal wave functions

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