Corpus ID: 219177606

Improved characterization of the eigenvalue behavior of discrete prolate spheroidal sequences

  title={Improved characterization of the eigenvalue behavior of discrete prolate spheroidal sequences},
  author={Santhosh Karnik and J. Romberg and M. Davenport},
The discrete prolate spheroidal sequences (DPSSs) are a set of orthonormal sequences in $\ell_2(\mathbb{Z})$ which are strictly bandlimited to a frequency band $[-W,W]$ and maximally concentrated in a time interval $\{0,\ldots,N-1\}$. The timelimited DPSSs (sometimes referred to as the Slepian basis) are an orthonormal set of vectors in $\mathbb{C}^N$ whose discrete time Fourier transform (DTFT) is maximally concentrated in a frequency band $[-W,W]$. Due to these properties, DPSSs have a wide… Expand

Figures from this paper


Spectral Decay of Time and Frequency Limiting Operator
For fixed $c,$ the Prolate Spheroidal Wave Functions (PSWFs) $\psi_{n, c}$ form a basis with remarkable properties for the space of band-limited functions with bandwidth $c$. They have been largelyExpand
Discrete Prolate Spheroidal Wave Functions: Further Spectral Analysis and Some Related Applications
The DPSWFs can be used for the approximation of classical band-limited functions, as well as those functions belonging to periodic Sobolev spaces and new non-asymptotic decay rates of the spectrum of the operator Q ~ N, W. Expand
Fast Algorithms for the Computation of Fourier Extensions of Arbitrary Length
Two $\mathcal{O}(N\log^2N)$ algorithms are presented for the computation of these approximations for the case of general $T$, made possible by exploiting the connection between Fourier extensions and Prolate Spheroidal Wave theory. Expand
The Fast Slepian Transform
The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computationalExpand
Fast Multitaper Spectral Estimation
Thomson’s multitaper method using discrete prolate spheroidal sequences (DPSSs) is a widely used technique for spectral estimation. For a signal of length N, Thomson’s method requires selecting aExpand
Non-Asymptotic behaviour of the spectrum of the Sinc Kernel Operator and Related Applications
Prolate spheroidal wave functions have recently attracted a lot of attention in applied harmonic analysis, signal processing and mathematical physics. They are eigenvectors of the Sinc-kernelExpand
Compressive Sensing of Analog Signals Using Discrete Prolate Spheroidal Sequences
By modulating and merging DPSS bases, this paper obtains a dictionary that offers high-quality sparse approximations for most sampled multiband signals, and this multiband modulated DPSS dictionary can be readily incorporated into the CS framework. Expand
Prolate spheroidal wave functions, fourier analysis, and uncertainty — V: the discrete case
  • D. Slepian
  • Mathematics
  • The Bell System Technical Journal
  • 1978
A discrete time series has associated with it an amplitude spectrum which is a periodic function of frequency. This paper investigates the extent to which a time series can be concentrated on aExpand
On the Numerical Stability of Fourier Extensions
This paper shows that Fourier extensions are actually numerically stable when implemented in finite arithmetic, and achieve a convergence rate that is at least superalgebraic, and demonstrates that they are particularly well suited for this problem. Expand
Approximating Sampled Sinusoids and Multiband Signals Using Multiband Modulated DPSS Dictionaries
This paper studies possible dictionaries for representing the discrete vector one obtains when collecting a finite set of uniform samples from a multiband analog signal and concludes that the information level of the sampled multiband vectors is essentially equal to the time–frequency area. Expand