776 research outputs found
Sinc interpolation of nonuniform samples
It is well known that a bandlimited signal can be uniquely recovered from nonuniformly spaced samples under certain conditions on the nonuniform grid and provided that the average sampling rate meets or exceeds the Nyquist rate. However, reconstruction of the continuous-time signal from nonuniform samples is typically more difficult to implement than from uniform samples. Motivated by the fact that sinc interpolation results in perfect reconstruction for uniform sampling, we develop a class of approximate reconstruction methods from nonuniform samples based on the use of time-invariant lowpass filtering, i.e., sinc interpolation. The methods discussed consist of four cases incorporated in a single framework. The case of sub-Nyquist sampling is also discussed and nonuniform sampling is shown as a possible approach to mitigating the impact of aliasing
Efficient Sampling of Band-limited Signals from Sine Wave Crossings
This correspondence presents an efficient method for reconstructing a
band-limited signal in the discrete domain from its crossings with a sine wave.
The method makes it possible to design A/D converters that only deliver the
crossing timings, which are then used to interpolate the input signal at
arbitrary instants. Potentially, it may allow for reductions in power
consumption and complexity in these converters. The reconstruction in the
discrete domain is based on a recently-proposed modification of the Lagrange
interpolator, which is readily implementable with linear complexity and
efficiently, given that it re-uses known schemes for variable fractional-delay
(VFD) filters. As a spin-off, the method allows one to perform spectral
analysis from sine wave crossings with the complexity of the FFT. Finally, the
results in the correspondence are validated in several numerical examples.Comment: To appear in the IEEE Transactions on Signal Processin
Regularized sampling of multiband signals
This paper presents a regularized sampling method for multiband signals, that
makes it possible to approach the Landau limit, while keeping the sensitivity
to noise at a low level. The method is based on band-limited windowing,
followed by trigonometric approximation in consecutive time intervals. The key
point is that the trigonometric approximation "inherits" the multiband
property, that is, its coefficients are formed by bursts of non-zero elements
corresponding to the multiband components. It is shown that this method can be
well combined with the recently proposed synchronous multi-rate sampling (SMRS)
scheme, given that the resulting linear system is sparse and formed by ones and
zeroes. The proposed method allows one to trade sampling efficiency for noise
sensitivity, and is specially well suited for bounded signals with unbounded
energy like those in communications, navigation, audio systems, etc. Besides,
it is also applicable to finite energy signals and periodic band-limited
signals (trigonometric polynomials). The paper includes a subspace method for
blindly estimating the support of the multiband signal as well as its
components, and the results are validated through several numerical examples.Comment: The title and introduction have changed. Submitted to the IEEE
Transactions on Signal Processin
Numerical Analysis of the Non-uniform Sampling Problem
We give an overview of recent developments in the problem of reconstructing a
band-limited signal from non-uniform sampling from a numerical analysis view
point. It is shown that the appropriate design of the finite-dimensional model
plays a key role in the numerical solution of the non-uniform sampling problem.
In the one approach (often proposed in the literature) the finite-dimensional
model leads to an ill-posed problem even in very simple situations. The other
approach that we consider leads to a well-posed problem that preserves
important structural properties of the original infinite-dimensional problem
and gives rise to efficient numerical algorithms. Furthermore a fast multilevel
algorithm is presented that can reconstruct signals of unknown bandwidth from
noisy non-uniformly spaced samples. We also discuss the design of efficient
regularization methods for ill-conditioned reconstruction problems. Numerical
examples from spectroscopy and exploration geophysics demonstrate the
performance of the proposed methods
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