Periodically nonuniform sampling of bandpass signals

It is known that a continuous time signal x(i) with Fourier transform X(ν) band-limited to |ν|<Θ/2 can be reconstructed from its samples x(T0n) with T0=2π/Θ. In the case that X(ν) consists of two bands and is band-limited to ν0<|ν|<ν0 +Θ/2, successful reconstruction of x(t) from x(T0n) requires an additional condition on the band positions. When the two bands are not located properly, Kohlenberg showed that we can use two sets of uniform samples, x(2T0n) and x(2T0n+d1), with average sampling period T0, to recover x(t). Because two sets of uniform samples are employed, this sampling scheme is called Periodically Nonuniform Sampling of second order [PNS(2)]. In this paper, we show that PNS(2) can be generalized and applied to a wider class. Also, Periodically Nonuniform Sampling of Lth-order [PNS(L)] will be developed and used to recover a broader class of band-limited signal. Further generalizations will be made to the two-dimensional case and discrete time case

Identification of fast-changing signals by means of adaptive chaotic transformations

The adaptive approach of strongly non-linear fast-changing signals identification is&nbsp;discussed. The approach is devised by adaptive sampling based on chaotic mapping “in yourself”&nbsp;of a signal. Presented sampling way may be utilized online in the automatic control of chemical&nbsp;reactor (throughout identification of concentrations and temperature oscillations in real-time), in medicine (throughout identification of ECG and EEG signals in real-time), etc. In this paper, we&nbsp;presented it to identify the Weierstrass function and ECG signal

Multidimensional random sampling for Fourier transform estimation

This research considers the Fourier transform calculations of multidimensional signals. The calculations are based on random sampling, where the sampling points are nonuniformly distributed according to strategically selected probability functions, to provide new opportunities that are unavailable in the uniform sampling environment. The latter imposes the sampling density of at least the Nyquist density. Otherwise, alias frequencies occur in the processed bandwidth which can lead to irresolvable processing problems. Random sampling can mitigate Nyquist limit that classical uniform-sampling-based approaches endure, for the purpose of performing direct (with no prefiltering or downconverting) Fourier analysis of (high-frequency) signals with unknown spectrum support using low sampling density. Lowering the sampling density while achieving the same signal processing objective could be an efficient, if not essential, way of exploiting the system resources in terms of power, hardware complexity and the acquisition-processing time. In this research we investigate and devise novel random sampling estimation schemes for multidimensional Fourier transform. The main focus of the investigation and development is on the aspect of the quality of estimated Fourier transform in terms of the sampling density. The former aspect is crucial as it serves towards the heart objective of random sampling of lowering the sampling density. This research was motivated by the applicability of the random-sampling-based approaches in determining the Fourier transform in multidimensional Nuclear Magnetic Resonance (NMR) spectroscopy to resolve the critical issue of its long experimental time

Coding gain in paraunitary analysis/synthesis systems

A formal proof that bit allocation results hold for the entire class of paraunitary subband coders is presented. The problem of finding an optimal paraunitary subband coder, so as to maximize the coding gain of the system, is discussed. The bit allocation problem is analyzed for the case of the paraunitary tree-structured filter banks, such as those used for generating orthonormal wavelets. The even more general case of nonuniform filter banks is also considered. In all cases it is shown that under optimal bit allocation, the variances of the errors introduced by each of the quantizers have to be equal. Expressions for coding gains for these systems are derived

ADAPTIVE SAMPLING

This paper introduces a new method for signal representation. It is shown that a periodic signal is uniquely defined by its local extrema if the band limit ratio of the signal is less than an octave. A way of adaptive sampling, introduced among these lines, exhibits advantageous properties of possible interest, e.g., for the detection of the pitch frequency

Compressive Sensing of Analog Signals Using Discrete Prolate Spheroidal Sequences

Compressive sensing (CS) has recently emerged as a framework for efficiently capturing signals that are sparse or compressible in an appropriate basis. While often motivated as an alternative to Nyquist-rate sampling, there remains a gap between the discrete, finite-dimensional CS framework and the problem of acquiring a continuous-time signal. In this paper, we attempt to bridge this gap by exploiting the Discrete Prolate Spheroidal Sequences (DPSS's), a collection of functions that trace back to the seminal work by Slepian, Landau, and Pollack on the effects of time-limiting and bandlimiting operations. DPSS's form a highly efficient basis for sampled bandlimited functions; by modulating and merging DPSS bases, we obtain a dictionary that offers high-quality sparse approximations for most sampled multiband signals. This multiband modulated DPSS dictionary can be readily incorporated into the CS framework. We provide theoretical guarantees and practical insight into the use of this dictionary for recovery of sampled multiband signals from compressive measurements