102 research outputs found
Nonlinear behaviors of bandpass sigma delta modulators with stable system matrices
It has been established that a class of bandpass sigma-delta modulators may exhibit state space dynamics which are represented by elliptical or fractal patterns confined within trapezoidal regions when the system matrices are marginally stable. In this brief, it is found that fractal or irregular chaotic patterns may also be exhibited in the phase plane when the system matrices are strictly stabl
Nonlinear behaviors of bandpass sigma delta modulators with stable system matrices
It has been established that a class of bandpass sigma delta modulators (SDMs) may exhibit state space dynamics which are represented by elliptical or fractal patterns confined within trapezoidal regions when the system matrices are marginally stable. In this paper, it is found that fractal patterns may also be exhibited in the phase plane when the system matrices are strictly stable. This occurs when the sets of initial conditions corresponding to convergent or limit cycle behavior do not cover the whole phase plane. Based on the derived analytical results, some interesting results are found. If the bandpass SDM exhibits periodic output, then the period of the symbolic sequence must equal the limiting period of the state space variables. Second, if the state vector converges to some fixed points on the phase portrait, these fixed points do not depend directly on the initial conditions
Stability of sinusoidal responses of marginally stable bandpass sigma delta modulators
In this paper, we analyze the stability of the sinusoidal responses of second order interpolative marginally stable bandpass sigma delta modulators (SDMs) with the sum of the numerator and denominator polynomials equal to one and explore new results on the more general second order interpolative marginally stable bandpass SDMs. These results can be further extended to the high order interpolative marginally stable bandpass SDMs
Estimation of an initial condition of sigma-delta modulators via projection onto convex sets
AbstractâIn this paper, an initial condition of strictly causal
rational interpolative sigma-delta modulators (SDMs) is
estimated based on quantizer output bit streams and an input
signal. A set of initial conditions generating bounded trajectories
is characterized. It is found that a set of initial conditions
generating bounded trajectories but not necessarily
corresponding to quantizer output bit streams is convex. Also, it is
found that a set of initial conditions corresponding to quantizer
output bit streams but not necessarily generating bounded
trajectories is convex too. Moreover, it is found that an initial
condition both corresponding to quantizer output bit streams and
generating bounded trajectories is uniquely defined if the loop
filter is unstable (Here, an unstable loop filter refers to that with
at least one of its poles being strictly outside the unit circle). To
estimate that unique initial condition, a projection onto convex set
approach is employed. Numerical computer simulations show that
the employed method can estimate the initial condition effectively
Noise analysis of modulated quantizer based on oversampled signals
In this paper, a noise analysis of a modulated quantizer is performed. If input signals are oversampled, then the quantization error could be reduced by modulating both the input and the output of the quantizer. The working principle is based on the fact that convolutions of bandpass signals would spread wider in the frequency spectrum than that of lowpass signals. Hence, by filtering the high frequency components, the signal-to-noise ratio (SNR) could be increased. Numerical simulation results show that the modulated quantization scheme could achieve an average of 13.0960dB to 21.4700dB improvements on SNR over the conventional scheme, depends on the types of bandlimited input signals
Analysis of Nonlinear Behaviors, Design and Control of Sigma Delta Modulators
M PhilSigma delta modulators (SDMs) have been widely applied in analogue-to-digital
(A/D) conversion for many years. SDMs are becoming more and more popular in power
electronic circuits because it can be viewed and applied as oversampled A/D converters
with low resolution quantizers. The basic structure of an SDM under analytical
investigation consists of a loop filter and a low bit quantizer connected by a negative
feedback loop.
Although there are numerous advantages of SDMs over other A/D converters, the
application of SDMs is limited by the unboundedness of the system states and their
nonlinear behaviors. It was found that complex dynamical behaviors exist in low bit
SDMs, and for a bandpass SDM, the state space dynamics can be represented by elliptic
fractal patterns confined within two trapezoidal regions. In all, there are three types of
nonlinear behaviors, namely fixed point, limit cycle and chaotic behaviors. Related to the
unboundedness issue, divergent behavior of system states is also a commonly discovered
phenomenon. Consequently, how to design and control the SDM so that the system states
are bounded and the unwanted nonlinear behaviors are avoided is a hot research topic
worthy of investigated.
In our investigation, we perform analysis on such complex behaviors and
determine a control strategy to maintain the boundedness of the system states and avoid
the occurrence of limit cycle behavior. For the design problem, we impose constraints
based on the performance of an SDM and determine an optimal design for the SDM. The
results are significantly better than the existing approaches
Theory and practical issues of sigma delta modulators-part I: theory
This invited seminar is discussed on practical issues of sigma delta modulators
Integrated chaos generators
This paper surveys the different design issues, from mathematical model to silicon, involved on the design of integrated circuits for the generation of chaotic behavior.ComisiĂłn Interministerial de Ciencia y TecnologĂa 1FD97-1611(TIC)European Commission ESPRIT 3110
Signal Reconstruction From Nonuniform Samples Using Prolate Spheroidal Wave Functions: Theory and Application
Nonuniform sampling occurs in many applications due to imperfect sensors, mismatchedclocks or event-triggered phenomena. Indeed, natural images, biomedical responses andsensor network transmission have bursty structure so in order to obtain samples that correspondto the information content of the signal, one needs to collect more samples when thesignal changes fast and fewer samples otherwise which creates nonuniformly distibuted samples.On the other hand, with the advancements in the integrated circuit technology, smallscale and ultra low-power devices are available for several applications ranging from invasivebiomedical implants to environmental monitoring. However the advancements in the devicetechnologies also require data acquisition methods to be changed from the uniform (clockbased, synchronous) to nonuniform (clockless, asynchronous) processing. An important advancementis in the data reconstruction theorems from sub-Nyquist rate samples which wasrecently introduced as compressive sensing and that redenes the uncertainty principle. Inthis dissertation, we considered the problem of signal reconstruction from nonuniform samples.Our method is based on the Prolate Spheroidal Wave Functions (PSWF) which can beused in the reconstruction of time-limited and essentially band-limited signals from missingsamples, in event-driven sampling and in the case of asynchronous sigma delta modulation.We provide an implementable, general reconstruction framework for the issues relatedto reduction in the number of samples and estimation of nonuniform sample times. We alsoprovide a reconstruction method for level crossing sampling with regularization. Another way is to use projection onto convex sets (POCS) method. In this method we combinea time-frequency approach with the POCS iterative method and use PSWF for the reconstructionwhen there are missing samples. Additionally, we realize time decoding modulationfor an asynchronous sigma delta modulator which has potential applications in low-powerbiomedical implants
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