9 research outputs found
Design of near allpass strictly stable minimal phase real valued rational IIR filters
In this brief, a near-allpass strictly stable minimal-phase real-valued rational infinite-impulse response filter is designed so that the maximum absolute phase error is minimized subject to a specification on the maximum absolute allpass error. This problem is actually a minimax nonsmooth optimization problem subject to both linear and quadratic functional inequality constraints. To solve this problem, the nonsmooth cost function is first approximated by a smooth function, and then our previous proposed method is employed for solving the problem. Computer numerical simulation result shows that the designed filter satisfies all functional inequality constraints and achieves a small maximum absolute phase error
Two-channel linear phase FIR QMF bank minimax design via global nonconvex optimization programming
In this correspondence, a two-channel linear phase finite impulse response (FIR) quadrature mirror filter (QMF) bank minimax design problem is formulated as a nonconvex optimization problem so that a weighted sum of the maximum amplitude distortion of the filter bank, the maximum passband ripple magnitude and the maximum stopband ripple magnitude of the prototype filter is minimized subject to specifications on these performances. A modified filled function method is proposed for finding the global minimum of the nonconvex optimization problem. Computer numerical simulations show that our proposed design method is efficient and effective
Recent works on optimization for signal processing
This invited presentation has discussed recent works on optimization for signal processing
Minimax passband group delay nonlinear phase peak constrained FIR filter design without imposing desired phase response
In this paper, a nonlinear phase finite impulse response (FIR) filter is designed without imposing a desired phase response. The maximum passband group delay of the filter is minimized subject to a positivity constraint on the passband group delay response of the filter as well as a specification on the maximum absolute difference between the desired magnitude square response and the designed magnitude square response over both the passband and the stopband. This filter design problem is a quadratic NP hard functional inequality constrained optimization problem. To tackle this problem, first, the one norm functional inequality constraint of the optimization problem is approximated by a smooth function so that the quadratic NP hard functional inequality constrained optimization problem is converted to a nonconvex functional inequality constrained optimization problem. Then, a modified filled function method is applied for finding the global minimum of the nonconvex optimization problem. By using a local minimum of the corresponding unconstrained optimization problem as the initial condition of our proposed global optimization algorithm, computer numerical simulation results show that our proposed approach could efficiently and effectively design a minimax passband group delay nonlinear phase peak constrained FIR filter without imposing a desired phase response
Energy Efficient Delay Sensitive Optimization in SWIPT-MIMO
In this paper, we consider joint antenna selection and optimal beamforming
for energy efficient delay minimization. We assume multiple-input multi-output
(MIMO) system with full duplex simultaneous wireless information and power
transfer (FD-SWIPT) where each sensor is equipped with a power splitting (PS)
system and can simultaneously receive both energy and information from the
aggregator (AGG). We show that the antenna selection and beamforming power
control policies are adaptive to the energy state information (ESI), the queue
state information (QSI) and the channel state information (CSI). We develop an
analytical framework for energy efficient delay-optimal control problem based
on the theory of infinite horizon partially observable Markov decision process
(POMDP). The infinite-horizon POMDP problem is transformed into an equivalent
value Bellman program and solved by near-optimal point-based Heuristic Search
Value Iteration (PB-HSVI) method under specific standard conditions. The
proposed solution outcome is a set of sub-optimal antenna selection and
beamforming control policies. Simulation results reveal an effective trade-off
between the contradictory objectives (i.e. delay and power consumption) and
show the enhancement in delay by using FD-SWIPT systems in comparison to Half
Duplex (HD)-SWIPT systems
Optimal design of orders of DFrFTs for sparse representations
This paper proposes to use a set of discrete fractional Fourier transform (DFrFT) matrices with different rotational angles to construct an overcomplete kernel for sparse representations of signals. The design of the rotational angles is formulated as an optimization problem as follows. The sum of the L1 norms of both the real part and the imaginary part of transformed vectors is minimized subject to different values of the optimal rotational angles. In order to avoid all the optimal rotational angles within a small neighbourhood, constraints on the sum of the L1 norms of both the real part and the imaginary part of the product of the individual optimal DFrFT matrices and training vectors being either stationary or nondifferentiable are imposed. Solving this optimization problem is very challenging not only because of the nonsmooth and the nonconvex nature of the problem, but also due to expressing the optimization problem in a nonstandard form. To solve the problem, first it is shown in this paper that this design problem is equivalent to an optimal sampling problem as follows. The absolute sum of the L1 norms of both the real part and the imaginary part of the frequency responses of a set of filters at the optimal sampling frequencies is minimized subject to similar constraints. Second, it is further shown that the optimal sampling frequencies are the roots of a set of harmonic functions. As the frequency responses of the filters are required to be computed only at frequencies in a discrete set, the globally optimal rotational angles can be found very efficiently and effectively
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