Optimal relaxed causal sampler using sampled-date system theory

This paper studies the design of an optimal relaxed causal sampler using sampled data system theory. A lifted frequency domain approach is used to obtain the existence conditions and the optimal sampler. A state space formulation of the results is also provided. The resulting optimal relaxed causal sampler is a cascade of a linear continuous time system followed by a generalized sampler and a discrete system

Truncated norms and limitations on signal reconstruction

Design of optimal signal reconstructors over all samplers and holds boils down to canceling frequency bands from a given frequency response. This paper discusses limits of performance of such samplers and holds and develops methods to compute the optimal L2 norm.\ud \u

L2 and L∞ optimal downsampling from system theoretic viewpoint

Downsampling is the process of reducing the sampling rate of a discrete signal. It has many applications in image processing, audio, radar etc. The reduction factor of the sampling rate can be an integer or a rational greater than one. This paper describes how sampled data system theory can be used to design an L2/L∞ optimal downsampler which reduces the sampling rate by an positive integer factor M from a given fast sampler sampling at h′ = h/M

Optimal relaxed causal sampling from system theoretic viewpoint

This paper studies the design of an optimal relaxed causal sampler using sampled data system theory. A lifted frequency domain approach is used to obtain the existence conditions and the optimal sampler. A state space formulation of the results is also provided. The resulting optimal relaxed causal sampler is a cascade of a linear continuous time system followed by a generalized sampler and a discrete system

A sampled-data approach to optimal non-causal downsampling

Downsampling is the process of reducing the sampling rate of a discrete signal. This paper describes how sampled data system theory can be used to design an L2 or L∞ optimal downsampler which reduces the sampling rate by a positive integer factor from a given fast sampler. This paper also describes the effect of noise on the optimal downsampling

Frequency-truncated system norms

Some applications require norm computation of frequency-truncated systems. A typical frequency- truncated system is one whose frequency response is rational in certain frequency bands and is zero in others. This note explains how to compute the $L^2$ norm of such systems

A locally convergent Jacobi iteration for the tensor singular value problem

Multi-linear functionals or tensors are useful in study and analysis multi-dimensional signal and system. Tensor approximation, which has various applications in signal processing and system theory, can be achieved by generalizing the notion of singular values and singular vectors of matrices to tensor. In this paper, we showed local convergence of a parallelizable numerical method (based on the Jacobi iteration) for obtaining the singular values and singular vectors of a tensor