Fast implementation of a general L/M rate changer by a filter bank structure

In this paper, we show that an L/M rate changer can be realized as a discrete time SISO (L,M) shift invariant system in form of a two-dimensional kernel function or a filter bank structure. Based on this realization, we can implement an L/M rate changer by a bank of filters with the average number of the coefficients in the filters in each channel is 1/L of the original L/M rate changer. Hence, the system is speed up by L. This helps the designer to design a sharp cutoff discrete time FIR filters in an L/M rate changer for some real time applications in video systems

Video denoising using fuzzy-connectedness principles

Fuzzy-connectedness principles are effective for image segmentation. In this paper, such a principle is applied to video denoising. Assume a video signal suffers from both additive white Gaussian noise and impulsive noise. The corrupted signal is filtered by a fuzzy system, which fuzzily connects a Wiener filter and a median filter together. The simulation results show that the fuzzy-connectedness approach produces desirable outputs

Simple and fast subband de-blocking technique by discarding the high band signals

In this paper, we propose a simple and fast post-processing de-blocking technique to reduce blocking artifacts. The block-based coded image is first decomposed into several subbands. Only the low frequency subband signals are retained and the high frequency subband signals are discarded. The remaining subband signals are then reconstructed to obtain a less blocky image. The ideas are demonstrated by a cosine filter bank and a modulated sine filter bank. The simulation result shows that the proposed algorithm is effective in the reduction of blocking artifacts

Sinusoidal response of a second-order digital filter with two’s complement arithmetic

In this paper, results of the sinusoidal response case are presented. It is found that the visual appearance of the trajectory of the sinusoidal response case is much richer than that of the autonomous and step response cases. Based on the state space technique, the state vectors to be periodic are investigated. The set of initial conditions and the necessary conditions on the filter parameters are also derived. When overflow occurs, the system is nonlinear. If the corresponding symbolic sequences are periodic, some trajectory patterns are simulated. Since the state space technique is not sufficient to efficiently derive the sets of initial conditions and the necessary conditions on the filter parameters, a frequency-domain technique is employed to figure out the set of initial conditions. When the symbolic sequences are aperiodic, an elliptical fractal pattern or random-like chaotic pattern is found

Edge detection using fuzzy switch

This paper is to switch various edge filters via a fuzzy approach

Effect of non-polynomial input to a switching circuit

In this paper, the validity of the state-space averaging method is analyzed. We assume that the state-space piecewise method is an exact model for a fast switching circuit. Based on this model, we compute the error predicted by the state-space averaging method. It is found that the error for a polynomial input is bounded by two polynomials with the same order as that of the input. And the percentage error is bounded by a constant. Hence, if the acceptable level is within that constant, then the state-space averaging method can be applied. Similar analysis is carried out on a non-polynomial input. A sinusoidal function is chosen because of its wide applications on AC circuits. Although a similar result is obtained, the percentage error for the sinusoidal input is much greater than that of the polynomial input. Hence, the state-space averaging method may not be so good for the AC analysis

Stabilization of (L,M) shift invariant plant

In this paper, a lifting technique is employed to realize a single input single output linear (L,M) shift invariant plant as a filter bank system. Based on the filter bank structure, a controller is designed so that the aliasing components in the control loop are cancelled and the loop gain becomes a time invariant transfer function. Pole placement technique is applied to stabilize the overall system and ensure the causality of the filters in the controller. An example on the control of a linear (L,M) shift invariant plant with simulation result is illustrated. The result shows that our proposed algorithm is simple and effective

Denoising by multiwavelet singularity detection

Wavelet denoising by singularity detection was proposed as an algorithm that combines Mallat and Donoho’s denoising approaches. With wavelet transform modulus sum, we can avoid the error and ambiguities of tracing the modulus maxima across scales and the complicated and computationally demanding reconstruction process. We can also avoid the visual artifacts produced by shrinkage. In this paper, we investigate a multiwavelet denoising algorithm based on a modified singularity detection approach. Improved signal denoising results are obtained in comparison to the single wavelet case

Admissibility of unstable second-order digital filter with two’s complement arithmetic

In this letter, we have extended the existing results on the admissible set of periodic symbolic sequences of a second-order digital filter with marginally stable system matrix to the unstable case. Based on this result, the initial conditions can be computed using the symbolic sequences. The truncation error of the representation of an initial condition due to the use of a finite number of symbols is studied

Autonomous response of a third-order digital filter with two’s complement arithmetic realized in cascade form

In this letter, results on the autonomous response of a third-order digital filter with two’s complement arithmetic realized as a first-order subsystem cascaded by a second-order subsystem are reported. The behavior of the second-order subsystem depends on the pole location and the initial condition of the first-order subsystem, because the transient behavior is affected by the first-order subsystem and this transient response can be viewed as an excitation of the original initial state to another state. New results on the set of necessary and sufficient conditions relating the trajectory equations, the behaviors of the symbolic sequences, and the sets of the initial conditions are derived. The effects of the pole location and the initial condition of first-order subsystem on the overall system are discussed. Some interesting differences between the autonomous response of second-order subsystem and the response due to the exponentially decaying input are reported. Some simulation results are given to illustrate the analytical results