Representation of perfectly reconstructed octave decomposition filter banks with set of decimators {2,4,4} via tree structure

In this letter, we prove that a filter bank with set of decimators {2,4,4} achieves perfect reconstruction if and only if it can be represented via a tree structure and each branch of the tree structure achieves perfect reconstruction

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

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

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

Can a second order bandpass sigma delta modulator achieve high signal-to-noise ratio for lowpass inputs

Institutively, second order SDMs usually achieve lower SNR than high order ones because high order loop filters can achieve better noise shaping characteristics. Moreover, the signal transfer function should be designed to have large values and the noise transfer function should be designed to have small values at the passband of loop filters in order to achieve good noise shaping characteristics, so SNR should be high if input signal bands match passbands of loop filters and low otherwise. Based on this argument, one may expect that SNR will be low when input signals have lowpass characteristics while loop filters have bandpass characteristics. However, since the above argument is based on the noise shaping theory which is formulated using a linear model, while quantizers in SDMs are nonlinear components, the linear model may not explain nonlinear system behaviors. In this letter, a counterexample is given to illustrate that a second order bandpass interpolative SDM may also give a very high SNR for lowpass inputs

Some new trajectory patterns and periodic behaviors of unstable second-order digital filter with two’s complement arithmetic

This letter shows some counter-intuitive simulation results that for some filter parameters in the extended boundaries of the stability triangle, the state vector will converge to a periodic orbit after some iterations, no matter what the initial conditions are. Also, a new pattern, which looks like a rotated letter ‘X’, is found. The center of the rotated letter is located at the origin and the slopes of the ‘straight lines’ of the rotated letter are equal to the values of the pole locations