This paper studies multidimensional linear periodically shift-variant digital filters (LPSV filters). The notion of a generalized multidimensional transfer function is presented for LPSV filters. The frequency characteristic of the filters is discussed in terms of this transfer function. Since LPSV filters can decompose the spectrum of an input signal into some spectral partitions and rearrange the spectrum, LPSV filters can serve as a frequency scrambler. To show the effect of multidimensional frequency scramble, 2-D LPSV filters are designed based on the 1-D Parks-McClellan algorithm. The resultant LPSV filters divide the input spectrum into some components that are permuted and possibly inverted with keeping the symmetric of the spectrum. Experimental results are presented to illustrate the effectiveness of frequency scramble for real images.

The main interest of this paper is the theoretical analysis of a recursive periodically time varying digital filter. The generalized transfer function of a recursive periodically time varying digital filter was obtained from its difference equation. It was proved that by making use of the generalized transfer function, we can not only derive the input and output relationship of a recursive periodically time varying digital filter easily but also obtain its equivalent structure effectively. An interesting property of a recursive periodically time varying digital filter was also derived by making use of its generalized transfer function. Moreover, it was completed in this paper the investigation of the generalized transfer functions and impulse responses of other periodically time varying models, including an input sampling polyphase model and an output sampling polyphase model. Meanwhile, the multirate Quadrature Mirror Filter bank system was proved by the authors to be a periodically time varying system. Several examples were also provided to illustrate the effectiveness of using the generalized transfer function to obtain the equivalent structure of a recursive periodically time varying digital filter.

In this paper, a design method is described for very low sensitivity fully-balanced narrow-band band-pass switched-capacitor filters (SCF's) whose worst-case sensitivities of the amplitude responses become zero at every reflection zero. The proposed method is based on applying the low-pass to high-pass transformation, the pseudo two-path technique and the capacitance-ratio reduction technique to very low sensitivity low-pass SC ladder filters. A design example of the band-pass SCF with a quality factor Q250 is given to verify the proposed method. The remarkable advantages of this approach are very low sensitivity to element-value variations, a small capacitance spread, a small total capacitance, and clock-feedthrough noise immunity inside the passband.

In a display system with a line-of-gaze (LOG) controller, it is difficult to make the directions and motions of a LOG-controlled object coincide as closely as possible in the display with the user's intended LOG-directions and motions. This is because LOG behavior is not only smooth, but also saccadic due to the problem of involuntary eye movement. This article introduces a flexible on-line LOG-control scheme to realize nearly perfect LOG operation. Using a mesh-wise cursor pattern, the first visual experiment elucidates subjectively that a Kalman Filter (KF) for smoothing and predicting is effective in filtering out macro-saccadic changes of the LOG and in predicting sudden changes of the saccade while movement is in progress. It must be assumed that the LOG trajectory can be described by a linear position-velocity-acceleration approximation of Sklansky Model (SM). Furthermore, the second experiment uses a four-point pattern and simulations to scrutinize the two physical properties of velocity and direction-changes of the LOG in order to quantitatively and efficiently resolve "moving" and "gazing". In order to greatly reduce the number of LOG-small-position changes while gazing, the proposed Gaze-Holding algorithm (GH) with a gaze-potential function is combined with the KF. This algorithm allows the occurrence frequency of the micro-saccade to be reduced from approximately 25 Hz to 1 or 2 Hz. This great reduction in the frequency of the LOG-controlled object moves is necessary to achieve the user's desired LOG-response while gazing. Almost perfect LOG control is accomplished by the on-line SM+KF+GH scheme while either gazing or moving. A menu-selection task was conducted to verify the effectiveness of the proposed on-line LOG-control method.

Complex filters are used to synthesize real filters in digital signal processing, but few in analog one. In this paper, we propose a leapfrog synthesis of complex analog filters. By shifting frequency response of an LCR network along the ω-axis, we have a complex filter with imaginary resistances, which is called an "LCRRi filter." The complex resonator is then used to simulate series- or parallel-arms of the LCRRi filter. We analyze nonideal properties of the complex resonator due to finite gain-bandwidth product of operational amplifiers and propose a compensation method to put a pole on correct location. Experimental results show good performance of the proposed method.

A new type of analog-to-digital (A/D) converter is introduced. The structure is based on a magnitude-preserving quadrature mirror filter (QMF) bank where the analysis bank is composed on IIR switched-capacitor (SC) filters. The analog output samples of the analysis filters are converted into digital form using individual A/D converters and combined by an IIR digital filter synthesis filter bank. This A/D converter is useful in applications where only the magnitude of the spectrum of the analog signal needs to be preserved. The structure incorporates the advantages of sub-band coding and reduces considerably the effect of mismatches among the sub-band A/D converters. In addition, the proposed scheme leads to an increase in the conversion speed by a factor of M when an M-channel QMF bank is used. An illustrative example verifying the good performance of the proposed approach is included.

This paper describes design considerations for high frequency active BPFs up to 100 MHz. The major design issues for high frequency active filters are the excess phase shift in the integrators and high power consumption of the integrators. Typical bipolar transistor based transconductors such as the Gilbert gain cell and the linearized transconductor with two asymmetric emitter-coupled pairs have been analyzed and compared. It has been clarified that the power consumption of the linearized transconductor can be much smaller than that of the Gilbert gain cell because of its high transconductance to working current ratio while maintaining a signal to noise ratio of the same order. A simple high-speed fully differential linearized transconductor cell is proposed with emitter follower buffers and resistive loads for excess phase compensation. A novel gyrator based transformation for the LC ladder BPF has been introduced. This transformation has resulted in a structure with simple capacitor-coupled active resonators which exactly preserves the original transfer function. A fourth order 10.7 MHz BPF IC was designed using the proposed transconductors. It was fabricated and has demonstrated the usefulness of the proposed approach. In addition, an experimental 100 MHz second order BPF IC with Q=14 has been successfully implemented indicating the potential of the proposed approach.

An integrator is quite a suitable active element for high-speed filters. The effect of its excess phase shifts, however, is severe in the case of high-Q filter realization. The deterioration due to the excess phase shifts cannot be avoided when only integrators are used as frequency-dependent elements like in leapfrog realization. This paper describes a design of second-order high-speed and high-Q filters with low sensitivity to excess phase shifts of integrators by adding a passive RC circuit. The proposed method can drastically reduce the effect due to the undesirable pole of an integrator, which is the cause of the excess phase shifts, compared to conventional filters using only integrators. As an example, a fourth-order bandpass filter with 5-MHz center frequency and Q=25 is implemented by the proposed method on a monolithic chip. The results obtained here show quite good agreement with the theoretical values. This demonstrates effectiveness of the proposed method and feasibility of high-speed and high-Q filters on a monolithic chip.

The design of N-dimensional (N-D) FIR filters requires in general an enormous computational effort. One of the most successful methods for design and implementation is the McClellan transformation. In this paper a numerically simple technique for determining the coefficients of the transformation is suggested. This appears to be the simplest available method for the design of N-D hyperspherically symmetric FIR filters with excellent symmetry.

This paper proposes a method to estimate the waveform of a specified sound source in a noisy and reverberant environment using a sensor array. Previously, we proposed an iterative method to estimate the waveform. However, in this method the effect of reflection sound reduces to 1/M, where M is the number of microphones. Therefore, to solve the reverberation problem, we propose a new method using inverse filters of the transfer functions from the sound sources to each microphone. First, the transfer function from each sound source to each microphone is measured by the cross-spectrum technique and each inverse filter is calculated by the QR method. Then the initially estimated waveform of a sound source is the averaged signal of the inverse filter outputs. Since this waveform still contains the effects of the other sound sources, the iterative technique is adopted to estimate the waveform more precisely, reducing the effects of the other sound and the reflection sound. Some computer simulations and experiments were carried out. The results show the effectiveness of our method.

This paper proposes a new adaptive algorithm of the FIR type digital filter for an acoustic echo canceller and similar application fields. Unlike an echo canceller for line, an acoustic echo canceller requires a large number of taps, and it must work appropriately while it is driven by colored input signal. By controlling the filter tap length and updating filter coefficients multiple times during a single sampling interval, the proposed algorithm improves the convergence characteristics of adaptation even if colored input signal is introduced. This algorithm is maned VT-LMS after variable tap length LMS. The results of simulation show the effectiveness of the proposed algorithm not only for white noise but also for colored input signal such as speech. The VT-LMS algorithm has better convergence characteristice with very little extra computational load compared to the conventional algorithm.

This paper describes a new trial of dynamical parameter estimation for the actual room acoustic system, in a practical case when the input excitation is polluted by a background noise in contrast with the usual case when the output observation is polluted. The room acoustic system is first formulated as a discrete time model, by taking into consideration the original standpoint defining the system parameter and the existence of the background noise polluting the input excitation. Then, the recurrence estimation algorithm on a reverberation time of room is dynamically derived from Bayesian viewpoint (based on the statistical information of background noise and instantaneously observed data), which is applicable to the actual situation with the non-Gaussian type sound fluctuation, the non-linear observation, and the input background noise. Finally, the theoretical result is experimentally confirmed by applying it to the actual estimation problem of a reverberation time.

This paper proposes a new adaptive algorithm for acoustic echo cancellers with four times the convergence speed for a speech input, at almost the same computational load, of the normalized LMS (NLMS). This algorithm reflects both the statistics of the variation of a room impulse response and the whitening of the received input signal. This algorithm, called the ESP (exponentially weighted step-size projection) algorithm, uses a different step size for each coefficient of an adaptive transversal filter. These step sizes are time-invariant and weighted proportional to the expected variation of a room impulse response. As a result, the algorithm adjusts coefficients with large errors in large steps, and coefficients with small errors in small steps. The algorithm is based on the fact that the expected variation of a room impulse response becomes progressively smaller along the series by the same exponential ratio as the impulse response energy decay. This algorithm also reflects the whitening of the received input signal, i.e., it removes the correlation between consecutive received input vectors. This process is effective for speech, which has a highly non-white spectrum. A geometric interpretation of the proposed algorithm is derived and the convergence condition is proved. A fast profection algorithm is introduced to reduce the computational complexity and modified for a practical multiple DSP structure so that it requires almost the same computational load, 2L multiply-add operations, as the conventional NLMS. The algorithm is implemented in an acoustic echo canceller constructed with multiple DSP chips, and its fast convergence is demonstrated.

Inverse filters can be designed in order to enhance the accuracy with which signals recorded in a given space can be reproduced in a given listening space. The problem is considered here of the design of an inverse filter matrix which enables K recorded signals to be accurately reproduced at K points in the listening space when transmitted via M loudspeaker channels. The analysis is sufficiently general to incorporate the case when the best (least squares) approximation is sought to the reproduction of K signals at L points in the space when LK. An analysis is presented which demonstrates that the approach suggested by the Multiple-Input/Output Inverse Filtering theorem of Miyoshi and Kaneda can be realised adaptively by using the Multiple Error LMS algorithm of Elliott et al.

This paper relates to a novel algorithm for fast estimation of the coefficients of the adaptive FIR filter. The novel algorithm is derived from a first order IIR filter experssion clarifying the estimation process of the NLMS (normalized least mean square) algorithm. The expression shows that the estimation process is equivalent to a procedure extracting the cross-correlation coefficient between the input and the output of an unknown system to be estimated. The interpretation allows to move a subtraction of the echo replica beyond the IIR filter, and the movement gives a construction with the IIR filter coefficient of unity which forms the arithmetic mean. The construction in comparison with the conventional NLMS algorithm, improves the covergence rate extreamly. Moreover, when we use the construction with a simple technique which limits the term of calculating the correlation coefficient in the beginning of a convergence process, the convergence delay becomes negligible. This is a very desirable performance for acoustic echo canceller. In this paper, double-talk and echo path fluctuation are also studied as the first stage for application to acoustic echo canceller. The two subjects can be resolved by introducing two switches and delays into the evaluation process of the correlation coefficient.

The realization of acoustic inverse filter is often difficult because of the non-minimum phase property and the long time duration of the impulse response of the acoustic enclosure. However, if the signals are divided into a large number of sub-bands, many of the sub-bands are found to be invertible. The invertibility of a sub-band signal depends on the zero distribution of the transfer function in the z-plane. In a multi-microphone system, the transfer functions between the sound source and the mirophones have different zero distributions. The method proposed here, taking advantage of the differences of zero distributions, selects the best invertible microphone in each sub-band, and reconstructs the full band signal by summing up the inverse filtered sub-band signals of the best microphones. The quality of the dereverberated signal using the proposed inverse filtering approach is improved with increasing number of microphones and sub-bands. When seven microphones are used and the number of sub-bands is 513, the quality of the dereverberated speech signals are almost the same with the original ones even when the revergeration time is about one second. The introduction of multi-microphones in addition to sub-band processing provides a new way of dealing with the non-minimum phase problem in deconvolution.

An acoustic echo canceller that also cancels room noise is proposed. This system has an additive (noise reference) input port, and a noise canceller (NC) precedes the echo canceller (EC) in a cascade configuration. The adaptation control problem for the cascaded echo and noise canceller is solved by controlling the adaptation process to match the occurrence of intermittent speech/echo; the room noise is a stationary signal. A simulation shows that adaptation using the NLMS algorithm is very effective for the echo and noise cancellation. Sub-band cancelling techniques are utilized. Noise cancellation is realized with a lower band EC. Hardware is implemented and its performance evaluated through experiments under a real acoustic field. The combination of the EC with NC maintains excellent performance at all echo to room noise power ratios. It is shown that the proposed canceller overcomes the disadvantages traditionally associated with ECs and NSc.

This paper presents a method for LSI implementation of a long-tap acoustic echo canceller algorithm using the residue number system (RNS) and the mixed-radix number system (MRS). It also presents a quantitative comparison of echo canceller architectures, one using the RNS and the other using the binary number system (BNS). In the RNS, addition, subtraction, and multiplication are executed quickly but scaling, overflow detection, and division are difficult. For this reason, no echo canceller using the RNS has been implemented. We therefore try to design an echo canceller architecture using the RNS and the NLMS algorithm. It is shown that the echo canceller algorithm can be effectively implemented using the RNS by introducing the MRS. The quantitative comparison of echo canceller architectures shows that a long-tap acoustic echo canceller can be implemented more effectively in terms of chip size and power dissipation by the architecture using the RNS.

An automatic macrocell generator has been developed and applied to the analog layout of SC and active-RC filters. The generator consists of a process independent generation procedure, a leafcell library, and a circuit description of the leafcells. The unit element arrays of the whole filter are generated together to minimize the array height of the entire filter macrocell, so that the area of the generated filter is as small as that of a manually laid out filter. Three SC filters and one active-RC filter were designed and fabricated by 1.5-µm CMOS technology, that successfully yielded an S/N ratio of more than 70 dB with a quick turn around time.

The purpose of our research is to get further improvement in the performance of order statistic filters. The basic idea found in our research is the use of a robust median estimator to obtain median differential order information which the classes of order statistic filter required in order to sort the input signal in the filter window. In order to give the motivation for using a median estimator in the classes of order statistic filters, we derive theorems characterizing the median filters and prove them theoretically using the characteristic that the order statistic filter has the performance for a monotonic signal equivalent with the FIR linear filter. As an application of median operation, we propose and investigate the Median Differential Order Statistic Filter to reduce impulsive noise as well as Gaussian noise and regard it as a subclass of the Order Statistic Filter. Moreover, we introduce the piecewise linear function in the Median Differential Order Statistic Filter to improve performance in terms of edge preservation. We call it the Piecewise Linear Median Differential Order Statistic Filter. The effectiveness of proposed filters is verified theoretically by computing the output Mean Square Error of the filters in parts of edge signals, impulsive noise, small amplitude noise and their combination. Computer simulations also show that the proposed filter can improve the performance in both noise (small-amplitude Gaussian noise and impulsive noise) reduction and edge preservation for one-dimensional signals.