Showing papers on "Filter design published in 1990"

Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial

Abstract: The basic concepts and building blocks in multirate digital signal processing (DSP), including the digital polyphase representation, are reviewed. Recent progress, as reported by several authors in this area, is discussed. Several applications are described, including subband coding of waveforms, voice privacy systems, integral and fractional sampling rate conversion (such as in digital audio), digital crossover networks, and multirate coding of narrowband filter coefficients. The M-band quadrature mirror filter (QMF) bank is discussed in considerable detail, including an analysis of various errors and imperfections. Recent techniques for perfect signal reconstruction in such systems are reviewed. The connection between QMF banks and other related topics, such as block digital filtering and periodically time-varying systems, is examined in a pseudo-circulant-matrix framework. Unconventional applications of the polyphase concept are discussed. >

A practical approach to harmonic compensation in power systems-series connection of passive and active filters

Abstract: The authors present a combined system with a passive filter and a small-rated active filter, both connected in series with each other. The passive filter removes load produced harmonics just as a conventional filter does. The active filter plays a role in improving the filtering characteristics of the passive filter. This results in a great reduction of the required rating of the active filter and in eliminating all the limitations faced by using only the passive filter, leading to a practical and economical system. The active filter has a much smaller rating than a conventional active filter. Experimental results obtained from a prototype model are shown to verify the theory developed. >

Federated square root filter for decentralized parallel processors

Abstract: An efficient, federated Kalman filter is developed for use in distributed multisensor systems. The design accommodates sensor-dedicated local filters, some of which use data from a common reference subsystem. The local filters run in parallel, and provide sensor data compression via prefiltering. The master filter runs at a selectable reduced rate, fusing local filter outputs via efficient square root algorithms. Common local process noise correlations are handled by use of a conservative matrix upper bound. The federated filter yields estimates that are globally optimal or conservatively suboptimal, depending upon the master filter processing rate. This design achieves a major improvement in throughput (speed), is well suited to real-time system implementation, and enhances fault detection, isolation, and recovery capability. >

Multidelay block frequency domain adaptive filter

Abstract: A flexible multidelay block frequency domain (MDF) adaptive filter is presented. The distinctive feature of the MDF adaptive filter is to allow one to choose the size of an FFT tailored to the efficient use of the hardware, rather than the requirements of a specific application. The MDF adaptive filter also requires less memory and thus reduces the hardware requirements and cost. In performance, the MDF adaptive filter introduces smaller block delay and is faster, making it ideal for a time-varying application such as modeling an acoustic path in a teleconference room. This is achieved by using a smaller block size, updating the weight vectors more often, and reducing the total execution time of the adaptive process. The MDF adaptive filter compares favorably to other frequency-domain adaptive filters when its adaptation speed and misadjustment are tested in computer simulations. >

Filter design for optical pattern recognition: multicriteria optimization approach.

Abstract: A method of constructing optimal multicriteria filters for optical pattern recognition is presented. In the particular case of synthetic discriminant function filters, this method is illustrated for double-optimization criteria, and filters that are not overspecialized are obtained, in contrast with traditional techniques. Furthermore, a rigorous comparison between different filters, with respect to the considered criteria, is provided with this approach.

Nonlinear techniques for interference suppression in spread-spectrum systems

Abstract: The binary nature of direct-sequence signals is exploited to obtain nonlinear filters that outperform the linear filters hitherto used for this purpose. The case of a Gaussian interferer with known autoregressive parameters is considered. Using simulations, it is shown that an approximate conditional mean (ACM) filter of the Masreliez type performs significantly better than the optimum linear (Kalman-Bucy) filter. For the case of interferers with unknown parameters, the nature of the nonlinearity in the ACM filter is used to obtain an adaptive filtering algorithm that is identical to the linear transversal filter except that the previous prediction errors are transformed nonlinearly before being incorporated into the linear prediction. Two versions of this filter are considered: one in which the filter coefficients are updated using the Widrow LMS algorithm, and another in which the coefficients are updated using an approximate gradient algorithm. Simulations indicate that the nonlinear filter with LMS updates performs substantially better than the linear filter for both narrowband Gaussian and single-tone interferers, whereas the gradient algorithm gives slightly better performance for Gaussian interferers but is rather ineffective in suppressing a sinusoidal interferer. >

Theory of two-dimensional multirate filter banks

Abstract: Results are presented on 2-D FIR (two-dimensional finite-impulse-response) filter banks for multirate applications. The theory is valid for all sampling lattices; conditions for alias-free and perfect signal reconstruction are derived. Synthesis structures for paraunitary and nonparaunitary polynomial matrices are derived, which yield perfect reconstruction filter banks. The degrees of freedom are given for these systems. Linear phase conditions are posed on the polyphase form of filter banks. which is used to derive a design structure for the restricted, but important, case of linear phase filter banks. >

CMOS active filter design at very high frequencies

Abstract: A study of the limitations of active CMOS filters at high frequencies suggests automatic means to compensate imperfections in the filter response introduced by active devices. The effects of nonzero FET output conductance, limited frequency response and noise on the filter characteristics, and dynamic range are analyzed, particularly for filters with high Q components. These are used to demonstrate a 3- mu m CMOS realization of a fourth-order bandpass filter with a 250-kHz passband centered at 12.5 MHz. The filter demonstrates that the maximum frequency of filter operation is not as seriously limited by device f/sub T/ as was previously thought, but that automatic means may be used to tune out the imperfections introduced in the filter elements by the limited voltage gain and frequency response of transistors. >

Performance analysis of LMS adaptive prediction filters

Abstract: The conditions required to implement real-time adaptive prediction filters that provide nearly optimal performance in realistic input conditions are delineated. The effects of signal bandwidth, input signal-to-noise ratio (SNR), noise correlation, and noise nonstationarity are explicitly considered. Analytical modeling, Monte Carlo simulations and experimental results obtained using a hardware implementation are utilized to provide performance bounds for specified input conditions. It is shown that there is a nonlinear degradation in the signal processing gain as a function of the input SNR that results from the statistical properties of the adaptive filter weights. The stochastic properties of the filter weights ensure that the performance of the adaptive filter is bounded by that of the optimal matched filter for known stationary input conditions. >

Analysis of discrete-time Kalman filtering under incorrect noise covariances

Abstract: Analysis tools are developed that can be effectively used to study the performance degradation of a filter when incorrect models of the state and measurement noise covariances are used. For a linear time-variant system with stationary noise processes, it is shown that under certain stability conditions on the system model, the one-step prediction error covariance matrix will converge to a steady-state solution even when the filter gain is not optimal. On the other hand, if the state transition matrix has an unreachable mode outside a unit circle, then the modeling errors in the noise covariances may cause the filter to diverge. Bounds on the asymptotic filter performance are computed when the range of errors in the noise covariance matrices are known. Using simple examples, insights into the behavior of a Kalman filter under nonideal conditions are provided. >

Optimized fast Hankel transform filters

Abstract: In the linear digital filter theory for calculation of Hankel transforms it is possible to find explicit series expansions for the filter coefficients. A method is presented for optimizing the Hankel filters calculated in this way. For a certain desired accuracy of computation, the sampling density and filter length are minimized by choosing the parameters determining the filter characteristics according to the analytical properties of the input function. A new approach to the calculation of the filter coefficients has been developed for these optimized filters. The length of the filters may be further reduced by introducing a shift in the sampling scheme.

Crosstalk analysis and filter optimization of single- and double-cavity Fabry-Perot filters

Abstract: Since Fabry-Perot (FP) filters are major candidates for use as demultiplexers in wavelength division multiple access (WDMA) networks, the authors have analyzed, in an exact and unified manner, the crosstalk degradation for several different variations of the basic FP filter, compared their performances, and optimized their design parameters. A description is given of the system model (a wavelength division multiple access system consisting of M connected transmitters and receivers with each transmitter consisting of an on-off modulated fixed-frequency laser, with the 'off' power level equal to zero) and the parameters used throughout, along with a brief discussion of relevant Fabry-Perot equations and terms and the four different filter structures analyzed. The crosstalk is examined for the cases of a single-cavity FP filter, a double-pass FP filter, a two-stage double-cavity FP filter, and a vernier double-cavity FP filter. The criteria for the performance comparison were the worst-case crosstalk, BER, and crosstalk power penalty. >

Rugate filter design: the modified Fourier transform technique

Abstract: The Fourier transform technique developed for the design of variable refractive index coatings such as rugate filters is improved to achieve an accurate correspondence between optical properties and the refractive index profile. An application to the design of narrowband reflectors is presented.

Integral switched capacitor for filter/digital to analog converter for sigma-delta encoded digital audio

Abstract: A combined finite impulse response filter and digital-to-analog converter for converting sigma-delta over-sampled data into analog form. The filter removes out-­of-band noise energy from the reconstructed analog signal resuting from the sigma-­delta encoding process. The filter/converter is implemented in switched-capacitor technology. Further, a method of designing the optimum number of taps and the tap weight coefficients of the filter is given.

Tunable bandpass filter system and filtering method

Abstract: A tunable bandpass filter system and filtering method wherein the bandwidth of a tunable bandpass filter is adjusted as a function of the fundamental frequency of an input signal. Either a constant bandwidth or a constant quality factor tunable bandpass filter may be used. The center frequency of the tunable bandpass filter is adjusted in direct proportion to the product of the fundamental frequency and the number of a selected harmonic thereof. In the case of a constant bandwidth filter the bandwidth is adjusted in direct proportion to the quotient of the fundamental frequency divided by a selected filter quality factor. In the case of a constant quality factor filter, the bandwidth is indirectly controlled by adjusting the center frequency while adjusting the quality factor in inverse proportion to the harmonic number. The output amplitude of the filter is measured to determine the amount of distortion in the input signal. The fundamental frequency may be determined by measuring the input signal.

Tracking analysis of the sign algorithm in nonstationary environments

Abstract: A tracking analysis of the adaptive filters equipped with the sign algorithm and operating in nonstationary environments is presented. Under the assumption that the nonstationary can be modeled using a random disturbance, it is shown that the long-term time average of the mean-absolute error is bounded, and that there exists an optimal choice of the convergence constant mu which minimizes this quality. Applying the commonly used independence assumption, and under the assumption that the nonstationarity is solely due to the time-varying behavior of the optimal coefficients, it is shown that the distributions of the successive coefficient misalignment vectors converge to a limiting distribution when the adaptive filter is used in the system identification mode. Finally, under the additional assumption that the signals involved are zero mean and Gaussian, a set of nonlinear difference equations is derived that characterizes the mean and mean-squared behavior of the filter coefficients and the mean-squared estimation error during adaptation and tracking. Results of several experiments that show very good correlation with the theoretical analyses are presented. >

Adaptive convergent decision feedback equalizer

Abstract: An adaptive convergent decision feedback equalizer apparatus and method is disclosed for reducing intersymbol interference (ISI) in a data communication system. ISI is cancelled by generating and subtracting an estimation of the interference from a received signal. the estimation is generated by a N-tap transversal filter in which individual delayed received signals stored in the taps are multiplied by the respective adaptable tap coefficient and summed to form a digital representation of the ISI present. The present invention takes two steps to reduce the probability of coefficient adaptation from diverging. First, the DFE performs a coefficient modification only when the delayed received signal is a particular filter tap is a maximum or minimum level of the selected line code. A second step to eliminate divergence addresses the start up coefficient determination and errors in ISI estimation as the filter coefficients grow in size. On start up, only the first P number of DFE taps are chosen for modification and the remaining taps are held at zero. P is a number of taps for which the sum of the uncancelled ISI and the voltage error of an incorrect ISI estimation yields less than 0.5 probability of an error. After a minimum time (t min ) which insures convergence, the remaining taps (N-P) are enabled.

Real-time integration and differentiation of analog signals by means of digital filtering

Abstract: The performance of digital infinite impulse response (IIR) integrators and differentiators, calculated by means of a maximum likelihood estimator for transfer functions, is compared with that of their finite impulse response (FIR) counterparts and that of classical numerical integration and differentiation. An original design method that generates stable and reduced-order IIR filters in the complex domain (amplitude as well as phase constraints) is presented. In contrast to common opinion, it is shown that it is possible to design easy realizable IIR integrators and differentiators with an arbitrary small amplitude and phase error. Although there is no FIR alternative for IIR integrators, both FIR and IIR methods give competitive results for differentiators. It is shown that, owing to the design of pure delay filters, the (optimal) fractional delay integrators and differentiators can be used in case the original waveform and one (or more) of its (higher order) derivatives and (or) integrals are required. >

Hypercomplex numbers in digital signal processing

Abstract: A new number system, reduced biquaternions (RBs), is introduced. They are related to the quaternions and biquaternions proposed by W.R. Hamilton (1969). It is shown that a further reduction of systems degree will occur if RBs are used. An example shows the realization of a fourth-order real filter by means of a first-order RB filter. With the introduction of the RBs a new method is obtained for the design of wave digital Hilbert transformers. >

2-D FIR eigenfilters: a least-squares approach

Abstract: The 1-D eigenfilter approach is extended to the design of 2-D FIR (finite-impulse-response) filters. By minimizing a quadratic measure of the error in the 2-D frequency band, an eigenvector of an appropriate matrix is computed to obtain the filter coefficients. The method is not only simple but also is optimal in the least-squares sense. Several numerical design examples for arbitrarily shaped 2-D filters are used to illustrate the effectiveness of the approach. >

Optimal FIR filters for time-varying state-space models

Abstract: An optimal FIR (finite impulse response) filter and smoother is introduced for the time-varying state-space model. The suggested filter has an FIR structure and utilizes finite observation. It is shown that the impulse response of the optimal FIR filter can be obtained by a simple Riccati-type matrix differential equation. Especially for time-invariant systems, this FIR filter reduces to previously known simple forms. For implementation, a recursive form of the optimal FIR filter and smoother is derived by using adjoint variables, and computational algorithms are suggested. It is also shown by sensitivity analysis that the proposed optimal FIR filter alleviates potential divergence characteristics of the standard Kalman filter. >

Decimation filter as for a sigma-delta analog-to-digital converter

Abstract: A single stage multi-rate finite impulse response filter is used as the decimating filter for a sigma-delta analog-to-digital converter. The filter uses 2048 22-bit coefficient values to produce a sampled data output signal having a sampling rate of 49 KHz and a sample resolution of 16 bits from an input signals having a sampling rate of 3.072 MHz and a sample resolution of one bit. The filter uses a single read-only memory (820) to hold the 2048 coefficient values. The coefficient values are distributed to eight four-way multiplexed accumulators by a circuitry which includes a signal multiplexer (822) and a barrel shifter (824). The accumulators use unsigned arithmetic to calculate the output sample values. A value CO, representing a normalizing offset (812) and gain applied to each of the coefficient values, is selected such that 2048 times CO is a value which overflows the accumulator, leaving a value of zero in the accumulator.

Generalization of the linear matched filter concept to nonlinear matched filters

Abstract: A nonlinear matched filter based image correlator is investigated. The linear matched filter is expressed as a bandpass function containing the amplitude and phase of the Fourier transform of the reference signal. The bandpass filter function is then applied to a kth law nonlinear device to produce the nonlinear matched filter function. Analytical expressions for the nonlinear matched filter are provided. The effects of the nonlinear transfer characteristics on the correlation signals at the output plane are investigated. The correlation signals are determined in terms of the nonlinear characteristics used to transform the filter. We show that the nonlinear filter results in a sum of infinite harmonic terms. Each harmonic term is envelope modulated due to the nonlinear characteristics of the device, and phase modulated by m times the phase modulation of the linear filter function. The correct phase information of the filter is recovered for the first-order harmonic of the series. The envelope of each harmonic term is proportional to the kth power of the Fourier transform magnitude of the reference signal. We show that various types of filter such as the continuous phase-only filters can be produced simply by varying the severity of the nonlinearity. Nonlinear filters provide higher correlation peak intensity and a better defined correlation spot.

Reconciling steady-state Kalman and alpha-beta filter design

Abstract: The deterministic design of the alpha-beta filter and the stochastic design of its Kalman counterpart are placed on a common basis. The first step is to find the continuous-time filter architecture which transforms into the alpha-beta discrete filter via the method of impulse invariance. This yields relations between filter bandwidth and damping ratio and the coefficients, alpha and beta . In the Kalman case, these same coefficients are related to a defined stochastic signal-to-noise ratio and to a defined normalized tracking error variance. These latter relations are obtained from a closed-form, unique, positive-definite solution to the matrix Riccati equation for the tracking error covariance. A nomograph is given that relates the stochastic and deterministic designs. >

A design method for a periodically time-varying digital filter for spectrum scrambling

Abstract: A spectrum scrambling method is presented using the bifrequency map. It is proposed that a periodically time-varying digital filter can be designed using a bifrequency map and a conventional filter design method. A structure for a periodically time-varying digital filter which can be implemented easily on a digital signal processor is presented. >

Design of recursive digital filters with variable characteristics

Abstract: A new method for changing the cut-off frequency of infinite impulse response (IIR) digital filters with a single parameter is derived. the method is based on the use of the Taylor series expansion of the lowpass-to-lowpass frequency transformation. the filter structure is a parallel connection of real or complex allpass sections. the tuning range is several octaves for narrowband filters. By taking also the complementary output, a power-complementary filter pair with tunable crossover frequency is readily obtained. Tunable centre frequency and bandwidth are obtained by incorporating a special lowpass-to-bandpass transformation into the structure. Design examples and a description of a signal processor implementation are included.

Stochastic gradient adaptive filters with gradient adaptive step sizes

Abstract: Two adaptive step-size gradient adaptive filters are presented. The step sizes are changed using a gradient descent algorithm designed to minimize the squared estimation error. The first algorithm uses the same step-size sequence for all the filter coefficients, whereas the second algorithm uses different step-size sequences for different adaptive filter coefficients. An analytical performance analysis of the first algorithm is also presented. Analyses and experiments indicate that (1) the algorithms have fast convergence rates and small midadjustment errors and (2) in nonstationary environments, the algorithms tend to adjust the step sizes so as to give close to the best possible performance. Several simulation examples demonstrating the good properties of the adaptive filters are also presented. >

Design of IIR digital filters with arbitrary log magnitude function by WLS techniques

Abstract: The authors propose a technique for designing IIR (infinite impulse response) digital filters to have an arbitrary log magnitude frequency response. The technique is based on an iterative weighted least-squares (WLS) approach in the frequency domain. A weight updating procedure is introduced to obtain a nearly optimal approximation to the given log magnitude function in the least-squares sense. The weighting function is updated using the results of the previous iteration in such a way that the weighted error approximates the log magnitude error. Filter coefficients at each iteration are efficiently computed using a fast recursive algorithm for a set of linear equations derived from the WLS problem. Several design examples demonstrate the rapid convergence of the design algorithm. The algorithm is extended to equiripple approximation by means of a minor modification of the weight updating procedure. >

A new algorithm to optimize Barker code sidelobe suppression filters

Abstract: The authors suggest a new algorithm for binary coding waveform sidelobe reduction after matched filtering and present a general method by which optimized sidelobe suppression filters for Barker codes can be obtained with a peak output sidelobe 2.62 dB lower than the results found in the literature (for 13-b Barker code). This optimization algorithm is also promising for other binary coding waveforms, such as truncated pseudonoise (PN) sequences and concatenated codes. This new approach can readily be applied to sidelobe-reduction filter design for other binary coding waveforms, such as truncated PN sequences, concatenated codes, etc., which often find their applications in radar systems and spread spectrum communication systems. >