Showing papers on "Filter design published in 1986"

Exact reconstruction techniques for tree-structured subband coders

Abstract: In recent years, tree-structured analysis/reconstruction systems have been extensively studied for use in subband coders for speech. In such systems, it is imperative that the individual channel signals be decimated in such a way that the number of samples coded and transmitted do not exceed the number of samples in the original speech signal. Under this constraint, the systems presented in the past have sought to remove the aliasing distortion while minimizing the overall analysis/reconstruction distortion. In this paper, it is shown that it is possible to design tree-structured analysis/reconstruction systems which meet the sampling rate condition and which result in exact reconstruction of the input signal. The conditions for exact reconstruction are developed and presented. Furthermore, it is shown that these conditions are not overly restrictive and high-quality frequency division may be performed in the analysis section. A filter design procedure is presented which allows high-quality filters to be easily designed.

Frequency-response masking approach for the synthesis of sharp linear phase digital filters

Abstract: If each delay element of a linear phase low-pass digital filter is replaced by M delay elements, an (M + 1) -band filter is produced. The transition-width of this (M + 1) -band filter is 1/M that of the prototype low-pass filter. A complementary filter can be obtained by subtracting the output of the (M + 1) -band filter from a suitably delayed version of the input. The complementary filter is an (M + 1) -band filter whose passbands and stopbands are the stopbands and passbands, respectively, of the original (M + 1) -band filter. If the frequency responses of the original ( M + 1) -band filter and its complementary filter are properly masked and recombined, narrow transition-band filter can be obtained. This technique can be used to design sharp low-pass, high-pass, bandpass, and bandstop filters with arbitrary passband bandwidth.

Numerical aspects of different Kalman filter implementations

Abstract: A theoretical analysis is made of the error propagation due to numerical roundoff for four different Kalman filter implementations: the conventional Kalman filter, the square root covariance filter, the square root information filter, and the Chandrasekhar square root filter. An experimental analysis is performed to validate the new insights gained by the theoretical analysis.

Design of almost minimax FIR filters in one and two dimensions by WLS techniques

Abstract: The design of Finite Impulse Response (FIR) filters in one or several dimensions can be performed with good computational efficiency using a Weighted Least Square (WLS) design. Minimax design, which is often preferred, is computationally burdensome, principally in two dimensions. This paper draws attention to the design of minimax filters using iterative WLS techniques for one-dimensional filters and extends the approach to two-dimensional filters. For two dimensions the techniques apply to both rectangular and hexagonal sampling grids. Examples demonstrate flexibility and good computational efficiency. The paper also illustrates a promising new approach to filter design which couples the very general WLS methodology to the less manageable but often preferred minimax performance criterion.

Efficiency data transmission technique

Abstract: Partial response and quadrature partial response data transmission system characterized by increased transmission rate, lower signal-to-noise ratio, low cost and simpler hardware implementation than prior art systems. A steep filter (almost rectangular) is connected to the output of a cosine filter, forming a composite filter, wherein the cut-off frequency of the rectangular filter is less than the Nyquist frequency by a predetermined amount which is inversely proportional to the amount in percentage by which the data transmission rate exceeds the Nyquist rate. The system is thus capable of signalling at the Nyquist rate and greater, without requiring that channel filter parameters or the basic clock rate be adjusted. A smaller number of signal levels can be selected (as compared to previously existing methods) for spectrally efficient applications, and the resulting more robust system can also be used to transmit PAM, QAM, and other baseband or modulated signals.

Optimal Edge Detector Design I: Parameter Selection and Noise Effects

Abstract: This paper comments on the optimality of the Laplacian of a Gaussian edge detection filter which localizes edges through zero crossings in the filtered image. The arguments of both Marr and Hildreth, and Dickey and Shanmugam are reviewed to establish that the filter is optimal in the sense of maximizing output image energy near edge features. This filter's principal advantage over other edge detectors is that its response is user-adjustable through selection of a single parameter, the Gaussian standard deviation. However, no clear method for the selection of this parameter has been provided. The problem is addressed here by applying the filter to two ideal periodic edge models blurred by a Gaussian distribution point-spread function. The observed response to the edge spacing and blur standard deviation is then translated into a filter parameter design procedure. The problems of optimum filter performance in the presence of additive Gaussian noise are then addressed. The problem of selecting the sampled filter's coefficient word size is dealt with in a companion paper.

Application of Autoregressive Moving Average Parametric Modeling in Magnetic Resonance Image Reconstruction

Abstract: The modeling of data is an alternative to conventional use of the fast Fourier transform (FFT) algorithm in the reconstruction of magnetic resonance (MR) images. The application of the FFT leads to artifacts and resolution loss in the image associated with the effective window on the experimentally-truncated phase encoded MR data. The transient error modeling method treats the MR data as a subset of the transient response of an infinite impulse filter (H(z) = B(z)IA(z)). Thus, the data are approximated by a deterministic autoregressive moving average (ARMA) model. The algorithm for calculating the filter coefficients is described. It is demonstrated that using the filter coefficients to reconstruct the image removes the truncation artifacts and improves the resolution. However, determining the autoregressive (AR) portion of the ARMA filter by algorithms that minimize the forward and backward prediction errors (e.g., Burg) leads to significant image degradation. The moving average (MA) portion is determined by a computationally efficient method of solving a finite difference equation with initial values. Special features of the MR data are incorporated into the transient error model. The sensitivity to noise and the choice of the best model order are discussed. MR images formed using versions of the transient error reconstruction (TERE) method and the conventional FFT algorithm are compared using data from a phantom and a human subject. Finally, the computational requirements of the algorithm are addressed.

Digital filter switch for data receiver

Abstract: A digital filter switch for use with a data receiver incorporates first and second squaring units connected to the outputs of first and second band-pass filters tuned to the separation and character frequencies in a signal transmission. The outputs of the squaring units are interconnected via an adder to the input of a low-pass filter, which produces the output data signal.

A digital filter bank for digital audio systems

Abstract: The design of a linear phase digital filter bank for audio system frequency response equalization is shown. This filter bank uses frequency response masking and complementary filtering principles to achieve very sharp frequency response for each band, unity gain at all frequencies with no ripple when all the gain weightings of the filter bank outputs are unity, and extremely low hardware complexity.

Efficient Approximation of Kalman Filter for Target Tracking

Abstract: A Kalman filter in the Cartesian coordinates is described for a maneuvering target when the radar sensor measures range, bearing, and elevation angles in the polar coordinates at high data rates. An approximate gain computation algorithm is developed to determine the filter gains for on-line microprocessor implementation. In this approach, gains are computed for three uncoupled filters and multiplied by a Jacobian transformation determined from the measured target position and orientation. The algorithm is compared with the extended Kalman filter for a typical target trajectory in a naval gun fire control system. The filter gains and the tracking errors for the proposed algorithm are nearly identical to the extended Kalman filter, while the computation requirements are reduced by a factor of four.

Bandwidth compression for television signals

Abstract: A video signal received from a source (10) is bandwidth-compressed by filters (12, 14, 16), filter (14) being a temporal filter and filter (16) being a spatial filter. Selection of the filter to be used is dependent upon picture content. The transmitter reconstitutes in interpolators (44, 46) the signal which would be regenerated at the receiver, determines which filter gives the best results, and transmits an indication of which filter has been used in a digital signal associated with the analogue video signal. Preferably a determination of motion vectors associated with the signal is made and the digital signal indicates which of the determined motion vectors is applicable to different areas of te picture. By transmitting the control signal digitally with the analogue video signal the receiver circuitry is greatly simplified while its reliability is improved.

A Transformation for Digital Simulation of Analog Filters

Abstract: One method of simulating an analog filter on a digital computer is to transform the continuous-time differential equation of the filter into a corresponding discrete-time difference equation. This paper describes the useful properties of the step-invariant transformation.

Low sensitivity digital LDI ladder filters with elliptic magnitude response

Abstract: A method of designing elliptic LDI [I] type switched-capacitor filters is known [2], [3]. However, this method cannot be extended directly to digital filter design and implementation. Preliminary results involving the design of a fifth-order digital LDI ladder filter have been proposed 141. In this contribution a complete design method for low sensitivity digital LDI ladder filters which have elliptic magnitude response is presented. A relationship between the bilinear and LDI transformed impedances is investigated. A precompensation procedure together with the bilinear transformation are applied to transform an elliptic analog ladder filter into a realizable digital LDI ladder filter. A voltage-current signal flowgraph ( V/I SFG) simulation method is adopted in this design procedure. The design procedure provides a method of realizing the bilinear transformed transfer function using the LDI as a building block. An example of fifth-order elliptic LDI low-pass filter design is given. The effects of multiplier coefficient quantization on both the digital elliptic LDI ladder filter and an equivalent wave digital ladder are compared.

Phase-locked loop coefficient generator for a filter arrangement having a non-rational ratio between input and output sampling frequencies

Abstract: In a sample rate converter having a non-rational conversion factor the input samples coincide with low-rate clock pulses and the output samples coincide with high-rate clock pulses, or inversely. It comprises a filter coeffi­cient generator 3 which, based on the distance (deviation) between a low-rate clock pulse and the immediately preceding or immediately subsequent high-rate clock pulse, con­tinuously supplies a series of filter coefficients. To de­termine the deviation a phase-locked loop (30) is provided, with a phase detector (301) receiving the low-rate clock pulses as well as synthetic low-rate clock pulses and supplying a discrete-time phase difference signal u(.) which is applied to a processor circuit (302). This circuit supplies the desired deviation d(.) and a reference number N which is applied to a counter circuit (304). This circuit also re­ceives the high-rate clock pulses and each time after re­ceiving the number of clock pulses corresponding to the reference number it supplies a synthetic low-rate clock pulse. In the processor circuit 302 a filtering operation (3021) is first performed on the discrete-time phase dif­ference signal u(.) so that control signal samples H(.) are obtained. An auxiliary sample s(.) is subtracted from such a control signal sample and the difference is divided by a weighting factor incr. of the number P thus obtained those bits whose significance is less than 2° represent the deviation d(.), while the other bits represent the reference number N. By subsequently multiplying the deviation d(.) by the weighting factor incr, a new auxiliary sample s(. + 1) is obtained.

Zero-tracking adaptive filters

Abstract: A new type of adaptive filter is proposed which can directly estimate and track its own zeros. The adaptation algorithm adapts the zeros of the filter and hence, indirectly, the filter coefficients. To first order in the adaptation parameter, the new algorithm is equivalent to the usual LMS algorithm, and thus it shares the same convergence properties with the latter. The cases of adaptive prediction, the adaptive Pisarenko method, and adaptive point-source location are discussed in detail.

Non linear adaptive filters

Abstract: A non-linear adaptive filter is described having a linear filter connected in parallel with a non-linear filter. The linear filter provides fast adaption until it has modelled the linear contribution of each coefficient. Thereafter the non-linear filter continues to adapt until the error signal has been reduced to an acceptable level. In a preferred embodiment a plurality of unit delay devices provide taps to sub-processing units each of which is arranged to be adapted according to a linear algorithm during an initial part of a training period, and to a non-linear algorithm after said initial part. The filter has particular use in echo cancellers for data modems.

Modifications to the McClellan, Parks, and Rabiner computer program for designing higher order differentiating FIR filters

Abstract: Simple modifications to the McClellan, Parks, and Rabiner linear phase finite impulse response (FIR) filter design program are suggested to allow the design of an nth-order differentiating FIR filter of arbitrary length for any n. Two illustrative examples are also provided.

Fast multiplierless architecture for general purpose VLSI FIR digital filters with minimized hardware

Abstract: A digital transversal filter which employs a multiplierless algorithm for effecting convolutions of samples of a digital input word by the filter coefficients. Each of the samples of an input word is bit sliced into segments of two or more bits, and convolutions are carried out in parallel on all segments using only adders and registers. The convolution products are then summed in a pipeline adder tree to derive the convolution of the complete input word. This architecture provides high frequency capability and significantly lower transistor count and hardware complexity, enabling efficient very large scale integration (VLSI) implementation.

Modal S-matrix method for the optimum design of inductively direct-coupled cavity filters

Abstract: A rigorous field theory method is described for the computer-aided design of a class of rectangular waveguide filters, where the cavities are coupled by irises, E-plane integrated metal inserts, broadside oriented strip obstacles, or multiple quadratic posts. These coupling elements enable low-cost manufacturing, since accurate and inexpensive metal-etching techniques, or materials with standard dimensions may be utilised. The design method is based on field expansion in suitably normalised eigenmodes which yield directly the modal scattering matrix of two appropriate key building blocks for this kind of filter, the step-wall discontinuity and the N-furcated waveguide section of finite length. The theory includes the finite thickness of the diaphragms, strips or posts as well as the immediate higher-order mode interaction of all discontinuities. The stop-band characteristic of the filter is taken into account in the optimisation process. Optimised data are given for Ku-, E-, W-, and D-band filter examples, whereby it is shown that the theory is also very appropriate for broadband designs. The theory is verified by measured results for a six resonator iris coupled Ku-band filter, with a midband frequency of 15.2 GHz and a seven-resonator metal insert D-band filter, with a midband frequency of 142.5 GHz, showing measured minimum insertion losses of 0.2 dB and 1.4 dB, respectively.

Multipliers for residue-number-arithmetic digital filters

Abstract: A recently proposed residue-number-arithmetic digital filter offers major cost and speed advantages over binary-arithmetic digital filters, but suffers one major drawback. The filter coefficients must be constant, since the lack of a fast method of multiplication by a fraction in residue arithmetic requires the coefficients to be realised by a fixed table look-up read-only memory. Two multipliers are proposed which realise a completely general fractional multiply and are suitable for digital-filtering applications.

Sinusoidal disturbance rejection with application to helicopter flight data estimation

Abstract: This paper is concerned with the problem of eliminating sinusoidal disturbances from data while producing minimal distortion to the underlying data. A particular example of this problem arises in the filtering of helicopter data which are corrupted by sinusoidal disturbances due to rotor motion. It is shown that an optimal solution to the problem can be found using Kalman filtering theory. The properties of the optimal filter are analyzed using recent results on filtering for nonstabilizable systems. These results are then used to motivate a particular near-optimal filter which has enhanced robustness properties relative to the optimal filter. It will also be shown that an identical filter can be derived using recent results on the evaluation of recursive discrete Fourier transforms. This link between time and frequency domain methods leads to a rather complete understanding of the characteristics of the filter. Specific results are presented showing the application of the filter to real helicopter data.

Noise canceling system

Abstract: Under the condition where a plurality of background noise sources exists, there are arranged a first receiver, primarily receiving desired voice, and a plurality of second receivers each primarily receiving noise from a corresponding noise source. Filter coefficients of equivalent noise-producing filters, each having a frequency transmission characteristic equivalent to that of transmission path from its corresponding noise source to the first receiver, are estimated based upon mutual-correlation coefficients among the outputs of the first and second receivers and auto-correlation coefficients of the respective outputs of the second receivers. The noise signals from the equivalent noise-producing filters are subtracted from the output of the first receiver, thereby canceling the background noise. The filter coefficients estimation may be performed by using a maximum of the mutual-correlation coefficients between the outputs of the first receiver and the respective second receivers.

Optimal Edge Detector Design II: Coefficient Quantization

Abstract: A companion paper describes the design and implementation of the Laplacian of a Gaussian edge detection filter which localizes edges through zero crossings in the filtered image. Accuracy in the presence of noise has been found to be proportional to the square root of the filter's standard deviation. Digital implementation of any continuous filter requires sampling and coefficient quantization. The sampled filter was examined, but a method is proposed here for selection of a minimum coefficient word size for direct-form implementation to satisfy in-band rejection bounds.

Reducing noise in ultrasonic images

Abstract: Techniques are disclosed for producing improved ultrasonic cross-sectional images of a body subject to a number of consecutive and at least partly overlapping scans by the pulse echo method to produce digital image signals corresponding to the received echoes. The illustrated systems includes an ultrasonic transducer scanner energized by a transmitter, and a receiver configuration which processes the received echo signals for display on a TV monitor. To reduce the image-quality-limiting noise while retaining a satisfactory representation of moving parts in the zone under examination, image signals corresponding to corresponding scanning dots of consecutive scans are combined in the receiver circuit which utilizes time-discrete non-linear filtering with filter coefficients which vary as a function of the filter input signal. This arrangement and the related process produce improved images.

The analog median filter

Abstract: Discrete median filters are a special class of ranked-order digital filters used for smoothing signals. In this paper, the analog median filter is defined and proposed for analysis of the standard discrete median filter in cases with a large sample size or when the associated statistics would be simpler in the continuum. Discrete filters are shown to be a subclass of analog filters. Also, an equivalence among analog filters and limits of discrete filters is established. Finally, several stochastic interpretations of the analog median filter are presented including necessary and sufficient conditions on input processes which guarantee the existence of output distributions for multiple passes of the analog median filter

Noise canceling apparatus

Abstract: In order to eliminate background noise infiltrating into an input audio signal, a noise-canceling apparatus includes: first and second acoustic pickups for primarily picking up the audio signal and noise, respectively; a filter receiving the output of the second acoustic pickup; a subtracter for subtracting the output of the filter, when the audio signal is silent, from the output of the first acoustic pickup; and a coefficient determination for determining coefficients of the filter so as to make the filter generate a noise signal corresponding to a signal generated by passing the noise through a transmission path having a transmission frequency characteristic from the noise source to the first acoustic pickup. The coefficients of the filter are determined on the basis of mutual-correlation coefficients between the outputs of the first and second pickups and self-correlation coefficients of the output of the second pickup, thereby improving the processing efficiency.

Computer Generation of Digital Filter Banks

Abstract: In order to reduce the design time of digital filter bank circuits, a design system has been developed. The software consists of the filter compiler which converts high level filter descriptions to hardware descriptions and the layout generator which converts the hardware descriptions to a layout file. To verify the algorithms before fabrication, a test system is employed. The development time of this system was kept to a minimum by designing the hardware to be easily micro coded and assembled. Several circuits have been fabricated and tested that were generated with this system, including a single bandpass filter chip, a 112-pole 16-channel filter bank for a speech recognition system and a 16-channel spectrum analyzer for consumer stereo applications. The speech recognition chip achieved a SNR of 80 dB with an area of 25 mm /sup 2/ in a 4-micron NMOS technology.

A coefficient sensitivity bound in 2-D state-space digital filtering

Abstract: For a SISO two-dimensional (2-D) state-space digital filter, a general upper bound on the sensitivity measurement of the filter's eigenfunctions is proposed. The bound for both equal and unequal word length registers of an optimal realization [11], [12] is calculated. It is shown that for a scaled equal wordlength realization, the bound has its minimum value.

Efficient multi-processor implementation of recursive digital filters

Abstract: Efficient computation method for the recursive digital filtering is studied in the multi-processor environment. The method solves the dependency problem by separate computations of the particular and transient solutions. The throughput of the algorithm increases linearly with the number of processors, making it possible to increase the throughput effectively by using multiple number of processors. The implementations of the algorithm using a vector-processor and a multiprocessor in a ring network are also studied.