Showing papers on "Filter design published in 1976"

Synthesis of minimum roundoff noise fixed point digital filters

Abstract: Beginning with an external specification of a digital filter, structures which minimize roundoff noise are investigated. After fixing the probability of overflow through an l_{2} scaling procedure, roundoff noise is studied via the internal structure of the filter using a state variable formulation. An output noise variance formula in terms of the internal structure is derived. Conditions for minimizing this output noise are established and realizations which meet these conditions are constructed. A new set of filter invariants called second-order modes are defined and shown to play a definitive role in minimal noise realizations. From these invariants, for example, one can calculate the minimal output noise variance of a given external specification. Numerical results are given which compare these new filter structures with the usual parallel and cascade connections of second-order filters, both theoretically and through simulations. For narrow-band filters, these new structures can be orders of magnitude better (in terms of output noise variance). One drawback of these new structures is a large increase in the number of multipliers needed to realize them. However, by applying the theory to subfilters connected in parallel and cascade, a good compromise between output noise and number of multipliers is obtained.

Digital filtering by polyphase network:Application to sample-rate alteration and filter banks

Abstract: The digital filtering process can be achieved by a set of phase shifters with suitable characteristics. A particular set, named polyphase network, is defined and analyzed. It permits the use of recursive devices for efficient sample-rate alteration. The comparison with conventional filters shows that, with the same active memory, a reduction of computation rate approaching a factor of 2 can be achieved when the alteration factor increases. A more substantial gain can be obtained in the direct realization of a uniform bank of recursive filters through combination of the polyphase network with a discrete Fourier transform (DFT) computer; savings in hardware also result from the low sensitivity of the structure to coefficient word lengths.

An adaptive recursive LMS filter

Abstract: An adaptive, recursive, least mean-square-digital filter is heuristically derived that has the computational simplicity of existing transversal adaptive filters, with the additional capability of producing poles in the filter transfer function. Simulation results are presented to demonstrate its capability.

Two-dimensional spectral factorization with applications in recursive digital filtering

Abstract: The concept of spectral factorization is extended to two dimensions in such a way as to preserve the analytic characteristics of the factors. The factorization makes use of a homomorphic transform procedure due to Wiener. The resulting factors are shown to be recursively computable and stable in agreement with one-dimensional (1-D) spectral factorization. The factors are not generally two-dimensional (2-D) polynomials, but can be approximated as such. These results are applied to 2-D recursive filtering, filter design, and a computationally attractive stability test for recursive filters.

Filtering in the time and frequency domains

Abstract: Long regarded as a classic of filter theory and design, this book stands as the most comprehensive treatment of filtering techniques, devices and concepts as well as pertinent mathematical relationships. Analysis and theory are supplemented by detailed design curves, fully explained examples and problem and answer sections. Discussed are the derivation of filtering functions, Fourier, Laplace, Hilbert and z transforms, lowpass responses, the transformation of lowpass into other filter types, the all-pass function, the effect of losses on theoretical responses, matched filtering, methods of time-domain synthesis, and digital filtering. This book is invaluable for engineers other than those who are filter design specialists who need to know about the possibilities and limits of the filtering process in order to use filters competently and confidently in their system designs.

A digital filter bank for spectral matching

Abstract: A new digital filter bank design is proposed for the processing of speech waveforms where spectral pattern matching techniques are applicable. Outputs in decibels from the 30 channels of the filter bank are computed every 12 ms. Care has been taken to select a time window and filter center frequency and bandwidth values that take into account the acoustic characteristics of speech. A distance metric is proposed for comparing a spectral frame with previously derived reference patterns. The metric incorporates procedures for crude speaker/microphone normalization, signal level normalization, background noise normalization, and procedures for emphasizing differences in the region of spectral peaks.

Further considerations in the design of decimators and interpolators

Abstract: In this paper several issues concerning the design and implementation of multistage decimators, interpolators, and narrow-band filters are discussed. In particular, the question of designing these systems in terms of minimum storage rather than minimum computation rate is examined. It is shown that a design which uses finite impulse response (FIR) filters for each stage, and which is minimized for storage is essentially minimized in terms of computation rate as well. The problem of further improvements in designing decimators and interpolators by taking advantage of DON'T CARE frequency bands is also discussed. For the early stages in a multistage design it is shown that fairly significant reductions in filter order can be achieved in this manner. A third issue in the design process is the question of practical schemes for efficient implementation of multistage decimators and interpolators in both hardware and software. One such efficient implementation is discussed in this paper. Finally, the problem of designing multistage decimators and interpolators using elliptic infinite impulse response (IIR) filters is discussed. It is shown that multistage IIR designs can be somewhat more efficient computationally than single-stage designs; however, the storage efficiency of the multistage IIR design is worse than that of the single-stage IIR design.

Adaptive recursive least mean square error filter

Abstract: An adaptive recursive filter is disclosed which, in a preferred embodiment, comprises first and second adaptive transversal filters selectively coupled together to minimize the mean square error of the output data of the recursive filter based upon observations of input data to the recursive filter. Each transversal filter includes a tapped delay line with a variable weight on each tap. The output data of the recursive filter is developed by combining the outputs of the first and second transversal filters. The input data is applied to the first transversal filter, while the output data is applied to the second transversal filter. The output data is also combined with a reference signal to provide an error signal. A function of that error signal is utilized to update the weights of all of the taps in both transversal filters in order to cause the weights to automatically adapt themselves to minimize the mean square error of the output data of the recursive filter.

Recursive digital filter synthesis via gradient based algorithms

Abstract: The three gradient-based algorithms of 1) steepest descent, 2) Newton's method, and 3) the linearization algorithm are applied to the problem of synthesizing linear recursive filters in the time domain. It is shown that each of these algorithms requires knowledge of the associated recursive filter's first-order sensitivity vectors, and, in the case of the Newton method, second-order sensitivity vectors as well. Systematic procedures for generating these sensitivity vectors by computing the response of a companion filter structure are then presented. Using the ideal low-pass filter as a design objective, it is then demonstrated that the linearization algorithm is particularly well suited for recursive filter design. On the other hand, the steepest descent and Newton methods are found to work rather poorly for this class of problems. Reasons for these empirical observed results are postulated.

The design and operation of practical charge-transfer transversal filters

Abstract: Some of the design considerations for charge-transfer split-electrode transversal filters are discussed. Clock frequency, filter length, and chip area are important design parameters. The relationship of these parameters to filter performance and accuracy is described. Both random and tap weight quantization errors are considered, and the optimum filter length is related to tap weight error. A parallel charge-transfer channel, which balances both capacitance and background charge, and a coupling diffusion between split electrodes greatly improves accuracy. A one-phase clock is used to simplify the readout circuitry. Two off-chip readout circuits are described, and the performance of two low-pass filters using these readout circuits is given. Signal to noise ratios of 90 dB/kHz and an overall linearity of 60 dB have been achieved with this readout circuitry.

A 500-stage CCD transversal filter for spectral analysis

Abstract: The operation and design of 500-stage charge-coupled device (CCD) transversal filters are described. The filters have been mask programmed for implementing two spectral analysis techniques: 1) bandpass filtering and 2) Fourier analysis using the chirp z transform (CZT) algorithm. The bandpass filter has a measured fractional 3 dB bandwidth of 0.0108 and 38 dB sidelobe rejection. The dynamic range is 75 dB with less than 45 dB total harmonic distortion. A sliding transform is defined which is useful for calculations of the power spectral density and is shown to be particularly advantageous in a CCD-CZT implementation. Using the sliding transform, a 500-point spectrum is calculated using CCD's with resolutions which can be varied from 1-200 Hz. The dynamic range of the power spectral output was measured to be 80 dB. A discussion is given of the performance limitation of a general CCD filter due to the inherent characteristics of the device. The results are evaluated for the 500-stage devices described above and indicate that sample rates from 25 Hz to 10 MHz are possible with a dynamic range approaching 100 dB while retaining high linearity.

A Simple and Versatile Fourier Domain Digital Filter

Abstract: A number of signal processing operations can be carried out on spectra using a digital filter based on a simple trapezoid function. The filter is applied to the Fourier transform of the spectral signal. Several signal processing examples are presented to illustrate the capabilities of this filter. These examples include filtering and diagnosis of high frequency noise on a signal, removal of fixed frequency noise, minimization of quantization noise, and differentiation and approximate deconvolution for the purpose of resolution enhancement.

Image processing system using incoherent radiation and spatial filter hologram

Abstract: A linear optical processing system in which a spatial filter in the form of a Fourier transform hologram is included with a lens for processing incoherent electromagnetic radiation. Such a system provides a given real, two-dimensional transfer function for spatially filtering incoherent radiation within a range of spatial frequencies 0 ≦ω≦Ω. The filter is made by forming a mask of a graph of a point spread function which is the inverse transform of the desired transfer function, and employing the mask in a coherent system to produce a Fourier transform hologram of the mask. Spatial filters are designed for providing the resultant systems with various transfer functions, including (a) a directional response for passing substantially higher spatial frequency components in a first direction than are passed in a second direction; (b) a selective attenuator response; (c) a notch filter response; (d) a correctional filter response; and (e) a linear minimum mean square error response. The systems are useful for recognizing specified patterns from a plurality of patterns and for determining the concentration of a species of particulate matter having a predetermined specific pattern within a sample of particles.

Fast automatic processing of resistivity soundings

Abstract: The difficulty in using master curves as well as classical techniques for the determination of layer distribution (e/sub i/, rho/sub i/) from a resistivity sounding arises when the presumed number of layers exceeds five or six. The principle of the method proposed here is based on the identification of the resistivity transform. The resistivity transform can be easily derived from the experimental data by the application of Ghosh's linear filter, and another method for deriving the filter coefficients is suggested. For a given theoretical resistivity transform corresponding to a given distribution of layers (thicknesses and resistivities) various criteria that measure the difference between this theoretical resistivity transform and an experimental one derived by the application of Ghosh's filter are given. A discussion of these criteria from a physical as well as a mathematical point of view follows. The proposed method is then exposed; it is based on a gradient method. The type of gradient method used is defined and justified physically as well as with numerical examples of identified master curves. The practical use for the method and experimental confrontation of identified field curves with drill holes are given. The cost as well as memory occupation and time of executionmore » of the program on CDC 7600 computer is estimated.« less

a Class of Convolutional Time-Varying Filters

Abstract: A linear time‐varying filtering process usually is realized by applying a number of time‐invariant filters to overlapping time regions of a trace and transitionally merging these different regions. We describe the design of a different type of linear time‐varying filter where the frequency spectrum of the filter is shifted along the frequency axis as a function of time without appreciable change in the spectrum shape. The design is based on a given time‐invariant filter with the desired spectrum shape. For long filter length, the design procedure is rather complicated. Furthermore, only a constant rate of frequency shift is possible. However, for many practical situations where the frequency shift over the filter length is much less than the bandwidth of the filter, the process of time‐varying filtering can be further simplified without appreciable frequency error. In fact, time‐varying filtering is achieved through modifying the complex signal representation of the original time invariant filter by a pre...

Input filtering apparatus for loudspeakers

Abstract: Improved input filtering apparatus for loudspeaker systems, and loudspeaker systems including such apparatus. The bass roll-off point of input filtering apparatus for loudspeakers is automatically adjusted to an optimum in accordance with the amplitude and spectral content of the audio signal being received at the time, thereby attenuating components in the signal liable to cause "bottoming" of the loudspeaker. The input filter apparatus comprises a first high-pass filter having a breakpoint frequency at or near the lower threshold of the audio frequency range, a second variable bandwidth, high-pass filter connected to receive the first high-pass filter output, a feedback circuit responsive to the second filter output to provide a feedback signal as a linear function thereof with a gain which is substantially inversely proportional to the square of the frequency, and circuit means including threshold means connected with the second filter and responsive to the said feedback signal to relatively rapidly increase the breakpoint frequency of the second filter in response to values of the feedback signal which exceed a threshold and to relatively showly reduce that breakpoint frequency in response to values of the feedback signal which do not exceed the said threshold. Bass equalization circuit means having a frequency response at the low end of the audio spectrum which is substantiallythe inverse of the frequency response of said loudspeaker means are provided between the output of the second filter and the loudspeaker drive circuit.

Case history of a surface-wave TV IF filter for color television receivers

Abstract: A surface-wave filter constitutes an attractive alternative for the design of the IF section of a television receiver. The detailed requirements for the TV IF channel are set forth, followed by a comparison of the conventional design with the new design involving a surface-wave filter. The surface-wave filter is introduced by a physical description of the transducer configuration. The procedure for fabricating surface-wave filters is described; it is very similar to that of making integrated circuits. The properties of the surface-wave filter are compared with the requirements in terms familiar to electrical engineers, emphasizing advantages and an occasional disadvantage. In a final section, some areas of possible improvement are indicated, showing that this TV IF filter is an advanced first generation device and that further improvements can be expected.

Filters using Bessel-type polynomials

Abstract: Bessel-type polynomials are defined and shown to be useful in constructing a variety of transfer functions in filter theory. A generalized Bessel filter and a generalized Bessel rational filter are considered and shown to include a number of special cases of Bessel-type filters. The greater flexibility of the generalized filters is exploited to obtain a variety of filter responses.

Self-adaptive digital filter for noise and phase jitter reduction

Abstract: A new adaptive digital tuning filter for tracking a sinusoidal signal within a frequency band is described. The input signal representative of both said sinusoidal signal and noise is fed to a Hilbert transformer which provides the in-phase and quadrature components, x k and x k , respectively, of said sinusoidal signal. These components are applied to the input of a filter having a transfer function K where ##EQU1## WHERE φ = 2πFT, f is the tuned frequency of the filter, T is the signal sampling period and a is a constant close to unity. The output signals y x and y x of the filter are applied to a computing means which provides a frequency control signal e k such that e.sub.k = x.sub.k y.sub.k - y.sub.k x.sub.k The above value of φ is adjusted through a conventional gradient method where φ.sub.k + 1 = φ.sub.k + μe.sub.k and controls are provided to adjust φ in a direction to change e k toward zero. Application of the adaptive tuning filter to cancellation of the main component of phase jitter in a modem is also described.

Design technique for a class of stable two-dimensional recursive digital filters

Abstract: A technique is presented for the design of stable two-dimensional recursive digital filters. The stability of the resulting filters is guaranteed, and hence repeated application of cumbersome stability tests is obviated. The transfer function of the filter is obtained from a one-dimensional prototype by applying a new transformation technique in the frequency domain. To illustrate the approach some design examples of low-pass filters are given.

Design of 2-dimensional recursive digital filters

Abstract: A method is proposed for designing 2-dimensional recursive digital filters with circular symmetry and zero phase. The method is based on transformations of the squared magnitude function of a 1-dimensional digital filter and on the stabilisation of the resulting digital filter. Design results are given.

Transversal Filter Design and Application in Satellite Communications

Abstract: A brief literature survey of transversal filters is followed by a design example of a binary transversal filter. A particular application in the modulator of the single channel per carrier data transmission equipment is described. Computer simulations and COS/MOS hardware implementation proved the validity and the feasibility of the theory described by Mueller. Design and evaluation of a linear phase filter approaching the Nyquist channel is the end result of our study.

Two dimensional optical phase grating filter

Abstract: A two dimensional optical phase grating filter is provided that is capable of limiting the transmittance of spacial frequency signals in one or more scan directions. The two dimensional grating of the present invention can be utilized as an optical low pass filter to improve image resolution in a color video system. In the color video system, the two dimensional grating filter could be designed to optically complement a dichroic stripe filter to prevent the introduction of spurious signals by any interference of luminance and chrominance signals. The design parameters of the present invention provide an improved cut-off characteristic with grating widths larger than one-half of the filter period. The two dimensional phase grating filter of the present invention can also be utilized in other optical systems, such as an automatic focusing system, where it is desired to pass only a certain spacial frequency as a monitored signal for the automatic adjustment of the focus of the optical system.

Filter having an automatically controlled variable cut-off frequency

Abstract: A device for measuring the frequency or period of an input signal independent of different frequency noise signals which may be superimposed on the input signal includes a filter circuit having a variable cut-off frequency. The output level of the filter circuit is detected by a level detector, the output of which electrically controls a variable element such as a variable resistor, a variable capacitance diode or the like which is included in the filter circuit. This controls the cut-off frequency of the filter circuit, so as to maintain its output level at a given level. In this manner, an input signal frequency is converted into a corresponding level, utilizing a declining portion adjacent to the cut-off frequency of the frequency response of the filter circuit. The converted level is utilized to vary the cut-off frequency of the filter circuit to maintain its output level constant, thereby automatically changing the cut-off frequency in accordance with the input signal frequency.

Correlated noise due to roundoff in fixed point digital filters

Abstract: It is shown that correlation between quantization error sources in finite precision fixed point digital filters can be significant even when a filter is driven by a random input. It is demonstrated that correlation coefficients can be estimated in terms of relative values of multiplying constants and the filter structure. A general formulation of filter output noise is developed in terms of the covariance matrices of the error sources. Thus the effects of correlation can be taken into account analytically for purposes of design and comparison.

Linear and Nonlinear Filtering Techniques

Abstract: Publisher Summary The application of filtering theory to engineering systems requires knowledge in four areas: mathematical theory, system modeling techniques, filter design, and filter implementation. For linear systems with linear measurements and Gaussian noise, the filter theory is well defined and is given by explicit algorithms for an optimal solution. In engineering practice, considerable experience is needed when the questions of modeling, design, and implementation are considered. The emphasis is on developing practical approaches to the development of filters, which lead to satisfactory system performance where “satisfactory” is defined by the design engineer. “Satisfactory” is used instead of “optimal” because the optimization of filter mechanization includes the factors that are difficult or impossible to describe mathematically, such as the trade-off between performance of the filter and computer size. The truly optimal solution would be used in evaluating the performance of the actual filter implemented. This chapter reviews the linear filter equations and discusses modeling. It presents the techniques to be used in evaluating the actual implemented filter, which is suboptimal, against the optimal solution. The chapter further presents some of the practical solutions to implementation problems; these include: filter partitioning, data pre-filtering, square root techniques, and filter divergence.

On Understanding the Matched Filter in the Frequency Domain

Abstract: A matched filter is viewed as a cascade of a spectral-phase matched filter and a spectral-amplitude shading filter. The former provides the peak output in time, and the latter guarantees that that peak has maximum signal-to-noise ratio (SNR), or the latter may alternatively be chosen to provide better time resolution.

A Recursive Digital Filter Using DPCM

Abstract: A recursive digital filter using differential pulse-code modulation (DPCM) is proposed. The filter can realize any rational transfer function without the need for a new design. Results on roundoff error and limit cycle oscillations are presented. The implementation of these filters is also discussed.

A reprogrammable filter bank using charge-coupled device discrete analog-signal processing

Abstract: A filter bank having up to 32 channels is formed by multiplexing a recursive two-pole delay line filter Thirty-two sets of filter constants are stored and addressed digitally while multiple delays are provided in analog form by a charge-coupled device (CCD) delay line The interface between the digitally stored constant and the delayed analog signal occurs in a four quadrant multiplying D/A where the delayed analog signal is weighted by the constant Sampling and clamping at the CCD interfaces insures accurate dipolar analog operation The filter hardware is described, the filter constants are derived, and the performance is documented