Showing papers on "Filter design published in 1978"

Algorithms for Least-Squares Linear Prediction and Maximum Entropy Spectral Analysis,

Abstract: : Experience with the maximum entropy method of spectral analysis suggests that it can produce inaccurate frequency estimates of short sample sinusoidal data, and it sometimes produces calculated values for the filter coefficients that are unduly contaminated by rounding errors. Consequently, this report develops an algorithm for solving the underlying least-squares problem directly, without forcing a Toeplitz structure on the model. This approach leads to more accurate frequency determination for short sample harmonic processes, and our algorithm is computationally efficient and numerically stable. The algorithm can also be applied to two other versions of the linear prediction problem. A FORTRAN program is supplied.

Use of the Butterworth low-pass filter for oceanographic data

Abstract: The characteristics of the Butterworth low-pass filter are well known in electrical engineering. Here we discuss its use for oceanographic records and compare its characteristics with other low-pass filters now in use: the cosine-Lanczos filter, the Gaussian filter, and the ideal filter. The Butterworth filter is recursive, i.e., past values of the output are used as input, so a phase shift is introduced unless the data are filtered forward and backward through the same filter. When this is done, the filtered signal differs only slightly from that of other low-pass filters. Because the Butterworth filter uses fewer multiplicative constants for the same effect, there is a reduction in computer time over other low-pass filters; the difference becomes more pronounced as more data points are used.

Stability of general two-dimensional recursive digital filters

Abstract: Two-dimensional recursive filters are defined from a different point of view. A general stability preserving mapping theorem is presented which allows most recursive filters of a particular type to be mapped into any other type of recursive filter. In particular, any type of filter can be mapped into a first-quadrant filter. This mapping is used to prove a number of general stability theorems. Among these is a theorem which relates the stability of any digital filter to its two-dimensional phase function. Furthermore, other stability theorems which are valid for any type of recursive filter are presented. Finally, a number of practical stability tests are developed including one which requires the testing of only several one-dimensional polynomial root distributions with respect to the unit circle.

Filter which tracks changing frequency of input signal

Abstract: A tracking band-pass filter useful for locking onto, and passing, an input signal which changes rapidly in frequency. The filter has a frequency pass band controlled by a rectangular voltage waveform which is derived from the output signal passed by the filter. The filter output signal is translated from a sine wave to a pulse wave. The period between each two successive pulses is measured by counting the cycles of an oscillator during each respective period. The time-representing count is inverted to a frequency-representing count which controls the duty cycle of a rectangular wave used to make the filter track the changing frequency of the input signal.

A design technique for circularly symmetric low-pass filters

Abstract: The design of two-dimensional (2-D) circularly-symmetric low-pass digital filters by cascading several rotated filters (a rotated filter is defined to be one produced by rotating a one-dimensional (1-D) continuous filter into a two-dimensional continuous filter which is in turn bilinearly transformed into a two-dimensional digital filter) is a well-known and useful technique. An alternate approach which is an extension of the above technique is presented. This new method is based on a spectral transformation from the one-dimensional discrete domain into the two-dimensional discrete domain. This approach retains most of the advantages of the original technique while permitting design entirely in the discrete domain, yielding filters with better stability characteristics, and facilitating frequency response optimization via nonlinear programming.

Computer-Aided Filter Alignment and Diagnosis

Abstract: The cavity resonant frequencies and coupling values of a wide range of bandpass filters, band-reject filters, and equalizers have been determined in situ by computer-adjusting analytic models to fit the scattering parameters measured on an automatic network analyzer. A higher order mode elliptic filter, a dual-mode quasi-elliptic filter, and a dual-mode band-reject filter are presented as examples. The general relationships between mechanical dimensions and circuit parameters are discussed. The circuit adjustment procedure is outlined, and equations for the sensitivity coefficients of several element types are tabulated.

On an adaptive algorithm for IIR filters

Abstract: The purpose of this communication is to discuss an IIR adaptive filter algorithm developed by Stearns [1], in terms of an example that appeared in a recent article [2]. The example concerns the approximation of a fixed second-order filter by a first-order adaptive filter, when subjected to a white noise input.

Minimization of Power System Stabilizer Torsional Interaction on Large Steam Turbine-Generators

Abstract: A unique filter design is reported which, when used in a Power System Stabili minimizes the stabilizer effect at the shaft torsional natural frequencies. The results of analytical studies illustrating the requirement to reduce such interaction and the effectiveness of the new filter for a specific application are presented. Field tests which support the conclusions of the analytical studies are included. An associated monitoring function is described which provides protection against torsional instability in the event of critical component failure in the stabilizer. Implementation considerations are discussed.

Frequency domain adaptive filter for detection of sonar signals

Abstract: An adaptive filter for sonar signals which operates on the complex spectral components of the received signal, which signal has been transformed into the frequency domain by means such as the Fast Fourier Transform The adaptive filter consists of a plurality of component filters, each of which operates on a single spectral component of the received signals The transfer coefficient of each component filter is described by a complex number and is adaptively adjusted by means of a computational feedback loop The feedback loop compares the product of the transfer coefficient and the complex spectral component of the received signal from a prior frequency transformation cycle, with the present spectral component to obtain an error signal The error signal, in turn, adaptively alters the magnitude and phase of the transfer coefficient A plurality of such component filters operate together to adaptively filter, in the frequency domain, the entire spectrum of the received signal

Narrow-band interference rejection using the complex linear prediction filter

Abstract: The properties of the complex linear prediction filter are considered as used in the prewhitening of narrow-band interference prior to detection or parameter estimation based on optimum (MMSE) linear filtering. The parameter dependence of the filter output power, gain, and frequency response is quantified through the analysis of a single narrow-band interference plus uncorrelated tap noise. It is shown how the filter aperture has its usefulness in controlling the width of the notch formed and the whitening of the rest of the spectrum while the depth of the notch formed is proportional to the inverse of the interference-to-noise ratio.

Weighting coefficients for certain maximally flat nonrecursive digital filters

Abstract: The weighting coefficients for maximally flat nonrecursive digital ruters have been derived for low-pass filters having equal passband and stopband widths. The solution is in closed form and can be readily evaluated even for large filter order. Asymptotically the coefficients of the finite series expansion converge to the Fourier series coefficients. Hilbert transformers and decimation filters are among the suggested applications for this form of filter.

The design of optimal multirate bandpass and bandstop filters

Abstract: Narrow-band bandpass and bandstop filters are inherently of high order and require a large computation rate. A multirate filter using decimators and interpolators can be designed to have bandpass or bandstop characteristics, often with a much smaller computation rate. This paper develops rules for designing such a filter by placing constraints on the filter approximation error and the aliasing error. The question of admissible decimation factors is investigated in detail. A method to minimize the computation rate is described. Several examples are presented.

Adaptive filter network

Abstract: An adaptive filter network comprising a controllable filter having an adjustable cut-off frequency and adapted for varying the pass-band of the network. The adaptive filter network further includes a serial arrangement of an algebraic adder for generating control signals, connected to the controllable filter; a weighting filter for converting the control signal spectrum in response to the load sensitivity variation with frequency; a threshold limiter for setting the noise reduction threshold level of the adaptive filter network; a control signal frequency corrector; and an amplitude detector for shaping control signals applied to the control input of the controllable filter. The network analysis of the input audio signal spectrum and the width of its pass-band is varied depending on the present frequency limit of the input audio signal wanted components.

Variable response notch filter for machine resonance elimination in a servo control system

Abstract: This invention relates to a flexible notch filter for use in a servo system to eliminate natural mechanical resonance. The filter is an improved "twin-T" type where the "in-phase" output of the filter is fed back into the filter. Varying the feedback varies the bandwidth of the filter. The improved filter further provides for attenuation control in addition to control of the center frequency of the filter. The advantage of this filter over prior art designs is that one filter may be manufactured and adapted to be used in many servo systems since the filter can be easily adjusted to effectively eliminate the natural resonating frequency of the machine in addition to reducing phase lag at frequencies below the center frequency of the notch filter.

Bounding filter: A simple solution to lack of exact a priori statistics

Abstract: Weiner and Kalman—Bucy estimation problems assume that models describing the signal and noise stochastic processes are exactly known. When this modeling information, i.e., the signal and noise spectral densities for the Weiner filter and the signal and noise dynamic system and disturbing noise representations for Kalman—Bucy filtering, is inexactly known, then the filter's performance is suboptimal and may even exhibit apparent divergence. In this paper a system is designed whereby the actual estimation error covariance is bounded by the covariance calculated by the estimator. Therefore, the estimator obtains a bound on the actual error covariance which is not available, and also prevents, its apparent divergence. The bounding filter can be of lower order than the original stochastic models; hence, a technique is devised of reducing the order of the filtering system and concurrently obtaining a figure of merit for its performance. For many cases, the design conditions devised for the steady-state Weiner filter apply to transient Kalman—Bucy filter performance.

On using the symmetry of FIR filters for digital interpolation

Abstract: By implementing an interpolating linear phase FIR filter in a modified direct form, it is possible to take advantage of the symmetry conditions and reduce the number of multiplications.

Optimal Receiver Filters for BPSK Transmission over a Bandlimited Nonlinear Channel

Abstract: In this paper we specify an optimal receiver filter for 2phase PSK transmission over a channel consisting of the tandem connection of a linear filter and a bandpass nonlinearity, with thermal noise added at the channel output. This filter minimizes the bit estimation error subject to the constraint that it be a linear filter. Our main aim is to consider satellite communication channels and as such the system nonlinearity is taken to have both AM/AM and AM/PM conversions. In these systems we assume the up-link signal-to-noise ratio is large and thus our work relates to large transmit terminal applications. In an example the probability of error performance of the optimal received filter is found to be 2 dB better in terms of the effective output SNR as compared with that of a standard choice for the receiver filter.

Modulation Considerations for a 91 Mbit/s Digital Radio

Abstract: The DRS-8 is a 91 Mbit/s long haul digital radio system designed for use in the Canadian 8 GHz frequency band. This paper discusses the considerations which lead to the choice of Quadrature Partial Response Signaling (QPRS) for this application. A method of implementing QPRS that circumvents power amplification difficulties and permits the use of simple conventional filtering and equalization is presented. The computer analysis program and the design strategy used in the system filter design are described. Details of the signal shaping filters as well as details of carrier and clock synchronization are given. Finally, measured system performance is presented and compared with computed performance.

Low bit rate cepstral vocoder using the log magnitude approximation filter

Abstract: By using the log magnitude approximation filter as the speech synthesizer, a low bit rate cepstral vocoder was obtained. The synthesis filter is of minimum phase and of pole-zero type, and this vocoder can provide a better spectral fit than that provided by all-pole model. The filter can be easily obtained without transforming the cepstrum to an impulse response and the computation for the filter coefficients is non-iterative. The spectral envelope information is transmitted in a form of cepstral values. Since the coefficient sensitivities of the synthesis filter is sufficiently small, a fairly coarse quantization of the cepstrum is allowed. A reasonable speech quality vocoder was realized at the overall bit rate of 1770 bits/s.

Analysis of electrical equivalent circuit elements of piezo-tuning forks by the finite element method

Abstract: A finite element method (FEM) employing three-dimensional (3D) linear piezoelectric solid elements is used to analyze the vibrational characteristics of piezo-tuning forks. From this information, the equivalent circuit elements such as equivalent inductance, capacitance, mass and capacitance ratio can be calculated. Stable piezo-tuning forks can easily be adapted as mechanical filters by addition of couplers. Besides the aforementioned equivalent elements, it is necessary in filter design to ascertain the ideal transformer ratios which relate to the coupling between the tuning forks forming the filter. A method for estimating these ratios is presented. An example of a particular tuning fork using two candidate materials, quartz and lithium tantalate, is given to illustrate the finite element analysis and the calculations of the equivalent circuit elements.

Connections between classical and statistical methods of FIR digital filter design

Abstract: Consider the weighted squared error between an FIR filter frequency response and a desired frequency response. The FIR filter coefficients that minimize this error are shown to satisfy a linear Toeplitz set of equations. Thus, the MMSE designs of [1] may arise also as solutions to a classical filter minimization problem. The solutions are linear phase, and identical with those of [1] when the desired frequency response and the weighting function have a special form.

The use of filtered Bessel functions in direct interpretation of geoelectrical soundings

Abstract: We start from the Hankel transform of Stefanescu's integral written in the convolutionintegral form suggested by Ghosh (1971). In this way it is possible to obtain the kernel function by the linear electric filter theory. Ghosh worked out the sets of filter coefficients in frequency domain and showed the very low content of high frequencies of apparent resistivity curves. Vertical soundings in the field measure a series of apparent resistivity values at a constant increment Δx of the logarithm of electrode spacing. Without loss of information we obtain the filter coefficient series by digital convolution of the Bessel function of exponential argument with sine function of the appropriate argument. With a series of forty-one values we obtain the kernel functions from the resistivity curves to an accuracy of better than 0.5%. With the digital method it is possible to calculate easily the filter coefficients for any electrode arrangement and any cut-off frequency.

On a generalization of the wave digital filter concept

Abstract: The design of digital filter structures imitating the behaviour of classical analogue networks has received considerable interest in the literature. Of particular interest has been the Wave Digital Filter first considered by Fettweis. We examine here a generalization in which the relationships between the voltages, currents and wave variables are considered as a linear transformation on the ABCD matrix of the analogue two-port network. The linear transformation is examined in some detail and conditions are derived which impose constraints on the elements of the matrices involved in the transformation. Finally a table giving thirteen transformations known to yield realizable digital filter structures is presented.

Method and apparatus for eliminating deadband in digital recursive filters

Abstract: Method and apparatus for eliminating deadband effects in digital recursive filters caused by rounding of the quantization of products within the filter, wherein the product is represented by a digital word, consists of truncating the absolute value of the product-representing word to the next lower digit by dropping a number of least significant digits determined by the value of the multiplier and if any of the dropped digits is a "one", adding a least significant "one" to the truncated number while retaining the sign of the pre-truncated word, and repeating the process at the cycling frequency of the filter, until a steady state is reached at which the difference between the input and output of the filter becomes zero. The concept is described as embodied in a digital system utilizing a recursive filter for reducing noise in a color television signal.

On 2-variable reactance functions for 2-dimensional recursive filter design

Abstract: The use of 2-variable reactance functions for designing stable 2-dimensional recursive filters is critically examined. The investigation shows that although the stability of the resulting filters is ensured, such functions do not preserve the amplitude characteristics of the 1-dimensional filter prototype over the 2-dimensional digital domain. A special choice of reactance functions that yields best design results is discussed.

Multiplexed filtering device

Abstract: In a multiplexed filtering device the first and second input signals are respectively sampled to give a third signal and sampled and delayed to give a fourth signal. An adder whose output is connected to the control electrode of a charge transfer device of a hybrid filter, adds alternately the third signal to a sampled signal corresponding to the third signal and coming from the recursive part of the hybrid filter and the fourth signal to a sampled signal corresponding to the fourth signal and coming from the recursive part of the hybrid filter. The output signals of the non-recursive part of the hybrid filter are summed by a reading amplifier, the output of which constitutes the output of the hybrid filter; after which they are demultiplexed and delayed for the restoration of the first input signal and only demultiplexed for the restoration of the second input signal.

Frequency band dividing filter using delay-line filter

Abstract: A frequency band dividing filter comprises a delay-line filter which is supplied with an input signal and produces a divided frequency band signal as an output, a circuit for deriving a delayed signal in which the input signal has been delayed by a predetermined amount of time, and a circuit for substantially performing subtraction of the delayed signal output signal of the delay-line filter, and producing another divided frequency band output signal. The delay-line filter comprises a plurality of delay circuits cascade connected, coefficient multipliers respectively supplied with the input signal and the output signal of the delay circuits and for multiplying specific coefficients to the signals thus supplied, and an adder for adding output signals of each of the coefficient multipliers.

Design of stable 2-D half-plane recursive filters using spectral factorization

Abstract: In this paper a new design algorithm for two-dimensional (2-D) recursive digital filters is presented, with emphasis on the general class of half-plane filters. A recently developed 2-D spectral factorization procedure and a nonlinear optimization algorithm are incorporated to iteratively converge to a stable, (locally) optimum filter. Details of the computations required in the implementation of the design procedure are presented, in addition to an example of its application.