Showing papers on "Filter design published in 1969"

A simple adaptive algorithm for real-time processing in antenna arrays

Abstract: A new adaptation algorithm designed for real-time data processing in large antenna arrays is presented. The algorithm is used to determine the set of filter coefficients (weights) which minimizes the mean-square error in a multidimensional linear filter. The algorithm forms an estimate of the target signal, which is assumed to be of interest, in the presence of interfering noises. It is assumed that the direction of arrival and spectral density of the target signal are known a priori. No such information is assumed to be available regarding the structure of the interfering noise field. The a priori target information is incorporated directly into the adaptation procedure using a modified gradient descent technique. The mathematical convergence properties of the algorithm are presented and a computer simulation experiment is used as an illustration. It is shown that as the number of iterations becomes large, the expected value of the adaptive solution converges to the minimum mean-square-error solution. It is further shown that the variance of the adapted filter about the optimum solution can be made arbitrarily small by appropriate choice of a scalar constant in the algorithm. These results are based on the assumption that the array signals are Gaussian and that successive time samples are statistically uncorrelated. Thus, the new algorithm is shown to converge to the optimum processor in the limit as the number of adaptations becomes large. Any disadvantage which may arise in the use of such an asymptotically optimum system is offset by the extreme simplicity of the adaptive procedure. This simplicity should prove to be particularly useful in many of the practical array processing problems recently encountered in seismic and sonar data processing.

A step-by-step active-filter design

Abstract: This article presents, in a simplified manner, a design method for active filters intended for those who are not filter specialists. By following the described five-step approach, a circuit designer who has some knowledge of passive filters will (without having to learn a whole new technology) be able to design active filters just as easily as he now handles conventional passive filters. Starting with the filter specification, it is shown sequentially how to realize a network that meets the prescribed requirements. Configurations and element values are given for the low-pass (LP), bandpass (BP), high-pass (HP), all-pass (AP), and band-elimination (BE), second-order active filter building blocks.

Linear Signal Processing and Ultrasonic Transversal Filters

Abstract: The role of linear transversal filters in signal processing is discussed in Section I. Linear filters for signal processing must often have complicated impulse responses, with large bandwidth and large time bandwidth product. The linear transversal falter, a delay line with weighted and summed taps, is ideally suited for the implementation of such filters because of its simplicity of synthesis. The filter's impulse response is derived by the application of some concepts from the theories of vector spaces and sampling, and is shown to be equal to the tap weighting function. Thus, the synthesis procedure consists merely of sampling the specified impulse response at appropriate intervals and using the sample values as the tap weights. The utility of the transversal filter in signal processing is illustrated by an example from scatterer distribution mapping. The illustration is applied to two hypothetical systems--a SONAR and an astronomical RADAR. In both these cases, it is not possible for a single filter to process the signal in real time. Signal processing in compressed time is discussed as an alternative to the use of a large number of filters in parallel. If the processing filter has a bandwidth capability in excess of the signal's bandwidth, the signal can be time compressed and processed serially in time. A generalized receiver, employing time compression, frequency translation, and multiple-output-port transversal filtering, is developed from these ideas. In Section II, a generalized transversal filter is described and analyzed. A delay line with multiple arrays of taps, each array with a multiplicity of weighting functions, has as the impulse response between any pair of ports the cross-correlation function of the weighting functions for the two ports. A number of implementations of transversal filters employing a variety of delay line types are described and some aspects of transduction and wave propagation in bounded media are presented in relation to these implementations.

Optimal linear filtering for linear systems with state-dependent noise

Abstract: The purpose of this paper is to determine the linear optimal filtering algorithm for a message generated by noisy observations of a linear dynamic system with state-dependent, stochastic disturbances. These disturbances can be considered as stochastic parameter variations. As a consequence of the state-dependent noiso the message process is non-Gaussian. Hence the filter obtained by solving the Wiener-Hopf equation is only the optimal linear operation on the data. The optimal filter is non-linear. Unfortunately the dynamical equations for optimal nonlinear filtering can only be solved approximately. We show that one approximation reduces to the linear optimal filter. As an application we determine the linear optimal filter for a second-order system. This example provides us with a comparison of the performance of the linear optimal filter with a filter designed neglecting the presence of the state-dependent disturbances.

The Stepped Digital Elliptic Filter

Abstract: The design and synthesis of various types of microwave elliptic function filters has been accomplished by a number of authors. However, one problem in this field which remains is the realization of compact narrow-band bandpass elliptic function filters. In this paper, a procedure is presented which enables this class of filters to be constricted in a compact digital form. Since the physical realization is in the form of an n-wire line, one-quarter of a wavelength Iong at the center frequency of the passband, where the impedance levels are stepped along the center of the coupled lines, the filter has been termed the stepped digital elliptic filter. The absence of awkward interconnections in the filter due to the stepped digital structure inherently implies that reasonable insertion loss characteristics may be achieved in the X-band region and above, and also simplifies the mechanical construction. It is shown that the resonant elements in the filter, due to the design procedure adopted, are relatively insensitive to the absolute bandwidth of the filter, and consequently fractional bandwidths of approximately 30 percent and below may be readily achieved while the normalized impedance values of the elements in the network remain of the order of unity. This latter result is similar to that obtainable from conventional interdigital filters but in the case of narrow bandwidths the stepped digital filter is considerably smaller in physical size. A systematic procedure is also formulated for the inclusion of the parasitic lumped end effect capacitances into the overall design procedure in order to maintain the equiripple passband and stopband responses. Experimental results are presented for a five-element, 11 percent bandwidth filter and are shown to be in good agreement with theoretical predictions.

Digital modified discrete fourier transform doppler radar processor

Abstract: A system for processing data from Doppler radar returns including a sample and hold circuit, an A/D converter and scratchpad memory which holds the binary data for insertion, on a return-by-return basis, into a main MOS memory. The data is orthogonally extracted from the main memory on a range-by-range basis, each range group or cell being delivered to a digital filter. The binary data is converted to binary logarithm form for addition to a log coefficient weighting function to perform a multiplication in the filter. The filter is a modified discrete Fourier transform filter which acts as a bandpass and eliminates images and clutter. The filtered data is again stored and then converted to analog form for video displays.

Quantization effects in digital filters

Abstract: : Quantization effects in digital filters can be divided into four main categories: quantization of system coefficients, errors due to A-D conversion, errors due to roundoffs in the arithmetic, and a constraint on signal level due to the requirement that overflow must be prevented in the comparison. The effects of quantization on implementations of two basic algorithms of digital filtering-the first-or second-order linear recursive difference equation, and the fast Fourier transform (FFT) - are studied in some detail. For these algorithms, the differing quantization effects of fixed point, floating point, and block floating point arithmetic are examined and compared. The ideas developed in the study of simple recursive filters and the FFT are applied to analyze the effects of coefficient quantization, roundoff noise, and the overflow constraint in two more complicated types of digital filters - frequency sampling and FFT filters. Realizations of the same filter design, by means of the frequency sampling and FFT methods, are compared on the basis of differing quantization effects. All the noise analyses in the report are based on simple statistical models for roundoff and A-D conversion errors. Experimental noise measurements testing the predictions of these models are reported, and the empirical results are generally in good agreement with the statistical predictions.

N-path filter using digital filter as time invariant part

Abstract: A time division multiplexed digital filter is used as the timeinvariant part of an N-path filter. The use of a multiplexed digital filter alleviates the problem of closely matching the transmission characteristics of each of the N-paths.

Optimum digital filters for signal to noise ratio enhancement

Abstract: Summary One of the main objectives of seismic digital processing is the improvement of the signal-to-noise ratio in the recorded data. Wiener filters have been successfully applied in this capacity, but alternate filtering devices also merit our attention. Two such systems are the matched filter and the output energy filter. The former is better known to geophysicists as the crosscorrelation filter, and has seen widespread use for the processing of vibratory source data, while the latter is. much less familiar in seismic work. The matched filter is designed such that ideally the presence of a given signal is indicated by a single large deflection in the output. The output energy filter ideally reveals the presence of such a signal by producing a longer burst of energy in the time interval where the signal occurs. The received seismic trace is assumed to be an additive mixture of signal and noise. The shape of the signal must be known in order to design the matched filter, but only the autocorrelation function of this signal need be known to obtain the output energy filter. The derivation of these filters differs according to whether the noise is white or colored. In the former case the noise autocorrelation function consists of only a single spike at lag zero, while in the latter the shape of this noise autocorrelation function is arbitrary. We propose a novel version of the matched filter. Its memory function is given by the minimum-delay wavelet whose autocorrelation function is computed from selected gates of an actual seismic trace. For this reason explicit knowledge of the signal shape is not required for its design; nevertheless, its performance level is not much below that achievable with ordinary matched filters. We call this new filter the “mini-matched” filter. With digital computation in mind, the design criteria are formulated and optimized with time as a discrete variable. We illustrate the techniques with simple numerical examples, and discuss many of the interesting properties that these filters exhibit.

A digital filter for biological data.

Abstract: Low pass digital filters are very suitable for use on stored biological data. This paper discusses the characteristics of the ideal data filter and the digital approximation to such a filter. The use of this filter with biological data is shown.

Filter design and evaluation

Abstract: Filter design and evaluation , Filter design and evaluation , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Coefficient Accuracy and Digital Filter Response

Abstract: The frequency response of a digital filter realized by a finite word-length machine deviates from that which would have been obtained with an infinite word-length machine. An “ideal” or “errorless” filter is defined as a realization of the required pulse transfer function by an infinite word-length machine. This paper shows that quantization of a digital filter's coefficients in an actual realization can be represented by a “stray” transfer function in parallel with the corresponding ideal filter. Also, by making certain statistical assumptions, the statistically expected mean-square difference between the real frequency responses of the actual and ideal filters can be readily evaluated by one short computer program for all widths of quantization. Furthermore, the same computations may be used to evaluate the rms value of output noise due to data quantization and multiplicative rounding errors. Experimental measurements verify the analysis in a practical case. The application of the results to the design of the digital filters is also considered.

Simultaneous Approximations in Filter Design

Abstract: An iterative approximation procedure, used to yield equiripple delay and attenuation characteristics for a resistanceterminated passive, lossless two-port, is described.

The Half-Wave Stepped Digital Elliptic Filter

Abstract: A design procedure for narrow-band bandpass TEM-line elliptic-function filters is presented. The proposed realization is in the form of a stepped-impedance digital n-wire line which is one-half of a wavelength long at midband and short circuited to ground at both ends, where the digital line is stepped in impedance along any arbitrary prescribed plane in the filter. Due to its physical form and mode of electrical operation, the filter has been termed the half-wave stepped digital elliptic filter. A detailed design procedure for the construction of the two characteristic admittance matrices which describe the digital n-wire line from the low-pass prototype element values is presented. It is also shown that the normalized impedance values of the elements in the filter are all of the order of unity and independent of the actual bandwidth of the falter except for the input and output transformer elements. A numerical example and experimental results on a seventh-degree 1-percent bandwidth filter with a center frequency at 3.7 GHz are given, demonstrating the significant improvements which may be obtained from the half-wave stepped digital elliptic filter over most other known form of microwave TEM-line narrow-band bandpass filter.

Reduced order Kalman filter

Abstract: The order of the Kalman filter equations for a wide class of aerospace navigation problems is reduced, yielding an optimal sequential linear filter with a substantial decrease in computer requirements. A theorem is proved generalizing the Kalman filter to handle step-wise correlated noise. An illustrative example is then presented in which computer computation time and storage requirements are reduced by more than half with negligible increase in programming complexity.

Variable-bandwidth filters using switching

Abstract: It is shown that, if a switching technique is used to scale the bandwidth of a lowpass filter, the resultant circuit has some of the characteristics of an N-path filter. The consequence of this is that the signal frequency must be bandlimited to avoid spurious responses at the switching frequency and its harmonics.

Discrete-time filtering apparatus

Abstract: In a discrete-time filter, sensitivity to coefficient variation is substantially reduced by using a unit delay interval, for the delay networks of the filter, which is not equal to the sampling interval. Furthermore, in realizing higher order filter systems, a plurality of such filters may be cascaded, each having a delay interval different from that of the other filters. The periods of repetition of the poles of the overall filter function are therefore different, resulting in improved filter performance.

A tuneable, Bandwidth-adjustable solid-state filter☆

Abstract: Tuneable adjustable solid state bandwidth filter using N path system for low pass to bandpass filter transformation

A Timed-Shared Digital Filter Realization

Abstract: A special-purpose computer organization of a time-shared digital filter suitable for real-time applications is described. The computer is organized in functional modules so that the order of the filter, the coefficients of the filter, the programming form of the filter, and the multiplexing scheme for the filter are readily adaptable to system needs.

Narrow Bandwidth Elliptic-Function Filters

Abstract: Although wide bandwidth microwave elliptic-function filters have previously been reported, this paper describes a circuit which provides, for the first time, a narrow bandwidth elliptic-function response at microwave frequencies. It is for narrow bandwidth applications (from 5 percent to a fraction of a percent) that the elliptic-function filter offers its most important advantages over other filter types--lower loss and greater selectivity. These features are verified by theoretical analysis and experimental data on a 1-percent bandwidth S-band stripline filter. The design of the filter, which is based upon the low-pass prototype, is simple to obtain with the relationships presented in this paper, and the elliptic-function response is readily realizable in printed or other TEM transmission lines. A waveguide elliptic-function filter is also discussed, but experimental verification of this has not yet been attempted.

Musical tone-forming circuitry including filter and random noise modulation

Abstract: A whistle or grass reed sound is simulated by an electronic musical circuitry comprising a portamento-type oscillator, a tone coloring filter for providing a tone signal having predetermined harmonics as well as a fundamental, a noise generator, a low-pass filter for deriving frequency components below 30 Hz from a noise signal output of the noise generator, and a modulator for amplitude modulating the tone signal from the tone coloring filter with the noise signal components of less than 30 Hz from the low-pass filter.

Maximization of Signal-to-Noise Ratio in an Optical Filter

Abstract: where xeE , S = {xeE :0 0, (ii) B is symmetric and positive definite, (iii) # > 0. This problem arises in the maximization of the signal-to-noise ratio in a spectral filter for infrared detectors (see [7]). The term 2 represents the incoming signal and + ,B is the variance of the background signal. The constraint S reflects the fact that the filter can transmit no more than 100 % and not less than 0 % of the total energy. A paper detailing the physics of the problem is in preparation. Although various general-purpose algorithms have been developed which may be applied to obtain solutions to this problem, the special nature of the objective function and the constraints can be exploited to obtain more efficient solution techniques. Two related algorithms are presented here and are both based on a parametric analysis of the problem. The second method is based on the first and offers some computational advantages that the first does not possess. The derivation of the second method involves the notion of the "conjugate function" [6] in a unique manner and should be of interest in itself since the practical applications of this notion have heretofore been extremely limited.

Tailored response microwave filter

Abstract: A multiple section microwave filter capable of being accurately tailored to special frequency response requirements over wide bandwidths in disclosed. The tailored response filter consists of an array of cascaded traveling-wave directional filters. Each filter section couples power out of a through transmission line into suitable microwave terminations. Due to the directional characteristics of traveling-wave directional filters, there is no interaction between sections. Thus the frequency response of the array is the product of the transfer functions of the individual sections. The coupling constants and the center frequencies of individual filter sections are tailored, i.e., synthesized, to result in a set of individual transfer functions which will produce the desired overall response. The tailored response filter can be used in wide bandwidth microwave systems for phase and amplitude weighting and for equalization functions.

Synthesis of Equally Terminated Low-Pass Lumped and Distributed Filters of Even Order (Correspondence)

Abstract: A Chebyshev-like polynomial of even order is described which, when used in low-pass filter design of even order, allows for the output to input resistance ratio of the filters to be specified independently of the passband ripple level. This is an improvement on the conventional theory, which requires that the resistance ratio be a junction of the passband ripple level. In particular, the important case of equally terminated lumped and distributed lowpass filters is considered in detail, and tables of element values are given for a large number of practical design specifications.

A nonlinear digital filter for industrial measurements

Abstract: A simple algorithm is presented for nonlinear filtering of a time series composed of a gaussian component, pulses and steps. The method used is a combination of simple statistical techniques. The main advantage is claimed to be a scheme for adaptation of the filter parameters.

Digital filter frequency shift modulator

Abstract: Unity gain feedback places a second-order digital filter on the borderline of stability. The filter therefore oscillates in a numerical sense. Two feedback multipliers, each capable of determining a different central coefficient (and thus different oscillation frequencies) are alternatively inserted into an independent feedback path under control of an input baseband data signal whereby the output frequency is shifted in accordance with the input data. Phase discontinuities and amplitude variations due to the frequency shift are eliminated by extracting the numbers stored in the filter when a data transition occurs and reinserting new numbers representing samples of the new frequency wave, the new numbers further defining points on the new wave having the same instantaneous amplitude and phase as the wave samples defined by the extracted numbers.

Digital filter receiver for frequency-shift data signals

Abstract: Sampled FSK data signals are converted to multibit numbers and processed by a digital filter receiver which includes a band-pass filter, a dual-resonator discriminator and a low-pass filter. The dc baseband data signal is reconstructed from the receiver output number by a ''''slicer'''' which detects the sign of the output numbers. The analog-to-number conversion is simplified by limiting the multibit numbers to be processed to two values, simulating the hard limiting of analog signals. Signal harmonics introduced by the nonlinearities of the analog-to-digital converter are substantially eliminated by fixing the sampling rate to a rate which interleaves, in the frequency spectrum, the filter aliases with the harmonies. The receiver is advantageously arranged to be time-shared by a plurality of channels.

Tone channels for multifrequency receivers

Abstract: A tone channel of the type used in multifrequency receivers has in cascade an input band-pass filter that has a frequency curve similar to that of overcoupled filters, a limiter-amplifier, and an output band-pass filter that has narrow band-pass characteristics. The center frequency of both filters is the frequency of a desired incoming tone. After a signal ceases, ringing of the input filter caused by signal is at the peak response points of the input filter at either side of the center frequency, and it is therefore not effective to prolong ringing in the output filter.

Physically Realizable Filtering for Data Transmission Systems

Abstract: In this paper, the design of physically realizable rational fuction transmitting or receiving filters for use in pulse transmission systems operating in the presence of Gaussian noise and intersymbol interference is explored. For the design, the three iteria considered are 1) mean-square error (MSE), 2) error probability, and 3) a weighted sum of the squares of the signal-to-noise ratios corresponding to all possible received signal patterns (MSSN). Expressions are obtained for the various error criteria in terms of the transnmission system poles and residues (coefficients of a partial fraction expansion), assuming that the transmitting and receiving filters and the transmission medium are given by physically realizable rational function forms. It is shown that optimization of the MSE criterion under a received signal amplitude constraint with respect to the receiving filter residues, for a fixed set of poles, leads to a set of linear equations readily solvable for the optimal residues. A suboptimal technique is used to specify "reasonable" pole values, thereby the poles are constrained to belong to some "standard" set of all-pole transmission functions, as for example, maximally flat delay or maximally flat magnitude. The bandwidth of the given pole configuration is determined to optimize the given error criterion. Numemical examples are presented to illustrate the filter design techniques developed. The results indicate that, in many cases, filter design under the MSE or MSSN error criteria leads to optimal or near optimal design under an error-probability criterion. A brief discussion is also given of the filter sensitivity to parameter variations.