Showing papers on "Adaptive filter published in 1968"

Filter Design Using Transformed Variables

Abstract: A concise description is given of some recently developed filter design techniques. The discussion includes equal-ripple and maximally flat passband filters with general stopbands, as well as equal-ripple stopband filters with general passbands. To solve the approximation problem and to improve numerical conditioning, the design is carried out exclusively in terms of one or two transformed frequency variables. A step-by-step description is given for the design of each filter type; the steps are so formulated that the erosion of significant digits is minimized. The design processes given are unique and are directly suitable for automatic computer programs. Experience with such programs, using the algorithms described in the paper, indicates that filters up to about degree 30 may be designed using only single precision in the calculations. A discussion of some practical predistortion techniques, as well as a listing of available tabulated filter design information, is also included.

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.

Optimum radar signal processing in clutter

Abstract: This paper considers the joint optimization of a class of radar signals and filters in a number of clutter-pins-noise environments. The radar signal processor in this case will be optimum in the sense that its output at the time of target detection yields the maximum ratio of peak signal power to total interference power. If the interference at the input to this signal processor is a Gaussian random process, this processor also yields the maximum probability of detection for a given value of false-alarm probability. The signals used are pulse trains and the filters are tapped delay lines. The purpose of signal design is to determine the optimum complex weighting for each pulse of the pulse train. Filter design yields the optimum complex weighting for the output taps of the delay line. Filter design for a specified signal is considered first. This is followed by combined signal and filter design and matched filter design. Constrained signal and filter design is investigated last. It should be emphasized that the optimizations require a knowledge of the clutter time-frequency distribution. For practical situations, when the clutter distribution is unknown, an adaptive filter is proposed that automatically provides the optimum filter weights for a given transmitted signal. When the clutter has a range-time extent less than the equivalent range-time extent of the signal, filter design alone yields nearly optimum performance. As the clutter becomes extended in range-time, it is necessary to consider jointly the design of signal and filter to obtain an optimum radar signal processor. In this report it is suggested that the signal be designed under the assumption of the clutter being extended over a broad range of Dopplers and that the signal processor consist of a bank of adaptive filters. Then each filter output yields the maximum ratio of peak signal to total interference power for this signal design.

Nonrecursive digital filters: Design methods for achieving specifications on frequency response

Abstract: A simple and effective method for designing a nonrecursive digital filter is described. This method is constructed so that it is convenient to implement the resulting filter by using the fast convolution application of the fast Fourier transform. For one representative example of a fast convolution implementation of a nonrecursive digital filter designed by the method in this paper, only as many multiplications (per output sample) were required by this implementation as were required by an implementation of a well-designed recursive digital filter achieving an equally effective frequency response. This method for designing nonrecursive digital filters permits the desired frequency response to be specified either numerically (at equally spaced frequencies), graphically, or analytically. Specifications are to be provided also for the permissible 1) resolution and 2) ripple. The ease with which this design method can achieve a specification on frequency response suggests the use of this method whenever the resulting nonrecursive filter can be conveniently implemented on a general-purpose digital computer. Adaptation of these methods to computing power spectra is described.

The design and applications of digital filters with complex coefficients

Abstract: The digital filter with complex coefficients finds applications in the digital processing of analytic signals and complex envelopes. A theory is developed for designing such filters based on low-pass analog prototypes and digital design techniques for real filters. An example of a filter designed according to this theory is presented. The relative advantages of real and analytic signal processing are discussed. It is shown that the filtering required by either processing technique requires essentially the same amount of signal operations, which is reasonable in view of the fact that the same amount of information is processed in both classes of filter.

Digital filtering with applications to electrocardiogram processing

Abstract: The first part of this paper is a description of the design of low-pass, bandpass, high-pass, and notched filter difference equations using Z-transform techniques. The difference equation coefficient word lengths are significantly reduced by using a set of second-order difference equations. These equations have a form that minimizes computation. The second part of the paper contains applications of these filters to the processing of electrocardiograms (ECG). The filters are included as subroutines in a program that also includes an adaptive muscle-tremor filter, an "optimum" ECG estimator, and optimum estimators for the arrival time of various parts of the ECG waveform. Clinical results are presented.

Digital filter synthesis by sampled-data transformation

Abstract: The design of digital filter transfer functions is facilitated by taking advantage of well-established design techniques developed for continuous (analog) filters. Digital approximations to continuous filter functions may be found by applying an appropriate sampled-data (z) transformation to the continuous filter transfer function. Three mathematical transformations are described that find the most application: 1) the standard z-transform, 2) the bilinear z-transform, and 3) the matched z-transform. The applicability of the three transformations is discussed and examples are presented of digital filters designed using these transformations.

Adaptive redundancy removal in data transmission

Abstract: This paper suggests an adaptive filter, similar to that used in automatic equalization, for use as a predictor in data compression systems. It discusses some of the applications of this adaptive predictor in digital data transmission. In the event of redundant data input to the system the predictor could be used to lower the transmitted power output required for a given error rate or to decrease the error rate while maintaining constant transmitted power. The action of these redundancy-removal and restoration systems is analyzed in simple cases involving Markov inputs.

A summary, by illustrations, of least-squares filters with constraints

Abstract: Several methods of combining a number of time series into a single series are discussed. They are all individual filtering followed by summation and are somewhat like Wiener filtering in that a least-squares criterion is used to design the filter coefficients. They differ from Wiener filtering in that signal information is given in the form of various constraints on the filter coefficients rather than being given as a signal correlation function. The equations are worked out explicitly for the case of two time series and three filter points and presented in such a way as to make generalization clear.

Adaptive radar clutter rejection

Abstract: A control loop in a radar receiver is jointly responsive to range gated video and a reference potential to establish a filter control signal. A plurality of range gated filters are responsive to the filter control signal to adjust the frequency response in a manner such that clutter is rejected yet the maximum frequency bandwidth is dynamically provided for moving target detection for varying clutter conditions. Each range gated filter has a filter element which is switchable such that the effective electrical properties of the element vary in accordance with the switching to thereby effect a change in the frequency characteristics of the filter. The switching rate is much higher than the pulse repetitive frequency of the radar such that the switching rate does not interfere with signals being processed through the filter. In one embodiment, a variable duty cycle pulse generator having a fixed frequency is utilized to effect control over the frequency characteristics of a filter.

Organizing a special-purpose computer to realize digital filters for sampled-data systems

Abstract: A special-purpose computer is organized to implement a programmable digital filter intended for use in sampled-data control systems. A canonical representation for the digital filter is selected and this form is implemented in functional blocks that are suitable for circuit integration. An analytical technique is discussed that helps determine acceptable quantization resolutions and round-off errors in the digital filter. Experimentation with the digital filter is performed in the pendulous integrating gyroscopic accelerometer control loop and in an analog computer simulation of the Saturn V thrust vector control system; the filter used as a digital compensator successfully stabilizes both sampled-data control systems. The performance of the digital filter is examined and organizational techniques to improve its characteristics are proposed.

Introduction to Digital Filters

Abstract: The purpose of this paper is to provide an introduction to the use of digital filters. Their capabilities and limitations are discussed, as well as application requirements as direct replacements for conventional active or passive filters in real-time situations. Basic operating principles are described, and amplitude and phase characteristics are illustrated. The technique offers many advantages among which are very accurate drift-free operation, ease in changing filter characteristics, and small physical size. In addition, a linear phase characteristic can readily be obtained with some types of digital filters. A design example of a linear phase low-pass filter is included.

Recursive bandpass digital filter

Abstract: A bandpass digital filter is described along with detailed formulas for implementing it. The method uses basic complex variable theory.

Digital Filter Design Techniques in the Frequency Domain

Abstract: In digital filtering, the spectrum is shaped using digital components as the basic elements. Although the physical realization is different, the aims of digital filtering are, thus, the same as those for continuous filtering. It is likely that digital filtering, already in extensive use for computer simulation of analog filters, will find increasing real-time application. Real-time digital filters have several advantages over their analog counterparts: a greater degree of accuracy can be attained in their realization; a larger variety can be built since certain realization problems (akin to negative elements) do not arise; no special components are needed to realize filters with time-varying coefficients; and they are of particular utility at very low frequencies where analog components become large and unwieldy. In contrast to the linear differential equations of continuous filter theory, linear digital filter theory is based on the mathematics of linear difference equations. Using the z-transform calculus, a number of digital filter design techniques are discussed. One technique is useful in designing a digital filter whose impulse response is like that of a given analog filter, whie other techniques are suitable for designing digital filters meeting specified frequency response criteria. Another yields filters with linear phase, specified frequency response, and controlled impulse response duration. The effect of digital arithmetic on digital filter behavior is considered.

A nonrecursive digital filter for data transmission

Abstract: High-speed digital data transmission systems often require special filter functions for spectral shaping with prescribed phase characteristics. One such filter is the cosine roll-off filter, which has applications in both serial and parallel data transmission systems. This filter is of special interest, because in such applications it is common to utilize two identical cosine roll-off filters in a cascade connection, i.e., one in the transmitter and one in the receiver. The composite response of the cascade connection has the raised-cosine roll-off characteristic, which yields low intersymbol interference. Because a linear phase characteristic is further required, the digital filter type chosen for this application is nonrecursive. The difference equation coefficients are determined from the coefficients of a Fourier series expansion of the magnitude-frequency characteristic in the form of a cosine series. The linear phase characteristic is the direct result of setting the sine terms of the Fourier series to zero. Two criteria have been selected as a measure of the digital filter performance: minimum stop-band attenuation and an RMS measure of intersymbol interference. Performance was calculated as a function of the number of terms in the cosine series used to approximate the desired function. Performance graphs, which summarize the results of this investigation, are included. The application of digital filtering techniques in the field of data transmission systems is shown to have practical value.

A Class of Finite Memory Interpolation Filters

Abstract: Sufficient conditions are given for an interpolation filter to have an impulse response that vanishes outside a finite interval of the time axis, that is to have a finite memory. These conditions are that the transfer function be of the form G(s)/G(z) , where G(s) is proper, rational, and has poles limited to the strip |Im s| ; and where 1/G(z) is a polynomial. The filters R_{mp} are included in this class, and these are characterized by the fact that their effect is to interpolate an (m + p - 1) -order polynomial in each interval through p past and m future points. The interpolation filters described can be used to derive digital filters that approximate an arbitrary linear timeinvariant continuous-time operator. It is shown that in the case of integration, the R_{mp} filters lead to well-known Lagrangian integration formulas.

Selective properties of digital filters obtained by convolution approximation

Abstract: The construction of a sequence of transfer functions of digital filters by means of various approximations in the time domain is shown. By means of an example, the frequency properties of attenuation and phase are discussed for four terms of this sequence.

Design and Application of an Adaptive Tracking Filter Control System

Abstract: The design of an adaptive tracking filter control system and its application to large flexible booster vehicles is described. The problem of elastic vehicle stability is considered along with its solution by conventional and adaptive techniques. The improvement in vehicle stability, which may be achieved with the adaptive tracking filter technique as compared to conventional techniques, is shown. The control system evolved uses two adaptive tracking filters to phase stabilize the first and second bending modes, in addition to conventional compensation techniques. The application of this adaptive technique to a vehicle in which the modal frequencies are in close proximity (<2.5 percent separation) is discussed. The mechanization of the adaptive control system involves the selection of design techniques and components that are electrically and physically compatible with the intended airborne application. The development of a suitable frequency tracking technique and tracking filter is described, in addition to the electronic and mechanical design of the adaptive control system prototype.

A Theoretical Discussion of Optimum Multichannel Filter Design

Abstract: : The design equations for both single-channel and multi-channel optimum least-squares ('Wiener') filters are derived and discussed. Specific examples of such filters are presented; for example, inverse filters, signal/ noise ratio enhancement filters, prediction filters, and maximum-likelihood filters. The single-channel and multichannel Levinson recursion algorithms for solving the design equations are discussed.

Derivation of a suboptimal linear filter

Abstract: A linear filter using sample extrapolation and averaging is derived and tested. Extensions to include correlated observation noise and incomplete measurement are discussed. The filter is easily implemented for low-order linear plants but is inferior to the Kalman filter for all but the simplest cases.

Online digital filtering

Abstract: The advantages of the recursive digital filter as a real-time signal processor are stated, and, as an example, a fourth-order Cheby?shev lowpass filter has been synthetised and programmed into an online computer. Typical responses are shown for pulse, step and low-frequency mixed sinusoidal signals.

Sensitivity of the Kalman Filter with Respect to Parameter Variations

Abstract: : Techniques are given for sensitivity analysis of the Kalman filter with respect to simultaneous variations in measurement noise, plant noise, dynamic model, sampling period, and filter gain These analytical techniques will greatly aid the design and evaluation of Kalman filters and other types of filters Two basic assumptions were used: There are nominal quantities about which variations may be taken, and The estimation-error covariances are the filter performance measures

The Design and Ap- plications of Digital Filters with Complex

Abstract: The digital filter with complex coefficients finds applications in the digital processing of analytic signals and complex envelopes. A theory is developed for designing such filters based on low-pass analog prototypes and digital design techniques for real filters. An example of a filter designed according to this theory is presented. The relative advantages of real and analytic signal processing are discussed. It is shown that the filtering required by either processing technique requires essentially the same amount of signal operations, which is reasonable in view of the fact that the same amount of information is processed in both classes of filter.

A Nonrecursive Digital Filter for Data

Abstract: High-speed digital data transmission systems often require special filter functions for spectral shaping with prescribed phase characteristics. One such filter is the cosine roll-off filter, which has applications in both serial and parallel data transmission systems. This filter is of special interest, because in such applications it is common to utilize two identical cosine roll-off filters in a cascade connection, i.e., one in the transmitter and one in the receiver. The composite response of the cascade connection has the raised-cosine roll-off characteristic, which yields low intersymbol interference. Because a linear phase characteristic is further required, the digital filter type chosen for this application is nonrecursive. The difference equation coefficients are determined from the coefficients of a Fourier series expansion of the magnitude-frequency characteristic in the form of a cosine series. The linear phase characteristic is the direct result of setting the sine terms of the Fourier series to zero. Two criteria have been selected as a measure of the digital filter performance: minimum stop-band attenuation and an RMS measure of intersymbol interference. Performance was calculated as a function of the number of terms in the cosine series used to approximate the desired function. Performance graphs, which summarize the results of this investigation, are included. The application of digital filtering techniques in the field of data transmission systems is shown to have practical value.