Showing papers on "Butterworth filter published in 1973"

Nth-root Stack Nonlinear Multichannel Filter

Abstract: A nonlinear multichannel filter is developed which appears to be particularly useful for enhancement of seismic refraction and teleseismic array data The basic filter involves the extraction of the Nth root of each element in the matrix forming the data set, where N is any positive integer, and the Nth power of the summation over the channels The filter is effective in reducing random noise, whereas identical signals which are in-phase on all channels are retained at the expense of some distortion The output from this nonlinear filter has far greater resolution in specifying phase velocity than any multichannel linear filter we have employed Examples of theoretical and actual field seismograms are presented after various forms of filtering to illustrate their effectiveness

Noise performance of RC-active quadratic filter sections

Abstract: A method for calculating the noise voltage at the output of quadratic filter sections is developed. Multiple-feedback low-pass, bandpass, and high-pass quadratic filter sections realized using differential-input single-ended output operational amplifiers are analyzed. The amplifiers are assumed to have infinite input impedance, infinite gain, and zero output impedance. The noise sources associated with the amplifiers are assumed to be statistically independent, but can have both white and l/f noise components. A noise analysis of a fourthorder maximally flat low-pass filter realized by cascading two quadratic filter sections is included.

Adjustable electronic tunable filter with simulated inductor

Abstract: A stable tunable Q bandpass filter adapted to have its parameters dynamically varied over a wide range of bandwidths and center frequencies. The filter includes a capacitor and a network coupled in parallel across the capacitor. The network includes a plurality of operational amplifiers coupled to simulate an inductor without utilizing coils. A feature of the filter is that it can be readily made adaptive to track an input signal which may randomly vary in frequency. A further feature of the invention is to have one input of each operational amplifier coupled directly to ground to minimize stray capacitance. The performance characteristics of this filter are in part attained by the method of component layout and shielding techniques used, in addition to the method of circuit excitation.

Filter having frequency-dependent transmission properties for electric analog signals

Abstract: In one illustrative embodiment, a basic filter circuit for discrete signals is provided corresponding in filter function to an analog ladder network containing inductive and capacitive components. The reactive components of the analog filter structure are realized in the basic filter circuit as one-port and two-port elements having time delay, while non-reactive components of the analog filter are realized as time-delay-free one-port and plural-port elements. Interface means connect the port elements together in a configuration corresponding to the configuration of the analog filter, with sets of adder and multiplier means of the interface circuitry which couple successive sets of the port elements to each other being correlated with the connective relationship (whether series, series-parallel or parallel) between the corresponding components or branches of the analog filter and with the parameters of the analog components, so that the basic filter circuit essentially simulates the analog filter structure in its filter characteristics.

On nonlinear filters involving transformation of the time variable

Abstract: A new type of nonlinear filter, called the E -filter, is introduced that involves a transformation of the independent variable of the input function. It is shown how an E -filter can be designed to filter out superimposed "noise" on a signal, leaving the large peaks of the signal unattenuated. Unlike a Iow-pass linear filter, the low-pass E -filter is almost frequency independent and so does not affect the amplitudes of large sharp peaks of the signal. It is shown that the E -filter can be realized in real time and that a wide class of E -filters have a filtering action which is independent of the dc level of the input signal.

Probability of Error in Binary Communication Systems with Causal Band-Limiting Filters--Part I: Nonreturn-to-Zero Signal

Abstract: Upper and lower bounds to probability of error in binary communication systems with intersymbol interference are presented. Closed-form formulas are given for systems with filters having a finite number of lumped elements. Explicit results are given when the filters are Butterworth filters of order N = 1, 2,..., 10 . Four systems are considered: with a sample detector (SD), with an integrate-integrated-and-dump detector (IDD), with a filter in receiver only, and with filters in receiver and transmitter. The transmitted signal is assumed to be of the nonreturn-nonreturn-to-zero (NRZ) form.

Filter network having negative feedback loops

Abstract: A filter network having an input terminal and an output terminal and a plurality of cascaded filter sections, each section having a designated frequency response, the bandpass or lowpass characteristics of each section being calculated by a formula, and including a plurality of negative feedback loops, one for each filter section except the first, each loop being coupled between the output terminal of the respective filter section and the input terminal of the filter network through a summing means, the gain of each feedback loop being calculated by a formula.

Electrical noise in low-pass FDNR filters

Abstract: The electrical noise performance of generalized impedance converter (GIC) low-pass ladder structures is derived. The concept of frequency-dependent negative-resistance (FDNR) elements has allowed low-sensitivity high-order low-pass ladder structures to be realized directly from the corresponding LC prototype. The electrical noise appearing at the output of the low-pass FDNR realization is derived for the equiterminated low-pass Butterworth realization, and it is shown that the output noise power spectral density may be obtained from a suitable noise model of the GIC. Experimental verification of the output noise spectral density is given.

Optimum Signal and Filter Design in Underwater Acoustic Echo Ranging Systems

Abstract: Optimization of the filter, the signal, and the signal and filter jointly are studied in the sonar environment under noise and reverberation limited conditions. The maximization of the receiver output signal-to-interference ratio is used as a performance criterion with unit energy constraint on both signal and filter. In the filter design problem, the optimum filter function is the solution of a linear integral equation. The kernel of the integral equation is a function of the target and medium scattering functions and the reverberation distribution. In the signal design problem, a similar type of integral equation is obtained as in the filter optimization problem. In the joint signal and filter design problem, it is shown that the optimum signal and filter functions are the solutions to a pair of linear integral equations with the largest (SIR)O. Several examples are investigated for different mediums and reverberation distributions with the finite matrix approximation method. An interative technique is used to compute the joint optimization of signal and filter.

Multimode waveguide: a low pass filter.

Abstract: It is shown in this paper that a multimode waveguide-represented by a ray model-acts like a low-pass filter with respect to the modulation. The response function is calculated and discussed in the case of an ideal, straightlined, loss-free system.

Probability of Error in Binary Communication Systems with Causal Band-Limiting Filters--Part II: Split-Phase Signal

Abstract: The probability of error is computed in four binary communication systems with N th order ( N = 1, 2,...,10 ) Butterworth filters and split-phase signals. The systems have either a sampling detector or an integrating-and-dumping detector; the filter is either in the receiver only or both in the receiver and transmitter. A lower bound to the probability of error is also computed for modified binary communication systems in which prior to the decision the contribution of the past transmitted symbols is eliminated. In all systems the sampling time is optimized and the effect of nonoptimal sampling time on probability of error is demonstrated.

Electric resonant transfer filter

Abstract: A resonant transfer filter is disclosed for use in a resonant transfer system having a normally open gate which is closed at a sampling frequency for the transfer of energy. The filter incorporates inductance elements and capacitance elements having values determined directly from the transmission function for filters in the resonant transfer mode developed by Cattermole and having a passband width of less than one-half of the sampling frequency. The filter element values are determined by first choosing a prototype filter configuration which approximates the system attenuation requirements and which is suitable for resonant transfer applications. The prototype element values are used as starting values which are revised or altered to decrease the difference between the Cattermole transmission function when computed using the starting element values, and later the altered values, and the ideal transmission function, equaling unity over the passband and zero in the stopband.

Band pass filter and detection circuit

Abstract: There is herein disclosed a combination involving a limiter, a first active high pass filter, and a level detector in cascade. The first high pass filter is paralleled by an arrangement of second active high pass filter and inhibit circuit in cascade. The first filter accepts frequencies above a first cut-off point and the second filter accepts frequencies above a higher cut-off point and the output of the inhibitor is used to inhibit the output of the first filter. The result is a band pass detector which responds to frequencies within the range defined by the cut-offs.

Electrical filter with a nyquist flank characteristic

Abstract: An electrical filter with a Nyquist flank characteristic is provided for generating a vestigial side-band characterized in that two identical exact separating filters are connected in cascade in such a way that the output of one filter section in the first separating filter is connected to the input of the second separating filter, and in which a signal injected at the input passes through two filter sections having the same attenuation characteristics, and in that two of the filter sections of the separating filters are terminated in identical ohmic resistances, and in that the characteristic functions assigned to the filter sections are self-reciprocal functions.

Pole frequency stabilized active rc filter

Abstract: In an active RC filter exhibiting a predetermined signal transfer characteristic, a reference signal is applied to the input of the filter and examined for phase shift at the low-pass signal output of the filter. A signal proportional to the variation in phase of the reference signal is used to alter a voltage controlled resistor, which in turn varies the pole frequency of the filter. The reference signal is cancelled from the signal appearing at the bandpass output of the filter to remove it from the final desired output of the filter.

Noise margins of bandpass filters

Abstract: It is shown that if a bandpass filter is obtained from a prototype low-pass filter by the usual low-pass to bandpass transformation, the white-noise margin and the (1/f)^2 noise margin of the resulting filter will be identical to the white-noise margin of the prototype low-pass filter. A method for using this general result for evaluating some types of integrals that arise in noise calculations is indicated.

A frequency-locked adaptive filter

Abstract: A frequency-locked RC active ladder filter is described, which is frequency-locked to a sinusoidal control tone. The tunable ladder filter is used as a frequency discriminator by using two of the filter branch voltages to generate a control voltage. The control voltage is then used to tune or frequency-scale the ladder filter transfer function to lock the filter to the frequency of the control tone. A simple linear frequency-signal control system is developed to describe the frequency-locked performance of the adaptive filter. The frequency-locked filter can be designed so that the sinusoidal control tone is rejected at the filter output, making it possible to adapt the filter transfer function during transmission of a message. A practical frequency-locked filter is given in which a frequency-locked third order elliptic lowpass filter is designed. The performance of the practical filter is analysed using a simple linear control system model.

Experimental Investigation into a Commutative Filter

Abstract: : A commutative filter is a bandpass filter capable of very high Q's, large range of resonant frequency (0 to 2 megahertz that can be electronically tuned), comb-filter frequency response, small bandwidth (independent of resonant frequency), and extremely small size (can be constructed of integrated circuits since no inductors are required). The purpose is to present the general theory and evaluation of a commutative filter, in which presentation the effects of 'leaky' capacitors and load resistance are considered. An eight-channel filter is built, and laboratory and theoretical results are compared for the transfer function, bandwidth, quality factor, and sensitivity of the commutative filter. The commutative filter is also investigated from the viewpoint of enhancement of signal-to-noise ratio.

Sampling interval drift in digital filters

Abstract: The effect of sampling interval drift on the digital filter magnitude function is considered for impulse invariant and bilinear transform design methods. For both types of filter designs a change in the sampling interval will cause critical filter frequencies to shift. The expression for this shift is shown to be the same for the two design methods. Finally, a time-domain analysis shows that the problem can be considered in terms of a perturbed input signal and an unperturbed filter