Showing papers on "Butterworth filter published in 1972"

The prolate filter: An ideal lowpass filter with optimum step-response

Abstract: An ideal lowpass filter permits no signal transmission outside of a prescribed frequency band centered around the origin. In this paper, it is shown that the ideal lowpass filter which provides the fastest monotonic step-response for a prescribed bandwidth is the prolate filter. The system-function of this circuit is obtained from the autocorrelation of the zero-order, zero degree angular prolate spheroidal wave function. The bandwidth and risetimes of the filter are related through the largest eigenvalue of the same wave function. The computation and realization of the optimum frequency- and time-responses is discussed in detail and is illustrated by a numerical example. It is also shown how the asymptotic forms of the optimum system function degenerate, for very small or very large risetimes, into the well-known Hadamard and Gaussian filter functions, respectively.

On designing sharp cutoff low-pass filters

Abstract: Effects of introducing single or multiple pairs of coincident j\omega axis zeros in all-pole Chebyshev filter transfer functions are investigated. It is shown that for the same order n , Chebyshev filters with finite j\omega axis zeros provide much sharper cutoff than all-pole Chebyshev filters. It is also shown that for the same n , the same number of pairs of zeros m , and the same locations of zeros, the cutoff slope and stopband characteristic of the finite zero Chebyshev filters are much better than those of the finite zero Butterworth filters. Graphs helpful in the design of such filters have been plotted and their use is illustrated by an example.

On maximally flat low-pass filters with ripple in the stopband

Abstract: Maximally flat (MF) low-pass filters of order n with exactly n , or n - 1 finite zeros are investigated and are compared with the same order Butterworth filter, i.e., the MF filter with no finite zeros. It is seen that the MF filter with finite imaginary zeros exhibits sharper cutoff at the edge of the passband and ripple in the stopband. It is shown that the MF filter that maximizes the magnitude of the slope at cutoff is characterized by equal ripple in the stopband. This filter is shown to be the Inverse Chebyshev. Expressions for cutoff slope and for transition bandwidth are derived and are compared with those of the Butterworth filter. The step responses of the Inverse Chebyshev and of the Butterworth are also compared.

Bucket-brigade tuned sampled data filter

Abstract: A tuned filter circuit having response characteristics of a tuned LC circuit includes bucket-brigade delay lines and gain factor components connected in feedback circuit relationship around a summing amplifier, and in forward circuit relationship. The resonant frequency of the filter is primarily controlled by the frequency of a digital clock input to the bucket-brigade delay lines. The filter Q and the filter transient response are controlled by the gains established by the gain factor components.

Active RC filter circuit

Abstract: A filter circuit is disclosed which uses an operational amplifier and a plurality of resistors and capacitors to obtain a variety of filter transfer functions. By modification of a basic circuit structure, bandpass, high-pass, low-pass notch, high-pass notch, and all-pass filter transfer functions are obtained.

1000 bit surface-wave matched filter

Abstract: A 1010 bit, biphase-coded, surface-wave matched filter on s.t.-cut quartz is described, and waveforms are shown. The matched filter was designed to operate with a 60 MHz carrier and 10 Mbit/s code rate (0.1 ?s tap spacing). Measurements indicate that the predicted performance is achievable by application of straightforward design procedures and fabrication techniques.

Easily integrable very-low-sensitivity active RC filter

Abstract: A new easily integrable active RC biquadratic filter, with all the capacitors earthed, is described. The biquads can be directly cascaded without buffer stages. The sensitivities of the Q factor and ω0 to the various passive and active components are very low. Further, the sensitivity of the Q factor with respect to the passive elements can be made zero, making the filter easy to tune. Experimental results which agree with the theory are given for a lowpass Butterworth filter.

Filter with periodic phase delay and insertion-loss ripple

Abstract: An analytical design procedure is presented for the lowpass prototype selective linear phase filter, from which bandpass-channel filters may be deduced, whose insertion-loss and phase-delay-error functions vanish at an optimum number of equidistant points in the passband. Synthesis is performed using an even-and-odd-mode decomposition for a symmetrical filter comprising capacitors and impedance invertors. Finally, explicit formulas are given for element values in the 2nd-, 4th- and 6th-degree networks from which a simple realisability condition is deduced for all positive coupling elements, and numerical results on a 12th-degree filter are presented to illustrate the typical response characteristics. The main application of the design technique is in the construction of channel filters in high-capacity communication systems which use frequency modulation, particularly at microwave frequencies where the compact physical devices are readily constructed

Design of digital filters using state-space realization†

Abstract: A procedure for the design of a digital filter, based on state-space.realization, is presented. The digital filter obtained has low sensitivity to eigenvalue variations. Also particularly attractive features are stability and low coefficient spread. The design technique is well suited for computer-aided design, starting from a prototype analogue filter function and the desired critical frequencies. Simulation results for different computer word-length are presented, and comparison is made with an analogue filter for both frequency and transient response.

Least-squares passband filters

Abstract: The mathematical properties and design techniques of a novel low-pass filter type are described. A fifth-degree filter is designed, analyzed, and compared with its elliptic counterpart. This evaluation shows that the discrimination, phase, and delay properties of the two circuits are comparable; also, the time response of the proposed filter is substantially similar to that of an elliptic function filter. However, the loss responses are quite different: the loss of the least-squares filter is much less over the lower 90 percent of the passband. As a consequence, it is anticipated that the new circuit is best suited for the filtering of signals having most of their energies at lower frequencies.

The design of an audio-frequency active RC band-pass filter for a specific engineering requirement

Abstract: An engineering requirement for an audio-frequency band-pass filter can be met with an active RC filter which uses positive impedance convertors to simulate the inductors of an LC filter. Because of the low sensitivity of this type of realization, the component tolerances required are compatible with thick film technology.

Energy transfer characteristics of Butterworth resonant circuits under pulsed-carrier operation

Abstract: This investigation considers the problem of pulsed-carrier energy transmission through ideal two-port m th-order Butterworth resonant networks of the low-pass, high-pass, bandpass, and band-reject class.