Ideal Frequency Response Research Articles

Design of circularly symmetric two-dimensional linear-phase low-pass FIR filters using closed-form expressions

A design technique is presented for two-dimensional linear phase low-pass FIR filters based on a constrained minimization formulation. The minimization criterion is a convex combination of two criteria representing measures of the error between the actual and ideal frequency responses in the pass and stop bands. The constraints can for example represent flatness conditions at the origin. The result is applied to the case of a circularly symmetric low-pass filter and closed-form expressions are derived for the elements of the relevant matrices which appear in the minimization criterion so that numerical integration can be avoided.

On the design of linear phase, FIR integrators for midband frequencies

The ideal frequency responses: 1/(j/spl omega/) (an integrator) and 1//spl omega/ (an integrating Hilbert transformer) are usually approximated by IIR structures. This paper suggests their FIR approximations. Maximal flatness at /spl omega/=/spl pi//2 yields exact mathematical formulas for computing the weights. The proposed designs are particularly suitable for the frequency range: 0.1/spl pi//spl les//spl omega//spl les/0.90/spl pi/.

Optimal design of infinite impulse response hilbert transformers

AbstractThis paper proposes a new method for designing the optimal infinite impulse response (IIR) Hilbert transformer. Until now, finite impulse response (FIR) filters have mostly been used in the design of the digital filter for the circuit such as the Hilbert transformer, where the linear‐phase response is required. Several methods have been proposed for designing the IIR filter, which, however, had problems in the complexity of the algorithm or the accuracy of the designed Hilbert transformer.This paper considers first the FIR Hilbert transformer as a model. the design of the tap coefficients for the IIR filter which gives the same output as that of the model, when the same input is given, is reduced to the parameter estimation problem when the Kalman filter is used for control. Then the IIR Hilbert transformer is designed in the time domain.To obtain a better response, an evaluation funclion is defined that represents the error from the ideal frequency response. the tap coefficients are fine‐adjusted by the Fletcher‐Powell method so that the evaluation function is minimized. By this approach, it is possible to design the IIR Hilbert transformer while maintaining the stability and the phase linearity, which are the features of the FIR filter. the 16th‐order IIR Hilbert transformer actually is designed by the proposed method, and it is shown that a performance better than the 30th‐ and the 31st‐order reference FIR Hilbert transformers can be realized.

Frequency response of prospectively gated phase-contrast MR velocity measurements.

The authors developed and experimentally verified expressions that describe the frequency response of prospectively gated phase-contrast magnetic resonance velocity measurements. Both interleaved and noninterleaved phase-contrast techniques were evaluated. The primary determinants of the frequency response were (a) the number of interleaved acquisitions (N), (b) the time between acquisitions (delta T), and (c) the degree of balance between the first moments of the velocity-encoding gradients. To quantify the last factor, an imbalance parameter (U) was defined. Depending on the chosen implementation and U, deviations from the ideal frequency responses were predicted and observed. The expressions also revealed an advantage of interleaved acquisitions that use a one-sided gradient configuration: no changes in the frequency response. The effects of concurrently encoding orthogonal velocity components with a Hadamard four-point scheme were examined.

Least squared error FIR filter design with transition bands

The authors propose the use of transition bands and transition functions in the ideal amplitude frequency response to allow the analytical design of optimal least-squared-error FIR digital filters with an explicit control of the transition band edges. Design formulas are derived for approximations to ideal frequency responses which use pth-order spline transition functions. A mixed analytical and numerical method for zero-error weight in the transition bands and passband and stopband error weighting functions with an integral squared error approximation are derived. A variable-order spline transition function is developed, and a method for choosing the optimal order to minimize the integral squared approximation error is given. >

Improvements in ultra-broadband TEM coupler design

A procedure which extracts the coupling factor profile from S-parameter measurements of a tapered directional coupler is presented. The difference between implemented and theoretical coupling is used together with knowledge of the cross-sectional dimensions of the coupler to produce a refined coupler design with a more ideal frequency response. Results showing the performance improvements using this technique are presented for a 3 dB quadrature coupler covering 750 MHz–26.5 GHz.

Suitability of fetal scalp electrodes for monitoring the fetal electrocardiogram during labour

As the limitations of heart-rate based intrapartum monitoring have become apparent, there is renewed interest in analysis of the fetal electrocardiographic waveform as obtained from a fetal scalp electrode. A high quality ECG signal is necessary for waveform analysis. This study examined the suitability of five commonly available scalp electrodes for collecting this signal by examining their physical and electrical characteristics, together with a randomised clinical trial in which the ECG trace quality was assessed in 50 patients. The frequency response of Copeland electrodes was such that they attenuate the ECG signal more than the baseline noise. Difficulties were experienced in obtaining optimum attachment and the long, semi-rigid design increased movement artefact resulting in significantly poorer quality ECG signals. Whilst the Hewlett-Packard double spiral electrode had a near ideal frequency response, certain design features made it difficult to apply and remain secure so the clinical signals were of intermediate quality. The Corometrics and Cetro single spirals had the most stable attachment to the scalp and a near ideal frequency response, so produced significantly better signal quality in the clinical trial. Currently, single spiral electrodes are the most suitable for electrocardiographic data collection.

Algebraic approach to two-dimensional recursive digital filter synthesis

An effective algorithm is developed for synthesizing two-dimensional recursive digital filters which approximate prescribed ideal frequency response specifications. The algorithm is based on an algebraic approach that uses the eigenvalue-eigenvector decomposition of the ideal filter's excitation-response matrix in conjunction with a recently developed signal-enhancement method. This results in a recursive filter which has a unit impulse that closely approximates the ideal filter's unit-impulse response. Illustrative examples and comparisons to an existing technique are included. >

Design of FIR partial response filters with equiripple stopband attenuation (class II, V)

AbstractThis paper considers the design of transmitter and receiver FIR digital filters with partial response of class II and V for data transmission. the filters are required to band‐limit the transmitting and receiving signal, while maintaining the overall impulse response with zero intersymbol interference (ISI). Two cases are considered: 1) the case where the transmitter itself has the zero ISI impulse response; and 2) the case where the transmitter and receiver filters are matched. In the former, the length of the filter is set to be equal to the number of samples between two zero‐cross points, which are at a certain symmetrical distance from the center of the ideal impulse response. Then a linear‐phase transfer function is derived with an equiripple approximation to the ideal amplitude frequency response. In the approxiamtion, the weight in the stopband is set as less than 1, and ISI of less than 1. percent is obtained. In the design of the matched filter pair, the overall order is set in the same way as in the former. Applying the Herrman‐Schuessler design method for the minimum phase‐shift filter in the frequency domain, the transfer function is derived.To realize ISI of less than 1 percent, it suffices to set the weight in the stopband less than 5 times in the passband. Although an effort was made to decrease ISI by successive approximation with the mirror zeros as the parameters, only a slight improvement was obtained. In either case, class V requires approximately a twice higher order than class II to realize the same attenuation and ISI.

Frequency and time domain analysis of linear systems with frequency dependent parameters

A modal analysis scheme is developed for systems with frequency dependent parameters which are assumed to be well represented by even order polynomials. The systems with frequency dependent parameters are transformed into equivalent systems with real constant parameters which give rise to identical frequency response matrices. Two example problems are considered in order to investigate the dynamic characteristics of the systems with frequency dependent parameters by using the proposed method.

Two-dimensional digital filters for geophysical applications: A simple design method leading to an easy implementation

A simple procedure for the design of two-dimensional digital filters will be presented. Its main interest is in the field of geophysical signal processing, since the design implies in these cases simple structures for the implementation. The 2-D problem is reduced to one, two or complicated cases to several 1-D problems. By 3 examples, relevant in geophysics, the power of this method will be demonstrated. The design is applicable for arbitrary ideal frequency responses, however the simple realization will be lost in general. The result is a suboptimal filter, which can be used, if desired, as an initial solution for an L ∞-approximation. However, the efficiency of the presented method is established by the fact that the design and implementation go hand in hand and are adapted to the special problem under consideration.

A computer analysis of electrochemical impedance data

CIRFIT, a computer analysis of electrochemical impedance data, minimizes the sum of squares of the radial difference between observed and calculated impedance data presented in either the complex impedance or admittance plane. CIRFIT requires no assumptions of ideal capacitive frequency response for the double layer in order to extract the values of solution resistance and polarization resistance that are important to corrosion rate analysis. Examples are presented of the use of CIRFIT for the analysis of corroding iron in tapwater and for model pit electrodes that have two time constants in 0.5 M NaCl.

Temporal and frequency response of avalanche photodiodes from noise measurements

This paper describes a method of obtaining the temporal and frequency response of avalanche photodiodes (APD) by performing simple noise measurements. From the measured noise spectrum and by using the Hilbert transformation technique, the complex transfer function of the detector is determined. response can then easily be calculated by means of fast Fourier transforming. The method has been applied on a high speed APD, with a bandwidth of ~2 GHz, and on a relatively slow APD, with a bandwidth of 0.2 GHz, to calculate the pulse response from a short optical pulse. The calculated pulse width for the fast APD was 215 psec, and the corresponding measured width was 210 psec, while for the slow APD the calculated and the measured widths both were 3.1 nsec. Also the shapes of the pulse responses showed excellent agreement. The method depends on the essentially identical frequency response of an APD and associated circuits for noise due to steady-state illumination and for a signal.

A Laguerre series approximation to the ideal Gaussian filter

It is shown that the ideal Gaussian frequency response can be more accurately approximated by using a Laguerre series approach instead of a Taylor series approach involving the same number of components. The resulting filters are physically realizable and their responses compare favourably with those of the conventional approximations to Gaussian filters.

Development of self-control using Premack's differential rate hypothesis: A case study

Premack in his theory of reinforcement (1959) focuses on the frequency of occurrence of responses rather than upon specific stimulus characteristics. Simply stated, for any pair of responses, the more probable one will reinforce the less probable one. One clinical implication of the Premackian hypothesis is in terms of “self-control” : using one type of behavior to control other types of behavior (Holland and Skinner, 1961). In this conceptualization of “self-control”, if the emission of a high-frequency reinforcing response is made contingent upon the emission of a low-frequency appropriate response, then the latter should increase in its frequency of occurrence; concurrently, the non-reinforced inappropriate response should decrease in its frequency of occurrence. In a clinical situation, developing procedures within this framework could maximize the efficiency of therapist-patient contacts; particularly, when the purpose is one of the patient learning to control and/or eliminate inappropriate behavior (Homme. DeBaca, Devine, Steinhorst, and Ricken. 1963; Goldiamond, 1965; Greenspoon and Brownstein, 1967). The programming of such a technique necessitates two considerations: selection and measurement of the responses involved. In terms of response-selection, an ideal low frequency response would be one incompatible with the inappropriate response to be conttolled. The high frequency, reinforcing response, for purposes of long-term effects and generalization from the specific learning situation, should be one already existing in the individual's behavioral repertoire (Ferster, 1967). Three operations are implied in the measurement process (Premack. 1959; McIntire, 1963): independent measurements of the respective frequencies of the selected responses, programming a situation which would insure the two responses occurring repeatedly in a contingent order, and some measure of the first response which would reflect an increment in frequency as a result of such pairing.

Loudspeaker Compensation Using Integrated Circuits

The principal axis frequency response of a loudspeaker is compensated using standard synthesis techniques and the desired flat response is obtained. The technique is based on a pole-zero cancellation of the loudspeaker response using integrated circuit operational amplifiers and resistance-capacitance components. Subjective tests with both male and female listeners confirm that the response is greatly improved. It is anticipated that in order to approximate an ideal frequency response for good listening, this type of compensator will be incorporated into the preamplifier.