Low-pass Case Research Articles

A theoretical and experimental investigation on a volume coil with slotted end-rings for rat MRI at 7 T

ObjectiveA volume coil with squared slots-end ring was developed to attain improved sensitivity for imaging of rat’s brain at 7 T.Material and MethodsThe principles of the high cavity resonator for the low-pass case and the law of Biot-Savart were used to derive a theoretical expression of B_1/i. The slotted-end ring resonator showed a theoretical 2.22-fold sensitivity improvement over the standard birdcage coil with similar dimensions. Numerical studies were carried out for the electromagnetic fields and specific absorption rates for our coil and a birdcage coil loaded with a saline-filled spherical phantom and a digital brain of a rat.ResultsAn improvement of the signal-to-noise ratio (SNR) can be observed for the slotted volume coil over the birdcage regardless of the load used in the electromagnetic simulations. The specific absorption rate simulations show a decrement for the digital brain and quite similar values with the saline solution phantom. Phantom and rat’s brain images were acquired at 7 T to prove the viability of the coil design. The experimental noise figure of our coil design was four times less than the standard birdcage with similar dimensions, which showed a 44.5% increase in experimental SNR.DiscussionThere is remarkable agreement among the theoretical, numerical and experimental sensitivity values, which all demonstrate that the coil performance for MR imaging of small rodents can be improved using slotted end-rings.

Low-frequency scattering by passive periodic structures for oblique incidence: low-pass case

We derive the low-frequency behavior of the scattering coefficients from a low-pass structure which is periodic in a plane, and finite in the normal direction. The analysis is for oblique incidence of arbitrary polarization on a structure which can be anisotropic in both electric and magnetic material properties, and may contain metal inclusions. The metal inclusions can be modeled both as perfect electric conductors (PEC) and with a finite conductivity. It is found that the low-frequency reflection and transmission coefficients are proportional to the sum and difference of the electric and magnetic polarizabilities per unit area of the periodic structure. If the metal inclusions are modeled as PEC instead of as a finite conductivity, the first-order low-frequency reflection is larger, whereas the first-order transmission is smaller.

Optimum masking levels and coefficient sparseness for Hilbert transformers and half-band filters designed using the frequency-response masking technique

Hilbert transformers and half-band filters are two very important special classes of finite-impulse response filters often used in signal processing applications. Furthermore, there exists a very close relationship between these two special classes of filters in such a way that a half-band filter can be derived from a Hilbert transformer in a straightforward manner and vice versa. It has been shown that these two classes of filters may be synthesized using the frequency-response masking (FRM) technique resulting in very efficient implementation when the filters are very sharp. While filters synthesized using the FRM technique has been characterized for the general low-pass case, Hilbert transformers and half-band filters synthesized using the FRM technique have not been characterized. The characterization of the two classes of filter is a focus of this paper. In this paper, we re-develop the FRM structure for the synthesis of Hilbert transformer from a new perspective. This new approach uses a frequency response correction term produced by masking the frequency response of a sparse coefficient filter, whose frequency response is periodic, to sharpen the bandedge of a low-order Hilbert transformer. Optimum masking levels and coefficient sparseness for the Hilbert transformers are derived; corresponding quantities for the half-band filters are obtained via the close relationship between these two classes of filters.

Limit cycle behavior in the double-loop bandpass Σ-Δ A/D converter

Hein and Zakhor analyzed the limit-cycle behavior of the low-pass double-loop converter. This brief demonstrates that the limit cycles in a bandpass /spl Sigma/-/spl Delta/ double-loop converter are identical to the low-pass case. It is shown that the double-loop converter can have two independent limit cycles occurring simultaneously. Simulations confirm that the bandpass converter state variables can be designed to stay within designed bounds, as in the low-pass (baseband) case, Hence, stability is improved as the likelihood of stages saturating and clipping is significantly reduced.

A novel DCT-based prefilter structure for efficient digital filter design

In this paper, we present a novel prefilter structure for FIR digital filter design based on the recursive discrete cosine transform (RDCT) filter bank. The proposed prefilter structure is suitable for designing the lowpass, bandpass and highpass digital filters simultaneously. In the lowpass case, the proposed prefilter structure can be simplified to the recursive running sum (RRS) section. In the bandpass and highpass cases, implementing the new prefilter only needs two multipliers and five adders regardless of the filter length and center frequency. Compared with the conventional equiripple design approach, the proposed prefilter-equalizer cascade exhibits approximately the same sensitivity to coefficient quantization. In addition, the new structure can reduce the roundoff noise and provide significant savings in the number of multipliers and adders at the expense of slightly larger filter length.

Maximizing the output energy of a linear channel with a time- and amplitude-limited input

The problem of maximizing the output energy of a linear time-invariant channel, given that the input signal is time and amplitude limited, is considered. It is shown that a necessary condition for an input mu to be optimal, assuming a unity amplitude constraint is that it satisfy the fixed-point equation=sgn (F( mu )), where the functional F is the convolution of mu with the autocorrelation function of the channel impulse response. It is also shown that all solutions to this equation for which mod mu mod =1 almost everywhere correspond to local maxima of the output energy. Iteratively recomputing mu from the fixed-point equation leads to an algorithm for finding local optima. Numerical results are given for the cases where the transfer function is ideal low-pass and has two poles. These results support the conjecture that in the ideal low-pass case the optimal input signal is a single square pulse. A generalization of the preceding fixed-point condition is also derived for the problem of maximally separating N outputs of a discrete-time, linear, time-invariant channel. >

Phase (delay) equalization of recursive digital filters

The purpose of this paper is to present a quasi-analytical procedure for designing equalized recursive digital filters satisfying prescribed amplitude specifications. The design procedure is based on the generation of a class of sampled-data polynomials designed as the arbitrary phase polynomials. The generation has been carried out by using Lagrange interpolation. The proposed procedure is applied to the design of low-pass and high-pass elliptic recursive digital niters. The procedure is simple and can be implemented by using a desk-top microcomputer. A BASIC program for the low-pass case was developed.

Selective linear phase switched-capacitor filters modelled on classical structures

Exact analytic techniques are given for the design of strays-insensitive lossless discrete integrator (LDI) switched-capacitor low-pass and high-pass filters, with phase linearity taken into consideration. An improved synthesis algorithm is also presented for the low-pass case. The given solutions appear for the first time in relation to switched-capacitor filters, but they rely on classical techniques in the area of passive (distributed) networks and cannot be obtained from lumped-element filters. Due to the paucity of useful results, a semi tutorial style is adopted in order to make the design techniques accessible to as wide a readership as possible.

Selective linear phase switched-capacitor filters modelled on classical structures

Exact analytic techniques are given for the design of straysinsensitive lossless discrete integrator (LDI) switched-capacitor low-pass and high-pass filters, with phase linearity taken into consideration. An improved synthesis algorithm is also presented for the low-pass case. The given solutions appear for the first time in relation to switched-capacitor filters, but they rely on classical techniques in the area of passive (distributed) networks and cannot be obtained from lumped-element filters. Due to the importance of the topic and the paucity of useful results, parts of the paper are written in a review-like semi-tutorial style, in order to make the design techniques accessible to as wide a readership as possible. This paper, together with [2] and [4], constitute a comprehensive procedure for the exact design of LDI low-pass and high-pass filters with or without phase linearity; thus completing the picture for these important classes of switched-capacitor filters.

Bessel filtering of brain stem auditory evoked potentials

It has been shown previously that conventional high-pass filtering of the brain stem auditory evoked potential (BAEP) results in significant wave form distortion. This distortion can be drastically reduced by using digital filters with zero-phase properties, but this approach requires the use of a digital computer. The Bessel filter is an approximation to a linear phase characteristic, and has the advantage that it may be implemented using analog circuitry. We have considered its use as an alternative-to-digital zero-phase filtering. For the low-pass case, the Bessel phase characteristic is approximately linear throughout the pass band. However, for the high-pass case there is significant phase non-linearity extending well into the pass band. Typical Bessel high-pass filters seriously distort the BAEP wave form; thus, these filters are not an acceptable alternative to the zero-phase digital approach.

Optimal low-sensitivity anti-aliasing and conversion filters

The problem of analyzing and synthesizing switched analog circuits for anti-aliasing purposes is investigated not only for the more common PCM/audio conversion (low-pass case) but also for PCM/FDM conversion (bandpass case), while possible other applications are pointed out. It is shown that by proper design the well-known low-sensitivity argument known from conventional doubly terminated reactance filters is again valid. Necessary and sufficient reaiizability conditions are given in quite simple form, thus facilitating the optimization even of higher order filters. Numerical and experimental results are presented.

Recurrent Continuant Synthesis of Maximally Flat Time Delay Filters

A new synthesis technique is applied to the synthesis of maximally flat time delay filters. Only the low pass case is considered as the other types may be derived from this by simple frequency transformations. It is shown that the recurrent determinant of a polynomial transfer function with a constant term other than unity can only be obtained in a modified form, being multiplied by the constant term.

Transition ratio of lowpass digital filters

The application of spectral transformations to digital filters has the effect of changing the transition ratio of the original filter. This phenomenon is examined in the letter and closed-form formulas are derived for the lowpass case.