Transition Bandwidth Research Articles

STUDY OF INTERSUBBAND OPTICAL TRANSITIONS IN GaAs/AlxGa1-xAs SUPERLATTICES

In this article, we investigate the properties (transition frequency, bandwidth, and dipole transition moment) of intersubband optical transitions by using the new general form of the Kronig-Penney model developed recently. The theoretical results are in good agreement with our experimental measurements of infrared absorption in a GaAs/AlxGa1-xAs superlattice.

FIR digital filter design with variable parameter window families

It is well known that the design of nonrecursive digital filters of the lowpass, symmetric bandpass and highpass types using the window function approach is simple and quite easy to implement. It has already been shown that the I0-sinh family of window functions gives designers flexibility because of its adjustable parameter. In this paper, two other well-known window function families, namely the I1-cosh and raised-cosine types, which have variable parameters to control the ripple, are considered. Expressions are derived for filter order in terms of ripple magnitude and transition band-width. The performance of these two families are compared with the modified zeroth-order Bessel (I0-sinh.) family and the results in the time and frequency domains are presented.

Design of narrow-band FIR bandpass digital filters with reduced arithmetic complexity

A computationally efficient realization of a symmetrical bandpass FIR filter is derived. The realization is composed of two branches, each consisting of a cascade of two FIR sections. In each branch, the first FIR section has a sparse impulse response with only every L th sample being nonzero. The second section generates the remaining samples via interpolation. The method is applicable to both linear and nonlinear phase cases. Approximate expressions for the optimal value of L and the corresponding number of multipliers and adders required in the overall realization are derived. In narrow-band implementations, the number of multipliers and adders is approximately proportional to 1/\sqrt{{\Delta}F} , where {\Delta}F is the desired relative transition bandwidth. Typically, the required number of multipliers and adders is 1/2 to 1/4 th of those in the conventional linear or nonlinear phase direct-form implementations. The total number of delays is only slightly larger than that required in the conventional implementations. The structure allows simple tuning of the center frequency of the bandpass filter and has good finite wordlength properties.

Estimates for the stability of low-pass filters

A measure of stability is defined for digital filters. It is shown that the stability of low-pass filters goes to zero as the filter characteristics approach that of an ideal low-pass filter. More precisely, estimates for the rate of convergence are given. It is shown that, except for constants, the stability of a low-pass filter is no greater than the square root of the reciprocal of the logarithm of the transition bandwidth. For linear phase filters the square root may be removed. These estimates are shown to be optimal for the case of linear phase filters.

Time domain and realization of a class of digital hybrid filter

AbstractThis paper describes a time‐domain design and realization of a digital hybrid filter with a specific cutoff frequency. The proposed realization is obtained by adding a single multiplier in a feedback loop to the low‐pass or high‐pass FIR filters with linear phase. The resulting hybrid filters can have the following improved frequency response: (1) Increased attenuation in the stop‐band (compared to that obtainable with a Kaiser windowed FIR filter of the same order) for the same transition bandwidth; (2) almost constant amplitude response in the stopband and no zero‐cross ripple; (3) no degradation of phase linearity in the pass‐band; and (4) almost constant phase response in the stopband. Also the hybrid filter designed and realized in this way is always stable and does not generate limit cycles. The time‐domain design and realization of digital hybrid filters of this class are introduced and a design example of a low‐pass hybrid filter is given.

Equiripple stopband characteristic for circularly symmetric 2-D recursive filters

A circularly symmetric 2-D recursive digital filter whose magnitude-squared response approximates a Gaussian function in the two frequency variables has a separable transfer function. Such a circularly symmetric filter has a monotonic frequency response. One may, therefore, want to sharpen the response in the transition band. Due to the separability feature, it is shown how to obtain an equiripple characteristic in the stopband without affecting the circular symmetry in the passband. This reduces the transition bandwidth.

Characteristic function for quasielliptic filters

The characteristic function of a new class of sharp-cutoff filters is derived in closed form. The magnitude response of these filters has the same transition bandwidth as the elliptic filters, and its attenuation poles can easily be adjusted to produce either equal-ripple or general stopband attenuation.

Resonance CARS line shapes: Excited state parameters for flavin adenine dinucleotide

CARS line shapes have been measured as a function of excitation frequency for two vibrational modes, 1635 and 601 cm−1 of FAD. They are satisfactorily reproduced, over the visible absorption band, using reasonable parameters in a simple scattering model. Line shape variations from positive Lorentzian through dispersive to negative Lorentzian reflect the frequency dependence of the real and imaginary part of the Raman susceptibility when the background contribution is relatively large. The frequencies at which these features are found depend on the electronic transition frequency and bandwidth, as well as on the vibrational frequency. A method is given for determining the vibrational frequency from CARS bands with non-Lorentzian lines shapes.

Performance comparisons for nonrecursive digital filters with nonlinear phase characteristics

This letter presents a comparison between the performance, in terms of ripple and transition bandwidth, of nonrecursive digital filters with arbitrary phase characteristics and those with a linear phase response. Results are given which show that filters can be designed to have an arbitrary phase response, yet give as good a gain response as filters with linear phase.

Nonrecursive digital filters with crescent ripple

The letter describes the results obtained on designing nonrecursive digital filters having crescent ripple. It is shown that the geometric mean of the maximum passband ripple and the maximum stopband ripple, when plotted against the normalized transition bandwidth, give a similar curve to that obtained for equiripple designs.

On the transition width of finite impulse-response digital filters

Several properties of finite-duration impulse-response (FIR) digital filters designed to have the maximum possible number of ripples are discussed and illustrated with examples. Such filters have been called extraripple filters. Among the properties of such filters are as follows. 1) Extraripple low-pass filters with fixed passband ripple δ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> and stopband ripple δ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> achieve the local minimum of transition width in the class of linear phase filters with fixed impulse-response duration of N samples. 2) For the case δ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> = δ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> the minimum transition width is roughly independent of F <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> , the passband cutoff frequency. 3) For the case δ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> < δ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> , the minimum transition width decreases with increasing bandwidth. Several figures are included to show the relation between the transition width and bandwidth for low-pass filters.

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

Maximally flat (MF) low-pass filters of order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> with exactly <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> , or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n - 1</tex> 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.

Attenuation Characteristics and Realization of Odd-Order Generalized Inverse Chebyshev Filters

Tables of transition bandwidth ratio, zero transmission and minimum attenuation frequencies in the stopband, and element values for two kinds of realizations of odd-order generalized inverse Chebyshev filters with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> up to 11 and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> up to 3, all using minimum stopband loss as a parameter, are given.

Nomographs for Designing Elliptic-Function Filters

The elliptic-function filter is of considerable importance because of its ability to provide simultaneously small pass band ripple, large stop band attenuation, and very sharp cutoff, with equal-ripple behavior in both the pass band and the stop band. The fundamental design parameters are the pass band ripple, the stop band attenuation, the transition bandwidth, and the number of poles required. They are interrelated in a rather complicated way involving certain elliptic functions, so that determination of a compatible set of parameters is both tedious and difficult. Two nomographs relating these parameters have been devised, by means of which suitable values can be determined easily and quickly. The ranges covered are: pass band ripple, from less than 0.05 up to 3 db; stop band attenuation, from 3 to 40 db (extendable to any value above 40 db simply by renumbering certain scales); transition bandwidth, 0.001 to 1 times the cutoff frequency, and number of poles, 1 to 20. Once a compatible set of parameters has been determined, the approximation function can be obtained in a straightforward manner. The necessary formulas are given, and the procedure for evaluating them is described briefly.