Equiripple Passband Research Articles

Design of stable IIR digital filters with equiripple passbands and peak-constrained least-squares stopbands

This paper describes an algorithmic development for the design of stable infinite impulse response (IIR) digital filters with equiripple passbands and peak-constrained least-squares stopbands. Central to the development is a re-formulation of the design problem as an iterative quadratic programming problem where the stability and equiripple passbands and peak-constrained requirements are met by imposing a system of linear inequality constraints while the LSS property is satisfied by minimizing a weighted least-squares type objective function.

An original approach to the design of bandpass cavity filters with multiple couplings

A novel approach to the design of general cavity filters with each cavity coupled to an arbitrary number of other cavities is presented. This approach is based on a suitable characterization of the filter structure which does not require one to model separately the cavities (resonators) and the coupling elements. Suitably defined equivalent admittances are associated with each cavity allowing one to design the filter structure once the parameters of a suitable low-pass prototype are given; an efficient procedure for the synthesis of such a prototype with equiripple passband response is also presented which allows one to arbitrarily prescribe transmission zeros placed in the complex plane (even asymmetrically). The described design approach is particularly convenient when the filter structure does not allow a simple modeling of the resonators and coupling elements separately. This is the case of slot-coupled cavity filters and of filter structures based on arrays of coupled transmission lines. It is also shown that the simplified design approach often adopted in the past, where only two coupled cavities at a time are considered, can produce large errors even in the case of filters with all attenuation poles at infinity (i.e., two couplings per cavity).

Design of selective lowpass sampled‐data and digital filters exhibiting equiripple amplitude and phase error characteristics

AbstractA method is presented for the design of reciprocal reactant sampled‐data and digital filters exhibiting equiripple passband and stopband amplitude characteristics and approximating a linear phase characteristic such that the phase error response is equiripple too. the passband amplitude characteristic approximates unity transmission and the stopband amplitude characteristic approximates zero. Odd‐ and even‐degree cases are considered separately. the stopband amplitude response is controlled by an arbitrary number of finite transmission zeros together with two (one) zeros at infinity for even (odd) transfer functions. All the available degrees of freedom are used for controlling the filter performances. Thus the resulting solutions are selective and have good amplitude and phase characteristics. A comparison between our method and a recently published method shows that this approach has higher stopband loss and smaller phase error ripple with wider bandwidth.

通過域等リップルハーフバンドＦＩＲフィルタの一設計法

A new algorithm for designing half-band FIR (Finite Impulse Response) filters with equi-ripple passband amplitude is developed. This algorithm is an analytical design method with which tap-gain coefficients of FIR filters are obtained by non-iterative calculation. The minimum stopband attenuation can be reduced within the limits of appropriate quantity by permitting equi-ripples in the passband without extending the transition width of FIR filters. A method to reduce the level of equi-ripples is also mentioned.

Automatic generation of CMOS continuous-time elliptic filters

A procedure for the generation of CMOS, continuous-time, high-frequency g m -C filters with finite tranmission zeros is presented. A third-order elliptic filter with 0.5 dB equiripple passband, 15 MHz cutoff frequency and -23 dB attenuation in the stopband is given as an example. The automatic generation method can be generalised to arbitrary high-order prototypes and higher-frequency filters derived from LC ladders

Practical Realization of a Selective MIC Low Pass Filter

A design method is presented for the practical realization of low pass filters having an equiripple passband response with three transmission zeros at infinity and the remainder at a finite real frequency. The filters are constructed in MIC configuration using both metalized alumina and teflon substrates. The experimental results are presented.

FIR digital filters with least-squares stopbands subject to peak-gain constraints

The use of digital filters with peak-constrained least weighted-squared errors (PCLWSE) is proposed. The emphasis is on PCLWSE filters with equiripple passbands and peak-constrained least-squares (PCLS) stopbands. The stopband energy is minimized subject to a constraint on the maximum stopband gain. A design algorithm is presented, and examples are discussed. Each example provides the unique optimal solution to the corresponding design problem. The tradeoff between the peak stopband gain and the total stopband energy is examined. It is shown that the most inefficient filters have minimax or least-squares stopbands. In particular, the stopband energy for minimax filters can be significantly reduced with almost no change in the peak stopband gain. Also, the peak stopband gain for filters with least-squares stopbands can be significantly reduced with almost no change in the total stopband energy. These results are supported by mathematical analysis, and examples are provided.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Narrow bandstop filters

The synthesis of narrow bandstop filters with arbitrary stopband and equiripple passband responses is demonstrated. A transformed frequency variable is used for iterative approximation with automatic bandwidth adjustment and prototype circuit realization.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Design of odd‐degree linear‐phase sampled‐data bandpass filters with equiripple amplitude response

AbstractThis paper presents a novel approach for the design and synthesis of odd‐degree sampled‐data filters. Initially, an efficient iterative scheme is described for the construction of a class of selective linear‐phase distributed bandpass filters with equiripple passband loss response. Then, the filter's transfer function is synthesized using classical distributed circuit networks. Finally, the equivalent switched‐capacitor filter could be constructed. the resulting switched‐capacitor networks are completely insensitive w.r.t. parasitic capacitances, as well as having low Cmax/Cmin Design tables and an illustrative example are also given.

Design of selective linear phase bandpass switched-capacitor filters with equiripple passband amplitude response

A novel approach is presented to the design and synthesis of switched-capacitor (SC) filters. An efficient iterative algorithm is described for the construction of a class of selective linear-phase bandpass filter with equiripple passband amplitude response. The solution is obtained in terms of digital linear phase bandpass polynomials. A novel SC implementation is performed using an approach based on the reflection filter concept. The synthesis of the SC filter follows the steps used in microwave filter synthesis. The resulting SC circuits are completely insensitive to parasitic capacitances. Design tables and an illustrative example are also given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Generalized equiripple all-pole lowpass filters

New families of equiripple all-pole lowpass filters are presented which have equiripple passbands and monotonic stopbands. The number of maxima in the pass-band is controlled so that both reduced critical Q and flatter group delay are realized in comparison with Chebyshev filters. Tables of parameters are provided for selected cases of these new filters.

Generalized Chebyshev band-pass prototype filters

Band-pass prototype filters are presented having an equiripple passband with single transmission zero at the origin, an odd number of transmission zeros at infinity and a multiple even number at a finite real frequency in one of the stopbands near the corresponding band edge. These prototypes can be easily and accurately synthesized using the alternating pole technique. The application of the alternating pole technique leads to the construction of a reactance (admittance) function. Thus the synthesis of a doubly terminated prototype network is reduced to the synthesis of a lossless one-port network of much lower degree with very little loss of accuracy.

Switched-capacitor LDI lowpass filters with improved selectivity

Generalised expressions are given for transfer functions of an extensive family of lowpass switched-capacitor LDI ladder filters with optimum equiripple (or maximally flat) passbands and an arbitrary number of transmission zeros at half the sampling frequency. These allow greater flexibility in the design and permit tradeoffs to be made among factors such as sampling frequency, element value spread and dynamic range. The previously studied LDI filters with monotonic stopbands can be recovered as degenerate special cases of the generalised ones presented here.

Predistortion techniques for increasing the element tolerances in equiripple passband niters revisited

A well established technique to increase the element tolerances in the design of selective passive filters, or to decrease the adverse effect of limited gain-bandwidth product of operational amplifiers is to use transfer function with a special type of magnitude response for which the passband ripple amplitude decreases with increasing frequency. Recently various techniques have been reported to construct this type of filtering functions but they are either entirely numerical or, at least, require numerical optimization of some relevant parameters. In this paper, an exact method is proposed to find the explicit expression for the predistorted characteristic function of these filters applicable to both polynomial filters and filters with finite attenuation poles of any degree. The ratio of the magnitudes of the first passband ripple to the last passband ripple can be prescribed in advance, according to the required specifications.

A Low-Pass Prototype Network Allowing the Placing of Integrated Poles at Real Frequencies

This paper details a procedure by which a number of attenuation poles can be placed at differing frequencies, giving an asymmetric or symmetrical response, the only restriction being that the network must be physically symmetrical. If a number of poles are placed on one side of the passband, this technique can be used to greatly increase the selectivity of a filter on this side, while maintaining an equiripple passband response. There are four possible arrangements for these filters. They can have even or odd degree with an even or odd number of integrated poles. Only three of these are realizable in a symmetrical network and these possibilities are dealt with individually. An example is given in the case of an odd-degree filter with an odd number of integrated poles placed at two frequencies on opposite sides of the passband.

A Novel Class of Generalized Chebyshev Low-Pass Prototype for Suspended Substrate Stripline Filters

A novel class of low-pass prototype filters having an equiripple passband response with three transmission zeros at infinity and the remainder at a finite real frequency is presented. The prototypes are synthesized using the alternating pole technique to obtain directly the even-mode or the odd-mode admittance and little accuracy is lost for prototypes up to degree 15. Tables of element values for commonly used specifications are included. The tables are useful for the design of TEM-mode microwave broad-band filters, diplexers, and multiplexers, particularly for a printed circuit form a realization. A design example of a low-pass microwave broad-band filter designed and constructed in suspended substrate stripline (SSS) configuration is given and experimental results are also presented.

Selective linear phase filters possessing a pair of J‐axis transmission zeros

AbstractA design technique is developed for prototype selective linear phase filters which have an equiripple passband amplitude response and a pair of j‐axis transmission zeros in the stopband while maintaining a linear phase characteristic in the passband. Since the basic technique requires numerical optimization techniques, the element values for several cases have been tabulated together with detailed response characteristics.One important result is that for certain characteristics, one internal cross‐coupling element may be designed to be zero. As a result, in the sixth degree case with only one extra cross‐coupling element between elements 1 and 6 a significant improvement in both the amplitude and group delay performance can be achieved as compared to the Chebyshev case. Owing to its importance, this case is investigated in detail and a 2.6 GHz post decoupled combline filter has been constructed based upon this prototype.

Optimum lowpass and bandpass filter approximation

AbstractThe attenuation characteristics of lowpass and bandpass rational filters are approximated by optimizing a weighted error criterion. The analytical approach yields the solution in terms of kernel polynomials, and if the weight function has a particular form, the solution may be given explicitly in terms of the Szegö–Bernstein polynomials; with other weight functions it is necessary to resort to numerical procedures. The solution exhibits a passband behaviour that depends on the chosen weight function; when the Szegö–Bernstein polynomials are used both lowpass and bandpass filters may exhibit equiripple passband attenuation.

Linear phase analog active filters with equiripple passband responses

The theory and design of analog active filters with an approximately linear phase characteristic and equiripple passband response is presented. The filters are similar to conventional linear phase transversal filters but do not have a periodic passband response. Hence prefiltering is not required.

Sharp-Cutoff Low-Pass Filters with Equiripple Pass-Band

The cutoff-slope and stop-band attenuation of low-pass filters with equiripple pass-band behaviour and with multiple pairs of coincident zeros at a suitable frequency in the stop-band have been investigated. Such a filter is shown to have better magnitude characteristic than that of other similar filters (with multiple pair of coincident zeros in the stop-band) reported recently in the literature.