Search

This paper first presents six (6) types of benchmark amplitude design specifications, including variable low-pass specification, variable high-pass specification, variable bandpass specification, variable bandstop specification, variable notch-frequency specification, and variable notch-width specification. The design specifications can be taken as typical benchmark specifications targeted at testing as well as validating the effectiveness of various newly developed algorithms for designing various typical variable filters (VFs). Then, the paper provides a novel unity-bounded (UB) function developed for ensuring the stability of those VFs with recursive structures. Finally, a wide variety of simulation results are included for validating the design performance as well as the assured stability by using both the benchmark design specifications and the novel UB function. [ABSTRACT FROM AUTHOR]

Digital notch filters are useful for removing sinusoidal signals with a single frequency or multi-frequencies. For some applications, the sinusoidal signals being processed may change frequencies, and thus the notch filter must also have a variable notch frequency. Such a digital filter with a variable notch-frequency (VNF) is called variable notch-frequency (VNF) digital filter. Generally speaking, a VNF filter has the ability to change its notch frequency continuously, and can remove sinusoidal signals with variable frequencies. To design a recursive VNF filter, guaranteeing its stability is the top-priority issue. In this paper, a recursive VNF filter is designed by utilizing the least Lp-norm criterion, and the stability is guaranteed through adopting the stability-guarantee methodology based on parameter transformations. To perform the parameter transformations, a function that meets a special condition is required, and such a function is called unity-bounded function. In this paper, various unity-bounded functions are developed for the parameter-transformation-based stability guarantee. The unity-bounded functions play a crucial role in the stability guarantee. This paper details how to design a stable VNF filter by incorporating the parameter transformations employing the unity-bounded functions into the Lp-norm minimization of the magnitude response. Theoretically, the stability of the recursive VNF filter resulting from the design is definitely guaranteed. Moreover, since the coefficients of the designed VNF are variable, changing the filter coefficients enables the user to get a VNF filter with updated notch frequency. [ABSTRACT FROM AUTHOR]

Because of the decrease in the band gap and the carrier recombination rate, the visible light photocatalysis performance of the mixed-phase TiO2 with oxygen vacancies is better than that of the pure-phase TiO2. In this study, two different acids were separately applied in the hydrothermal synthesis of TiO2 nanoparticles without any post-heat treatment. The reaction was carried out at a relatively low temperature not exceeding 140∘C. Both kinds of crystallized TiO2 powders show much more band gap reduction than that of commercial Degussa P25 TiO2 nanoparticles, which can be attributed to the oxygen vacancies. Under the visible light illumination-assisted photocatalytic degradation of methyl orange in water, the two mixed-phase TiO2 powders exhibited a steady photocatalytic activity upon increasing to five cycles. The highest photocatalytic efficiency of the two powders is 2.7 times than that of the P25 powder, which is regarded as an excellent photocatalyst for water purification. Mixed-phase TiO2 nanoparticles were synthesized by acid-assisted hydrothermal synthesis at 140∘C without any post-calcination. Compared with P25, the specific surface area of H-TiO2 (by HCl) and A-TiO2 (by acetic acid) is larger. At the same time, H-TiO2 and A-TiO2 have excellent photocatalytic performances when assisting in the degradation of methyl orange in water under visible light illumination. The stable high photocatalytic performance and the simple preparation methods of the H-TiO2 and A-TiO2 nanoparticles will promote the industrial application. [ABSTRACT FROM AUTHOR]

This paper proposes a novel method for the design of a recursive second-order (biquadratic) all-pass phase compensator with controllable stability margin. The design idea stems from the generalized stability triangle (GST) derived by the author for the second-order biquadratic digital filter. Based on the GST, a parameter-transformation method is proposed on the transformations of the denominator coefficients of the transfer function of the biquadratic phase compensator. The transformations convert the original denominator coefficients to other new parameters, and any values of those new parameters can guarantee that the GST condition is always satisfied. Optimizing the new parameters yields a biquadratic phase compensator that definitely meets a prespecified stability margin. That is, a biquadratic all-pass phase compensator can be designed to have an arbitrarily specified stability margin. This in turn avoids the occurrence that a recursive phase compensator may become unstable in the practical applications. Thus, the resulting biquadratic phase compensator has robust stability, which is extremely important during the practical filtering operations. A design example is given to show the stability margin guarantee as well as the approximation accuracy. [ABSTRACT FROM AUTHOR]

This paper proposes a two-step strategy for designing a variable-bandwidth (VBW) digital filter through minimizing the -norm of the magnitude-response error. This -norm design can be regarded as a generalized version of the existing weighted-least-squares (WLS) design. Equivalently, the WLS design is a special case of the -norm-minimization design for . This paper discusses the design of the recursive VBW filter with the transfer function whose denominator is expressed as the product of the second-order sections. As long as all the second-order sections are stable, the recursive VBW filter is also stable. To ensure that the designed recursive VBW filter is stable, we adopt the coefficient-conversion strategy that constrains all the denominator-parameter pairs of the second-order sections within the stability triangle. This paper also proposes a novel conversion function for performing the coefficient conversion. As a consequence, the designed VBW filter is definitely stable. A bandpass VBW filter is designed for showing the feasibility of the -norm-minimization-based design and verifying the stability guarantee. [ABSTRACT FROM AUTHOR]

Guaranteeing the stability is one of the most critical issues in designing a variable recursive digital filter. In this paper, we first present an odd-order recursive variable model (transfer function) that is used for designing an odd-order variable-magnitude (VM) digital filter, and then we replace the original coefficients of the denominator of the odd-order transfer function with a set of new parameters. These new parameters can ensure that they can take arbitrary values without incurring instability of the designed odd-order VM filter. To make the VM filter coefficients variable, we find all the VM filter coefficients as polynomial functions of the tuning parameter, which includes two phases. The first phase designs a set of recursive digital filters with fixed coefficients (constant filters), and the second phase utilizes a curve-fitting scheme to represent each coefficient as a polynomial function. As a result, the VM filter coefficients become variable, and the proposed parameter-substitution-based denominator coefficients ensure the filter stability. This is the most important contribution of the parameter-substitution-based design scheme. This paper uses the fifth-order demonstrative example to verify the stability guarantee as well as the design accuracy of the obtained the fifth-order VM filter. [ABSTRACT FROM AUTHOR]

In the design of recursive digital filters, the stability of the recursive digital filters must be guaranteed. Furthermore, it is desirable to add a certain amount of margin to the stability so as to avoid the violation of stability due to some uncertain perturbations of the filter coefficients. This paper extends the well-known stability-triangle of the second-order digital filter into more general cases, which results in dented stability-triangles and generalized stability-triangle. The generalized stability-triangle can be viewed as a special case of the dented stability-triangles if the two upper bounds on the radii of the two poles are the same, which is a generalized version of the existing conventional stability-triangle and can guarantee the radii of the two poles of the second-order recursive digital filter below some prescribed upper bound. That is, it is able to provide a prescribed stability-margin in terms of the upper bound of the pole radii. As a result, the generalized stability-triangle increases the flexibility for guaranteeing a prescribed stability-margin. Since the generalized stability-triangle is parameterized by using the upper bound of pole radii, i.e., the stability-margin is parameterized as a function of the upper bound, the proposed generalized stability-triangle facilitates the stability-margin guarantee in the design of the second-order as well as high-order recursive digital filters. [ABSTRACT FROM AUTHOR]

A digital communication channel must have linear-phase characteristic such that the transmitted signal will keep its waveform unchanged after the signal transmission. However, since the actual communication channels usually possess nonlinear phase, it is necessary to connect a phase-linearizing circuit (phase-circuit) to such a nonlinear phase channel for linearizing the whole phase characteristic. In this paper, we propose a new iterative optimization scheme that utilizes the second-order-cone-programming (SOCP) for designing a high-accuracy phase-circuit. By approximating the highly nonlinear design constraint as a second-order-cone (SOC) constraint, a phase-circuit can be successfully designed through iterating the SOCP scheme. As compared to other existing linear-programming (LP) design and SOCP design, this new iterative SOCP-based minimax design can further reduce the peak errors of the frequency response and phase response of the designed phase-circuit. As a consequence, the new design method can further improve the phase-circuit design accuracy. We will utilize two design examples to verify the performance improvements over other existing design techniques. [ABSTRACT FROM AUTHOR]