Complex Digital Filters Research Articles

IIR Cascaded-Resonator-Based Complex Filter Banks

The use of a filter bank of IIR filters for the spectral decomposition and analysis of signals has been popular for many years. As such, a new filter-bank resonator-based structure, representing an extremely hardware-efficient structure, has received a good deal of attention. Recently, multiple-resonator (MR)-based and general cascaded-resonator (CR)-based filters have been proposed. In comparison to single-resonator-based analyzers, analyzers with a higher multiplicity of resonators in the cascade provide lower side lobes and a higher attenuation in stopbands. In previous works, it was shown that the CR-based filter bank with infinite impulse response (IIR) filters, which is numerically more efficient than one with finite impulse response (FIR) filters, is suitable for dynamic harmonic analysis. This paper uses the same approach to design complex digital filter banks. In the previous case, the optimization task referred to the frequency responses of harmonic filters. In this work, the harmonic filters of the mother filter bank are reshaped so that the frequency response of the sum (or difference, depending on the parity of the number of resonators in the cascade) of two adjacent harmonic filters is optimized. This way, an online adaptive filter base can be obtained. The bandwidth of the filters in the designed filter bank can be simply changed online by adding or omitting the output signals of the corresponding harmonics of the mother filter.

Методика вибору гіперкомплексних числових систем для моделювання цифрових реверсивних фільтрів

Digital filter is a digital system, which is used for filtering a discrete signal. It can be implemented as a software method, and with the help of specialized equipment. In both cases, the digital filter can be used for filtering, both in real time and for a pre-stored signal value. In this paper, we consider only the algorithms for the synthesis of the software filter structure. However, it should be noted that on the basis of these structures, implementations and hardware solutions of digital filters can beat. The use of HNS for the synthesis of digital filter structures can give a tangible advantage. Digital filters with hyper complex parameters have greater momentum and better characteristics in integrated parametric sensitivity.The paper discusses the definition of hyper complex digital filter and the conversion of its transfer function to the form of hyper complex function. A technique for selecting a hyper complex number system has been developed for the equivalent of a hyper complex filter to a real analogue. It is shown that the main method for determining the expediency of using one or another HNS for the synthesis of the structure of a hyper complex digital filter is the general form of the normic denominator of the hyper complex transfer function of the filter. This turn should be a complete polynomial of the shift operator, and also contain all the components of the multiplier with the shift operator in the denominator.However, these conditions are only necessary in the synthesis of the hyper complex filter, since the system of equivalence equations may not have real solutions when fulfilling these conditions. In this case, it is necessary to switch to another HNS, if there is such an opportunity, or to switch to HNS of higher orders. The latter path needs further research.

Влияние режекторного фильтра на эффективность линеаризации фазочастотной характеристики аналогового полосового фильтра

The previously published works of the authors dealt with methods aimed at linearizing the phase frequency responses of analog filters using digital linearizing finite impulse response (FIR) filters. If the operating frequency band contains narrow-band interference, such interference often needs to be suppressed by using a narrow-band analog band-stop filter. However, when a band-stop filter is connected in series, the linearized phase frequency response may become distorted. The article examines the influence of a narrow-band analog band-stop filter on the effectiveness of linearizing the phase frequency responses of a complex analog band-pass filter using a complex band-pass linearizing digital FIR filter. The study was conducted using a circuit simulation program based on a model consisting of the following modules: a complex analog band-pass filter with a sixth-order Butterworth low-pass filter prototype, a narrow-band complex analog band-stop filter with a third-order Butterworth low-pass filter prototype, and a complex digital band-pass linearizing FIR filter. The article presents the results from studying the frequency band in which the phase frequency response linearity is distorted to an acceptable degree. A sharp change in the group delay time level takes place in the stopband vicinity. The frequency band in which the group delay ripple is larger than the pre-linearization group delay ripple is referred to as the linearization effect loss band. If the difference between the band-stop filter’s passband boundary frequencies is much (by dozens of times) smaller than the band of the complex band-pass filter, the linearization effect is retained over most of the passband. With the selected parameters and orders of the complex analog filter and band-stop filter, the frequency band in which the linearization effect vanishes is approximately seven times greater than the difference between the band-stop filter’s passband boundary frequencies. Such an approach is relevant in filtering narrow-band interference within the frequency band of broadband signals.

Two-stage method of Barkhausen noise measurement

A simple method of measuring the Barkhausen noise in two stages was developed. The purpose of the proposed method was to remove the magnetizing frequency component from the induced electromotive force signal without using complex analog or digital filters, which also suppress the Barkhausen noise. In the first stage, an instance of the electromotive force signal was temporarily recorded, and in the second stage another instance of the electromotive force signal subtracted from the previously recorded instance of the electromotive force signal was measured. Using this method we will obtain only the stochastic component of the electromotive force signal – the Barkhausen noise. The method is illustrated on measuring the Barkhausen noise in an electrical steel sample. The experiments proved that with this method we are able to remove the dominant continuous component from the induced electromotive force signal and we can simplify the measurement. The general problems associated with the method are discussed.

Design and Application of Digital Filter Based on Calculus Computing Concept

Calculus has been widely applied in engineering fields. The development of Integer order calculus theory is more mature in the project which can obtain fractional calculus theory through the promotion of integration order. It extends the flexibility of calculation and achieves the engineering analysis of multi-degree of freedom. According to fractional calculus features and the characteristics of fractional calculus, this paper treats the frequency domain as the object of study and gives the fractional calculus definition of the frequency characteristics. It also designs the mathematical model of fractional calculus digital filters using Fourier transform and Laplace transform. At last, this paper stimulates and analyzes numerical filtering of fractional calculus digital filter circuit using matlab general numerical analysis software and FDATool filter toolbox provided by matlab. It obtains the one-dimensional and two-dimensional filter curves of fractional calculus method which achieves the fractional Calculus filter of complex digital filter.

Non-Maximally Decimated Analysis/Synthesis Filter Banks: Applications in Wideband Digital Filtering

We present a new class of highly effective and low complexity digital filters for processing very wideband signals. Digital filtering for wideband signals is often limited by the number of arithmetic operations that has to be performed per input sampling interval. We will show the new architecture permits filtering to be performed on partitioned spectral segments of the input signal at significantly reduced sample rate. The digital filtering will be shown to include various tasks such as linear/non-linear phase finite impulse response (FIR) filtering, fractional delay filter among others. The proposed technique utilizes the framework of non-maximally decimated filter banks (NMDFBs) with perfect reconstruction (PR) property, which makes the filter bank design simpler and more flexible. Compact representation for the generalized DFT based NMDFBs as well as its efficient polyphase implementation will be provided. The digital filtering is made possible by incorporating the desired intermediate processing elements in between the analysis and synthesis filter banks. We will show this embedded intermediate processing elements can achieve spectral shaping/signal manipulation task, which is a generalization of the concept of manipulating a digital filter in the frequency domain. We also analyze both analytically and experimentally, the spectral shaping accuracy based on different design strategies.

A Signal Pre-processing Algorithm Applied for Ultrasonic Flow-Meter

In order to solve the problem of time difference ultrasonic flow meter’s low accuracy, against the basic characteristics of the sample data, a data-processing algorithm is proposed. First, we use shell sort do a data pre-processing to the samples, then remove the error of the sample space by complex digital filter, and use the error compensation algorithm to get the final sample results. Among them, the complex digital filter is mainly composed by median filtering algorithm, sliding window, Peters algorithm and the weighted average algorithm. This kind of data processing algorithm can effectively filter out the error of the sample space. It can also make a large improvement to the accuracy of ultrasonic flow meter while ensure the stability and real-time. DOI: http://dx.doi.org/10.11591/telkomnika.v11i9.3282

The digital function filters – algorithms and applications

Abstract The simple digital filters are not sufficient for digital modeling of systems with distributed parameters. It is necessary to apply more complex digital filters. In this work, a set of filters, called the digital function filters, is proposed. It consists of digital filters, which are obtained from causal and stable filters through some function transformation. In this paper, for several basic functions: exponential, logarithm, square root and the real power of input filter, the recursive algorithms of the digital function filters have been determined The digital function filters of exponential type can be obtained from direct recursive formulas. Whereas, the other function filters, such as the logarithm, the square root and the real power, require using the implicit recursive formulas. Some applications of the digital function filters for the analysis and synthesis of systems with lumped and distributed parameters (a long line, phase shifters, infinite ladder circuits) are given as well.

Neural Controller for UPS Inverters Based on B-Spline Network

This paper proposes a controller for uninterruptible power supply inverters based on a particular type of online-trained neural network, which is called the B-spline network (BSN). Due to its linear nature and local weight updating, the BSN controller is more suitable for real-time implementation than conventional multilayer feedforward neural controllers. Based on a frequency-domain stability analysis, a design methodology for determining the two main parameters of the BSN are presented. The model is found to be similar to that of an iterative learning control (ILC) scheme. However, unlike ILC, which requires a complex digital filter design that involves both causal and noncausal parts, the design procedure of the proposed BSN controller is straightforward and simple. Experimental results under various conditions show that the proposed controller can achieve excellent performance, comparable to that of a high-performance ILC scheme developed earlier. The proposed controller is an attractive alternative to both the multilayer feedforward neural controller and iterative learning controller in this and similar applications.

Complex digital Laguerre filter design with weighted least square error subject to magnitude and phase constraints

Complex coefficient optimal digital Laguerre filter design with arbitrary asymmetric frequency response is developed. The optimization scheme is based on the weighted least square error criterion with complex Chebyshev error used as its magnitude and phase constraints. Developed version of the active set method has been exploited to solve the resultant semi-infinite quadratic programming problem. A quick and practical approach is proposed to evaluate the suboptimal value of the Laguerre parameter close to its optimum value. The design technique can be applied to design of asymmetric FIR filters just by setting the Laguerre parameter equal to zero. The accuracy of the processes has been verified by illustrating some numerical examples.

Nonlinear Behaviors of First and Second-Order Complex Digital Filters With Two's Complement Arithmetic

For first-order complex digital filters with two's complement arithmetic, it is proved in this correspondence that overflow does not occur at the steady state if the eigenvalues of the system matrix are inside or on the unit circle. However, if the eigenvalues of the system matrix are outside the unit circle, chaotic behaviors would occur. For both cases, a limit cycle behavior does not occur. For second-order complex digital filters with two's complement arithmetic, if all eigenvalues are on the unit circle, then there are two ellipses centered at the origin of the phase portraits when overflow does not occur. When limit cycle occurs, the number of ellipses exhibited on the phase portraits is no more than two times the periodicity of the symbolic sequences. If the symbolic sequences are aperiodic, some state variables may exhibit fractal behaviors; at the same time, irregular chaotic behaviors may occur in other phase variables

Wave digital filters with minimum multiplier for discrete Hilbert transformer realization

This paper describes the design of wave digital filters for discrete Hilbert transformer realization. A method for designing real and complex half-band wave digital filters (WDFs) with a minimum number of multipliers is afforded where the multiplier coefficients for the adaptors are calculated directly from the digital domain transfer functions. This technique uses the equations derived for a class of infinite impulse response (IIR) filter and hence avoids the conventional technique of synthesizing a WDF from an analogue reference filter. The selection of the adaptor configuration is determined from the multiplier coefficient values. A minimum multiplier realization of real half-band WDFs can be obtained to meet the low-pass digital filter magnitude specifications. By applying a transformation equation, a complex half-band WDF suitable for the realization of the discrete Hilbert transformer with a minimum number of multiplier is obtained.

Realization of Modular Multidimensional Complex Digital Filters Using GIC Concept

It is known that complex digital filters possess certain advantages over real digital filters in processing complex signals such as increased computational speed and efficiency. In this paper, a simple and systematic procedure which can be implemented through a computer program is presented for realizing a specific class of multidimensional (M-D) complex digital filters. The proposed filter structures are derived from analog reference configurations comprising generalized immittance converters and resistors by making use of wave concept. These filters possess many salient properties such as low noise, low sensitivity and capability of realizing multiple transfer functions simultaneously which are inherited from the reference analog filters they are derived from. These features make them attractive for very large-scale integrated (VLSI) implementation. It is shown that the proposed filter structures can be obtained directly from the specified M-D discrete transfer function without the need for realizing any analog reference configuration.

Single sideband optical signal generation and chromatic dispersion compensation using digital filters

It is shown that signal processing for single sideband signal generation and electronic chromatic dispersion compensation can be implemented using low complexity digital filters. Effective compensation for the dispersion of up to 1700 km of standard fibre at 10 Gbit/s with 6-bit 20 GSa/s digital sampling was demonstrated.

FIR filter synthesis algorithms for minimizing the delay and the number of adders

As the complexity of digital filters is dominated by the number of multiplications, many works have focused on minimizing the complexity of multiplier blocks that compute the constant coefficient multiplications required in filters. Although the complexity of multiplier blocks is significantly reduced by using efficient techniques such as decomposing multiplications into simple operations and sharing common subexpressions, previous works have not considered the delay of multiplier blocks which is a critical factor in the design of complex filters. In this paper, we present new algorithms to minimize the complexity of multiplier blocks under the given delay constraints. By analyzing multiplier blocks in view of delay, three delay reduction methods are proposed and combined into previous algorithms. Since the proposed algorithms can generate multiplier blocks that meet the specified delay, a trade-off between delay and hardware complexity is enabled by changing the delay constraints. Experimental results show that the proposed algorithms can reduce the delay of multiplier blocks at the cost of a little increase of complexity.

Scale steerability of class of complexdigital filters

A class of digital filters is described which has good steerability in scale-space. This property is due to the use of Erlang functions in the frequency domain as basis filters. Weights for synthesising digital filters of arbitrary scale are estimated by least-squares techniques in the frequency domain, then applied in the time-domain.

Complex reference networks to realize transfer functions with arbitrary transmission zeros

This paper proposes a method of realizing arbitrary complex coefficient transfer functions with complex double resistively terminated lossless filters as the reference network for complex wave digital filters (CWDFs). For this purpose, the Darlington synthesis method, which is known for realizing arbitrary real coefficient transfer functions, is expanded into the complex domain. Furthermore, a new construction method for a digital adapter without a delay-free loop is presented. Finally, a complex coefficient transfer function using some realization method is constructed and the validity of the proposed method is confirmed. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(2): 12–23, 1997

Complex coefficient nonrecursive digital filter design using a least-squares method

A method for the design of complex-coefficient nonrecursive filters is described. In this method, a mean square error is formulated in a quadratic form. The filter coefficients are obtained by solving a system of linear equations using computationally robust and efficient algorithms. Examples are presented to demonstrate the efficacy of our method.

Complex coefficient reference networks with transmission zeros on imaginary axis

AbstractThis paper considers the complex coefficient transfer function with transmission zeros on the imaginary axis and presents a method to realize such a transfer function by a reactance network including imaginary resistors with double resistor termination. Using the obtained network and the reference network for the complex‐wave digital filter, the complex digital filter with transmission zeros on the imaginary axis can easily be extended, which is important in practice.In this paper, Brune's method modified by Belevitch as well as Fujisawa's method extended by Morimoto et al. are improved and the realizability condition is relaxed. Then, several construction examples are shown and the features of construction methods are compared and discussed.

Realizations of a first-order, lossless, digital two-pair

A unitary realization of the generalized first-order, lossless bounded complex (LBC) two-pair that is the basic building block for an LBC implementation of a bounded complex (BC) digital filter is derived. Strikingly, very simple expressions for the angle parameters are obtained and some special cases leading to structurally bounded realizations are treated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>