Methods of hardware analysis of non-stationary processes active spectrum

The purpose of this paper is to expose an active spectrum real time analysis main point. We use the meaning about adjusted time. As a result we propose a method of non-stationary processes active spectrum hardware analysis, and we show a possibility of creation of such parallel type analyzer, whose analyzing narrowband filters are adequate to such processes. These filters are band-pass filters or following one-band modulators, which are similar to known systems of automatic frequency following. Proposed method allows to improve essentially the main engineering factors of known analogous random processes spectrum analyzers.     

About principal possibility of automated following by active frequency of non-stationery processes spectrum by means of active filter

It is underlined explicit usefulness and efficiency of hardware analysis of active spectrum of non-stationery processes, necessity of automated following by frequency of input signal filters (AFFF) application as analyzing filters. It is mentioned drawbacks of analysis methods of such filters and necessity of approval possibility of frequency self-tuning of any type filters (FSAF) of high order. Possibility of FSAF and, hence, AFFF is proven in terms of application of some known features of manual regulation of electrical filters. By means of computer mathematical modeling in system VisSim/com it is proven AFFF possibility. It is underlined possibilities of some useful their application.     

Theory and design of two-parallelogram filter banks

It is well known that the analysis and synthesis filters of orthonormal DFT filter banks can not have good frequency selectivity. The reason for this is that each of the analysis and synthesis filters have only one passband. Such frequency stacking (or configuration) in general does not allow alias cancellation when the individual filters have good stopband attenuation. A frequency stacking of this nature is called nonpermissible and should be avoided if good filters are desired. In a usual M-channel filter bank with real-coefficient filters, the analysis and synthesis filters have two passbands. It can be shown that the configuration is permissible in this case. Many designs proposed in the past demonstrate that filter banks with such configurations can have perfect reconstruction and be good filters at the same time. We develop the two-parallelogram filter banks, which is the class of 2-D filter banks in which the supports of the analysis and synthesis filters consist of two parallelograms. The two-parallelogram filter banks are analyzed from a pictorial viewpoint by exploiting the concept of permissibility. Based on this analysis, we construct and design a special type of two-parallelogram filter banks, namely, cosine-modulated filter banks (CMFB). In two-parallelogram CMFB, the analysis and synthesis filters are cosine-modulated versions of a prototype that has a parallelogram support. Necessary and sufficient conditions for perfect reconstruction of two-parallelogram CMFB are derived     

Least-squares design of IIR filters with prescribed magnitude andphase responses and a pole radius constraint

This paper presents a method for the frequency domain design of infinite impulse response (IIR) digital filters. The proposed method designs filters approximating prescribed magnitude and phase responses. IIR filters of this kind can have approximately linear-phase responses in their passbands, or they can equalize magnitude and phase responses of given systems. In many cases, these filters can be implemented with less memory and with fewer computations per output sample than equivalent finite impulse response (FIR) digital filters. An important feature of the proposed method is the possibility to specify a maximum radius for the poles of the designed rational transfer function. Consequently, stability can be guaranteed, and undesired effects of implementations using fixed-point arithmetic can be alleviated by restricting the poles to keep a prescribed distance from the unit circle. This is achieved by applying Rouche's theorem in the proposed design algorithm. We motivate the use of IIR filters with an unequal number of poles and zeros outside the origin of the complex plane. In order to satisfy simultaneous specifications on magnitude and phase responses, it is advantageous to use IIR filters with only a few poles outside the origin of the z-plane and an arbitrary number of zeros. Filters of this type are a compromise between IIR filters with optimum magnitude responses and phase-approximating FIR filters. We use design examples to compare filters designed by the proposed method to those obtained by other methods. In addition, we compare the proposed general IIR filters with other popular more specialized structures such as FIR filters and cascaded systems consisting of frequency-selective IIR filters and phase-equalizing allpass filters     

Fast noniterative algorithm for designing high-accuracy lowpass FIRfilters with the evaluation of errors

We present an analytical approach to the design of zero-phase FIR digital passband filters. We describe an easy-to-implement, finite (noniterative) algorithm for determining low-pass filters, whose cost of calculations is O(nlog₂n). We give the evaluation of errors, taking into account the transition band, from which there follows the main result of this paper, wherein our filters are nearly optimal. We compare them with optimal filters optimal Kaiser's (1974) filters. It results that the errors of our filters are slightly greater than Kaiser's filters. However, a small modification of the presented algorithm may lead to filters that, in numerical tests, have errors like Kaiser's filters or even smaller if the cut-off frequency is not very close to 0 or π. Our-algorithms are especially efficient for the design of very accurate (i.e., very long) filters. In numerical calculations, we constructed, using 15 digit floating-point arithmetic filters with errors up to 10^-13, i.e., -260 dB. The main limitation of the filters in question is the negligence of weighting functions     

A new design algorithm for two-band orthonormal rational filterbanks and orthonormal rational wavelets

We present a new algorithm for the design of orthonormal two-band rational filter banks. Owing to the connection between iterated rational filter banks and rational wavelets, this is also a design algorithm for orthonormal rational wavelets. It is basically a simple iterative procedure, which explains its exponential convergence and adaptability under various linear constraints (e,g., regularity). Although the filters obtained from this algorithm are suboptimally designed, they show excellent frequency selectivity. After an in-depth account of the algorithm, we discuss the properties of the rational wavelets generated by some designed filters. In particular, we stress the possibility to design “almost” shift error-free wavelets, which allows the implementation of a rational wavelet transform     

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.     

Enhancement of clock component in a nonreturn-to-zero signal through beating process

For optical clock recovery of nonreturn-to-zero (NRZ) signals of more than 40 Gb/s, we propose and experimentally demonstrate a simple clock recovery scheme through beating process between the carrier frequency component and one of the clock frequency components in modulated NRZ signals. The proposed scheme consists of a circulator, a variable optical attenuator (VOA), and two fiber Bragg grating (FBG) filters. With FBG filters and a VOA, the proposed scheme can equalize the amplitudes of two extracted frequency components for a maximum clock-to-noise ratio (CNR). Through this scheme, we have squared the adjustment range of the VOA and achieved an enhanced CNR of more than 15 dB before the receiver in experiment. Bit error rate (BER) curves for back-to-back and 80 km transmissions showed that BERs of less than 10⁻¹¹ can be obtained without error floors for both cases. We expect that the proposed scheme can operate as an efficient clock extraction system for high-speed optical communications.     

Permutation filter lattices: a general order-statistic filteringframework

A general nonlinear filtering framework-permutation order-statistic filter lattices is introduced which defines a highly modular and robust class of filters which effectively addresses both the nonlinear characteristics of a system as well as the possible noise contamination. Permutation filters, much like polynomial filters, are flexible and modular where instead of having polynomial expansions we have permutation lattice expansions. At the simplest level in the filter lattice, permutation filters reduce to either a simple linear (FIR) or to an order statistic (OS) filter, but at higher levels in the lattice the obtained filters can model complicated nonlinear systems more accurately while still preserving their robust properties. In order to enhance the robustness of permutation fitters, we develop α-trimmed permutation indicators and their associated filter lattices. We conclude by presenting simulation examples where permutation filters are used in nonlinear system identification and in the rejection of narrowband interference in a direct sequence multiple access system. This paper, thus extends the potential of order-statistic filters which have been shown to be somewhat limited in general nonlinear estimation problems     

Novel First-Order and Second-Order Current-Mode Filters Using Multiple-Output Operational Transconductance Amplifiers

In this paper, a general structure using dual-output operational transconductance amplifiers (OTAs) is explored to derive new first-order and second-order multi-function filters using OTAs with multiple current outputs and with and without grounded capacitors. Two first-order all-pass filters that have been obtained are presented, together with an analysis of nonidealities of OTAs, viz., finite bandwidth and parasitic output and input resistance and capacitance. Second-order multi-function filters obtained by using OTA-C simulated inductances in the proposed general structure are also presented. The realization of quadrature oscillator using the proposed first-order all-pass networks is also considered. Detailed analysis of nonideal frequency performance of the OTAs as well as finite output and input impedances is presented. SPICE simulation results are also given for the proposed circuits.     

DFT-modulated filterbank transceivers for multipath fading channels

The orthogonal frequency division multiplexing (OFDM) transceiver has enjoyed great success in many wideband communication systems. It has low complexity and robustness against multipath channels. It is also well-known that the OFDM transceiver has poor frequency characteristics. To get transceivers with better frequency characteristics, filterbank transceivers with overlapping-block transmission are often considered. However these transceivers in general suffer from severe intersymbol interference (ISI) and high complexity. Moreover costly channel dependent post processing techniques are often needed at the receiving end to mitigate ISI. We design discrete Fourier transform (DFT) modulated filterbank transceivers for multipath fading channels. The DFT modulated filterbanks are known to have the advantages of low design and implementation cost. Although the proposed transceiver belongs to the class of overlapping-block transmission, the only channel dependent part is a set of one-tap equalizers at the receiver, like the OFDM system. We show that for a fixed set of transmitting or receiving filters, the design problem of maximizing signal-to-interference ratio (SIR) can be formulated into an eigenvector problem. Experiments are carried out for transmission over random multipath channels, and the results show that satisfactory SIR performance can be obtained.     

A method of optimal linear systems for following filtration of active spectrum of non-stationery process

It is shown a necessity of improve of known method of optimally matched filtering for following the spectrum of non-stationery processes. The essence of improvement lies in expansion of the conception of signals active spectrum, taking into account specificities of known following filters with self-tuning and application of known following filters with two integrators. It is proven that selecting of gain coefficients of three amplifies, which are contained in this filter, we can use them as separate section of band-pass filter for synthesis of optimal linear systems for following filtration the active spectrum itself for different signals type.     

On two-channel filter banks with directional vanishing moments.

The contourlet transform was proposed to address the limited directional resolution of the separable wavelet transform. One way to guarantee good approximation behavior is to let the directional filters in the contourlet filter bank have sharp frequency response. This requires filters with large support size. We seek to isolate the key filter property that ensures good approximation. In this direction, we propose filters with directional vanishing moments (DVM). These filters, we show, annihilate information along a given direction. We study two-channel filter banks with DVM filters. We provide conditions under which the design of DVM filter banks is possible. A complete characterization of the product filter is, thus, obtained. We propose a design framework that avoids 2-D factorization using the mapping technique. The filters designed, when used in the contourlet transform, exhibit nonlinear approximation comparable to the conventional filters while being shorter and, therefore, providing better visual quality with less ringing artifacts. Furthermore, experiments show that the proposed filters outperform the conventional ones in image approximation and denoising.     

Design of minimum-phase digital filters as the sum of two allpass functions using the cepstrum technique

A new and practical approach using the cepstrum technique is proposed in the design of minimum-phase digital filters as the sum of two allpass functions. The desired magnitude response is specified in the frequency domain. Its corresponding minimum-phase response is then obtained from the desired magnitude response. The desired phases for the two allpass filters are obtained from the magnitude and phase responses. For both filters to be stable, the corresponding denominator polynomials are minimum phase. The filter coefficients are obtained from the desired phases using the cepstrum technique. Design examples show that the method works well for both classical filter specification and general magnitude specification in the frequency domain.     

Optimal design of nonuniform multirate filter banks

The design of general nonuniform filter banks is studied. Contrary to uniform filter banks, in nonuniform filter banks, it may not be possible to achieve perfect reconstruction, but in some cases by using optimization techniques, we can design acceptable filter banks. Here, the initial finite impulse response (FIR) analysis filters are designed according to the characteristics of the input. By the design procedure, the FIR synthesis filters are found so that theH-norm of an error system is minimized over all synthesis filters that have a prespecified order. Then, the synthesis filters obtained in the previous step are fixed, and the analysis filters are found similarly. By iteration, theH-norm of the error system decreases until it converges to its final value. At each iteration, the coefficients of the analysis or synthesis filters are obtained by finding the least squares solution of a system of linear equations. If necessary, the frequency characteristics of the filters can be altered by adding penalty terms to the objective function.This research was supported by the Natural Sciences and Engineering Research Council of Canada.     

Performance analysis of instantaneous frequency-based interferenceexcision techniques in spread spectrum communications

Jammers characterized by their instantaneous frequencies can be effectively mitigated in direct sequence spread spectrum communications by using open-loop adaptive excision filters. The primary requirement for these filters is that they must possess a notch in tune with the jammer instantaneous frequency (IF) to annihilate the interference power at every time sample. The interference time-varying frequency can be obtained using existing IF estimators, including quadratic time-frequency distribution methods. Without focusing on any specific estimator, we develop expressions for the receiver performance using a general class of multiple-zero FIR excision filters and show the dependence of the bit error rate (BER) on the filter order and its group delay. The effect of inaccuracies in the jammer instantaneous frequency information on the receiver performance is considered and evaluated as a function of the filter notch bandwidth. The latter is defined by the filter zero multiplicity, which is shown to be an important factor in the analysis of the correlator signal-to-noise ratio (SNR)     

Synthesis of fiber-optic delay line filters

This paper deals with the synthesis of fiber-optic delay line filters and is organized as follows. We show how filters with negative coefficients can be implemented using positive structures and differential detection at the optoelectronic conversion. This possibility implies that not only lowpass, but bandpass and highpass filters with arbitrary transfer functions may be implemented. Synthesis methods for positive filters based on modified versions of well-known time and frequency domain techniques are presented which take into account the restriction on the positive nature of the filter coefficients. We make use of these results to describe the synthesis procedure for arbitrary filters using fiber-optic structures. Some designs of lowpass, bandpass and highpass filters are presented as examples, and a possible implementation of these structures with a view of future optoelectronic integration is presented     

Electrodynamic theory of multiport structures using magnetostatic waves in ferrite films and its applications

The paper presents an electrodynamic analysis of tunable multiport ferrite-dielectric structures with parallel transmission lines of an arbitrary type, coupled through propagating magnetostatic modes of magnetized multilayered ferrite films. The structures are supposed to be excited at one port by an incident electromagnetic wave, and amplitudes and phases of electromagnetic waves at other ports are obtained by an analytical procedure. The model holds for an arbitrary direction of a magnetizing field and describes the interaction of magnetostatic modes in ferrite films of a finite width. The solution is obtained in a self-consistent approach, i.e., a reaction of magnetostatic waves (MSWs) on transducers, which excite them, is taken into account. Derived closed-form expressions for response functions of multiports provide the base for the modeling of a wide class of MSW devices: multichannel adjustable filters and delay lines, directional couplers, frequency-selective power dividers, tunable oscillators and active filters, and multiport resonators. The theory is also valid for the analysis of multi-element, interdigital, and meander MSW transducers. Applications of a general theory are demonstrated for numerical calculations of frequency responses of surface and forward volume MSW filters, delay lines with new types of strip-line transducers (two-port and T-type), and for the analysis of a phenomenon of mutual coupling of transducers in conventional devices.