Thresholding implemented in the frequency domain

Image processing procedures are usually carried out in the spatial domain where the images are acquired and presented/utilized. The linear nature of the Fourier transform allows only those operations that are linear to be mapped into the frequency domain. In contrast, nonlinear operations and manipulations cannot be realized directly in the frequency domain. One of these nonlinear operations is thresholding. When operating in the spatial domain to segment image contents into object and background, thresholding is simple and efficient. However, it has no obvious representation in the frequency domain and cannot be carried out there in a straightforward fashion. In this paper, a means to relax the rigid linear limitation of the Fourier transform was investigated. A novel approach was established to achieve spatial thresholding using only frequency domain operations. The spatial grayscale or scalar data set (two-dimensional (2-D) image or three-dimensional (3-D) volume) was expanded into a binary volume in hyperspace having one more dimension than the original data set. The extended dimension is the gray level of the original data. Manipulating only on that dimension produces the effect of thresholding.     

Wavelet transform domain filters: a spatially selective noisefiltration technique

Wavelet transforms are multiresolution decompositions that can be used to analyze signals and images. They describe a signal by the power at each scale and position. Edges can be located very effectively in the wavelet transform domain. A spatially selective noise filtration technique based on the direct spatial correlation of the wavelet transform at several adjacent scales is introduced. A high correlation is used to infer that there is a significant feature at the position that should be passed through the filter. The authors have tested the technique on simulated signals, phantom images, and real MR images. It is found that the technique can reduce noise contents in signals and images by more than 80% while maintaining at least 80% of the value of the gradient at most edges. The authors did not observe any Gibbs' ringing or significant resolution loss on the filtered images. Artifacts that arose from the filtration are very small and local. The noise filtration technique is quite robust. There are many possible extensions of the technique. The authors see its applications in spatially dependent noise filtration, edge detection and enhancement, image restoration, and motion artifact removal. They have compared the performance of the technique to that of the Weiner filter and found it to be superior.     

Frequency and time domain comparison of selective polynomial filters with corrected phase characteristics

Two solutions to the polynomial filter’s transfer function synthesis problem are considered for comparison in the frequency and time domain: the broad class of filters with a critical monotonic amplitude characteristic (CMAC) in the passband and filters which use Chebyshev (C) polynomials. To complete the synthesis procedure for linear phase applications, group delay correctors are considered, for which a convenient approximation procedure is proposed here. Comparisons of the original functions and the corrected ones are performed in the frequency and time domain. It is shown that when CMAC and C are compared as such, the latter is by no means preferable from the selectivity point of view, while the opposite stands when the comparison is based on passband amplitude distortions. When phase-corrected filtering functions are compared, based on circuit complexity and time domain performance, the CMAC are shown to be preferable.     

Velocity filters for multiple interferences in two-dimensionalgeophysical data

A procedure for the velocity filtering of two-dimensional geophysical data is discussed. This procedure involves repeatedly applying multichannel filters to a small number of overlapping subarrays of the input data. The multichannel filters can be chosen so that the resulting velocity filter is capable of suppressing multiple interferences traveling at different velocities. The two-dimensional frequency-wavenumber expression of the velocity filter is derived. With this expression, it becomes possible to implement the filter using two-dimensional fast Fourier transform (FFT) techniques. Two examples which illustrate the performance of the derived filters are presented     

An efficient block adaptive decision feedback equalizer implemented in the frequency domain

In this paper, a new block adaptive decision feedback equalizer (DFE) implemented in the frequency domain is derived. The new algorithm is suitable for applications requiring long adaptive equalizers, as is the case in several high-speed wireless communication systems. The inherent "causality" problem appearing in the block adaptive formulation of the DFE equations is overcome by using tentative decisions in place of the unknown ones within each block. These tentative decisions are subsequently improved by using an efficient iterative procedure, which finally converges to the optimum decisions in a few iterations. This procedure is properly initialized by applying a minimization criterion that utilizes all the available information. The whole algorithm, including the iterative procedure, is implemented in the frequency domain and exhibits a considerable reduction in computational complexity, as compared with the conventional DFE, offering, at the same time, a noticeable increase in convergence speed. Additionally, the level of the steady-state MSE, which is achieved by the new algorithm, is practically insensitive to the block length.     

Computer-aided distortion analysis of switched capacitor filters in the frequency domain

A Volterra series-based distortion analysis technique for switched capacitor circuits is presented. The algorithm has been implemented in the DIANA-SC program and is completely compatible with other DIANA simulation modes. The efficiency of the method is based on the use of direct z-domain and compaction methods, while only one extra circuit analysis is needed for each higher order distortion fraction of interest. Nonlinear operational amplifiers and capacitors can be handled using polynomial models. Both harmonic and intermodulation distortion analysis modes are available. The method is demonstrated using a practical design example.     

Chebyshev approximation problem of multidimensional IIR digital filters in the frequency domain

This paper investigates the problem of simultaneous approximation of a prescribed multidimensional frequency response. The frequency responses of multidimensional IIR digital filters are used as nonlinear approximating functions. Chebyshev approximation theory and the notion of line homotopy are used to reveal the approximation properties of this set of IIR functions. A sign condition is derived to characterize a convex stable domain in this set. This sign condition can be incorporated into the optimization of the Chebyshev simultaneous approximation. The generally sufficient global Kolmogorov criterion is shown to be a necessary condition, for the characterization of best approximation, in the considered set of approximating functions. Thus, it can be incorporated, as a stopping constraint, in the design of the optimal filter. Moreover, the local Kolmogorov criterion is shown to be also necessary for the set of approximating functions. Finally, it is proved that the best approximation is a global minimum.

     

Design of stable IIR filters in the complex domain by automaticdelay selection

A major problem encountered when designing infinite impulse response (IIR) filters in the complex domain is to ensure that the filter is stable. Instability occurs frequently when the IIR filter approximates the inverse of a nonminimum phase system. This is often the case for equalization filters. Addition of delay to the target frequency response can result in a stable filter. However, to date, delay selection has been a matter of trial and error. The article presents an automated method for finding the delay     

Repetitive-based control for selective harmonic compensation in active power filters

This paper proposes a repetitive-based controller for active power filters, which compensates selected current harmonics produced by distorting loads. The approach is based on the measurement of line currents and performs the compensation of selected harmonics using a closed-loop repetitive-based control scheme based on a finite-impulse response digital filter. Compared to conventional solutions based on stationary-frame current control, this approach allows full compensation of selected frequencies, even if the active filter has limited bandwidth. Compared to synchronous-frame harmonic regulations on line currents, the complexity of the proposed algorithm is independent of the number of compensated harmonics. Moreover, it is more appropriate for digital signal processor implementation and less sensitive to rounding and quantization errors when finite word length or fixed-point implementation is considered. Experimental results on a 5-kVA prototype confirm the theoretical expectations.     

Design of IIR digital filters in the complex domain by transforming the desired response

In this paper, we present a new design method of infinite impulse response (IIR) digital filters with quasi-equiripple absolute error in the complex domain. This method is based on solving a least squares solution iteratively. At each iteration, the desired response for the least squares approximation is transformed to have equiripple error. This algorithm is efficient because there is no need for any initial value or complex optimization algorithm. By this method, a quasi-equiripple solution is obtained very quickly with less computational complexity. Moreover, by multiplying an arbitrary weighting function on the desired responses of passband and stopband, respectively, the error at the passband and stopband can be controlled. Finally, we show some examples to validate the proposed method.     

Mean-square performance of the family of adaptive filters with selective partial updates

In this paper we present a general formalism for the family of adaptive filter algorithms with selective partial updates. Based on this, the mean-square performance analysis of this family of adaptive filters is presented in a unified way. This analysis is based on energy conservation arguments and does not need to assume a Gaussian or white distribution for the regressors. We demonstrate through simulations that the results are useful in predicting the performance of this family of adaptive filters.     

Design of variable elliptical filters with direct tunability in 2D domain

Multidimensional Systems and Signal Processing - This paper proposes the design of transformation based two dimensional (2D) elliptical filters using multi-objective artificial bee colony (MOABC)...     

Reference current computation methods for active power filters: accuracy assessment in the frequency domain

This paper focuses on the steady-state response of existing methods for computing the reference current of active power filters. For each class of methods, the main source of discrepancy between the load harmonic current and the computed reference current is identified and the frequency spectrum of the resulting error is analytically determined. Although this topic has been partially addressed in previous publications, the proposed frequency-domain approach provides valuable qualitative information about how the errors are produced and distributed, which is masked when the analysis is carried out in the time domain. First, the frequency-domain formulation is separately presented for each method. Then, a comparison of the resulting errors is performed on a case study. Finally, some experimental results are given to validate the proposed frequency-domain analysis.     

Polarisation selective all-fibre Fabry-Perot filters with superimposed chirped Bragg gratings in high-birefringence fibres

Periodic highly birefringent filters with 50 and 100 GHz free spectral range and finesse of up to 20 are demonstrated. With a polarisation peak separation of 25 GHz, the polarisation crosstalk was measured to be less than -16 dB.     

An algebraic technique for designing active filters in the frequency domain for control and signal processing

This paper presents a straightforward algebraic method for designing feedback loops in the frequency domain. The emphasis here is on control system design, but the technique is applicable to active filter design as well. The object is to produce a practical analog filter with a minimum of design effort. The algebraic solution to the design problem is presented, and several examples are explored.     

Modeling of the seven-terminal transformer implemented in the LTGC-QO

In this paper a seven-terminal transformer has been designed. We have suggested its equivalent-circuit model. This transformer has a primary coil with a center tap and two secondary coils. Based on this transformer, a low-cost transformer-based gate-coupled quadrature oscillator (LTGC-QO) using 0.18 µm CMOS technology has been developed. The LTGC-QO consumes 7 mW at 1 V power supply. The simulated phase noise at 1 MHz offset is–116.3 dBc/Hz. The chip area is 400×500 µm.     

Synthesis and design of in-line N-order filters with N real transmission zeros by means of extracted poles implemented in low-cost rectangular H-plane waveguide

In this paper, an extension to the extracted pole technique for synthesizing N-order filters with N-transmission zeros at real frequencies is presented. In addition, a new bandpass rectangular waveguide H-plane low-cost configuration filter for high-power low-loss application (patent pending) that implements a filtering function with finite real frequency transmission zeros is proposed. This structure operates as a resonant cavity in transmission at central frequency of the bandpass and simultaneously introduces a controlled transmission zero out of the bandpass. Since every double-controlled electrical behavior cavity introduces a transmission zero, it is possible to introduce as many transmission zeros as the order of the filtering function. In order to validate the synthesis procedure and the new structure, different filters have been designed: a second-order filter with two transmission zeros, a third-order filter with one transmission zero, a fourth-order filter with two transmission zeros, and finally, an eighth-order filter with two transmission zeros. The last two have been manufactured, showing an excellent agreement between the measurement and theoretical simulation.     

N-path filters in which the switched filters are not lowpass sections

It is shown that the generalised transfer function for switched networks, derived by Acampora, is only valid when the circuits being switched are filters whose transfer functions have negligible magnitude above half the switching frequency.     

Digital signal processing. 1. Digital filters and the DFT

The wide availability of inexpensive and relatively fast digital signal processing chips has given rise to a great expansion in the application of these devices in many areas, particularly consumer electronics. The ease with which digital processing operations can now be performed has allowed the realisation of highly sophisticated signal processing algorithms. The paper introduces the first of two main areas of digital signal processing, namely digital filtering and Fourier transformation. An overview is presented of both finite impulse response and infinite impulse response digital filter types. These designs are later extended to cover the concept of an adaptive filter, which automatically trains or adapts its characteristics or frequency response to compensate for signal distortions or interference. Finally, the discrete Fourier transform is introduced for measuring the frequency spectrum of a signal