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Showing papers on "Prototype filter published in 1994"


Journal ArticleDOI
TL;DR: A novel approach to the design of M-channel pseudo-quadrature mirror filter (QMF) banks is presented, where it is possible to design a pseudo-QMF bank where the stopband attenuation of the analysis (and thus synthesis) filters is on the order of /spl minus/100 dB.
Abstract: A novel approach to the design of M-channel pseudo-quadrature mirror filter (QMF) banks is presented. In this approach, the prototype filter is constrained to be a linear-phase spectral-factor of a 2Mth band filter. As a result, the overall transfer function of the analysis/synthesis system is a delay. Moreover, the aliasing cancellation (AC) constraint is derived such that all the significant aliasing terms are canceled. Consequently, the aliasing level at the output is comparable to the stopband attenuation of the prototype filter. In other words, the only error at the output of the analysis/synthesis system is the aliasing error which is at the level of stopband attenuation. Using this approach, it is possible to design a pseudo-QMF bank where the stopband attenuation of the analysis (and thus synthesis) filters is on the order of /spl minus/100 dB. Moreover, the resulting reconstruction error is also on the order of /spl minus/100 dB. Several examples are included. >

233 citations


Journal ArticleDOI
TL;DR: The spectral performance of freestanding resonant metal-mesh bandpass filters operating with center frequencies ranging from 585 GHz to 2.1 THz is presented and Scalability of the filter spectra with mesh dimensions is demonstrated over a wide spectral range.
Abstract: The spectral performance of freestanding resonant metal-mesh bandpass filters operating with center frequencies ranging from 585 GHz to 2.1 THz is presented. These filters are made up of a 12-μm-thick copper film with an array of cross-shaped apertures that fill a circular area with a 50-mm diameter. The filters exhibit power transmission in the range 97–100% at their respective center frequencies and stop-band rejection in excess of 18 dB. The theoretically predicted nondiffracting properties of the meshes are experimentally verified through high-resolution beam mapping. Scalability of the filter spectra with mesh dimensions is demonstrated over a wide spectral range. Several modeling methods are considered, and results from the models are shown.

139 citations


Journal ArticleDOI
TL;DR: In this paper, the authors presented three methods for reducing the complexity of the masking filters, which can be realized as a cascade of a common subfilter and a pair of equalizers.
Abstract: It has been reported in several recent publications that the frequency response masking technique is eminently suitable for synthesizing filters with very narrow transition-width The major advantages of the frequency response masking approach are that the resulting filter has a very sparse coefficient vector and that the resulting filter length is only slightly longer than that of the theoretical (Remez) minimum The system of filters produced by the frequency response masking technique consists of a sparse coefficient filter with periodic frequency response and one or more pairs of masking filters Each pair of the masking filters consist of two filters whose frequency responses are similar except at frequencies near the band-edges In this paper, we present three methods for reducing the complexity of the masking filters The success of our technique is due to the fact that each pair of the masking filters can be realized as a cascade of a common subfilter and a pair of equalizers >

107 citations


Patent
14 Mar 1994
TL;DR: In this article, a bandpass enhancement filter (10) has a pass-band that tracks changes in spatial frequency due to the use of a zooming process upon a digital image signal.
Abstract: A bandpass enhancement filter (10) has a pass-band that tracks changes in spatial frequency due to the use of a zooming process upon a digital image signal The primary pass-band of the enhancement filter is derived from a combination of a plurality of secondary bandpass filter sections (30a-30d), each having a different frequency response and each responsive to a gain adjustment (34a-34d) A control signal (26) reflecting a particular zoom ratio is used in the adjustment of the gain applied to the filter sections, thereby proportioning the output of each filter section so that the combined output tracks the zooming process

100 citations


Book
30 Jun 1994
TL;DR: A thorough review of classic and modern filter design techniques, containing extensive practical design information of passband characteristics, topologies and transformations, component effects and matching is given in this paper.
Abstract: A book for engineers who design and build filters of all types, including lumped element, coaxial, helical, dielectric resonator, stripline and microstrip types A thorough review of classic and modern filter design techniques, containing extensive practical design information of passband characteristics, topologies and transformations, component effects and matching An excellent text for the design and construction of microstrip filters

83 citations


Journal ArticleDOI
TL;DR: In this paper, it is shown how a choice of filters can be made so as not to miss any signal of amplitude larger than a certain minimum value, called the minimal strength.
Abstract: Coalescing systems of compact binary stars are one of the most important sources for the future laser interferometric gravitational wave detectors. The signal from such a source will, in general, be completely swamped out by the photon-counting noise in the interferometer. However, since the wave form can be modeled quite accurately, it is possible to filter the signal out of the noise by the well known technique of matched filtering. The filtering procedure involves correlating the detector output with a copy of the expected signal called a matched filter or a template. When the signal parameters are unknown, as in the case of the coalescing binary signal, it is necessary to correlate the output through a number of filters each with a different set of values for the parameters. The ranges in which the values of the parameters lie are determined from astrophysical considerations and the set of filters must together span the entire ranges of the parameters. In this paper, we show how a choice of filters can be made so as not to miss any signal of amplitude larger than a certain minimum value, called the minimal strength. The number of filters and the spacing between filters in the parameter space are obtained for different values of the minimal strength of the signal. We also present an approximate analytical formula which relates the spacing between filters to the minimal strength. We discuss the problem of detection and false dismissal probabilities for a given data output and how a given set of filters determines these probabilities.

79 citations


Proceedings ArticleDOI
01 Jan 1994
TL;DR: In this paper, a survey of the most commonly used models for surface acoustic wave (SAW) devices are the impulse model, the equivalent circuit models, the Coupling-of-Modes model, and the matrix models.
Abstract: The most frequently used models for surface acoustic wave (SAW) devices are the impulse model, the equivalent circuit models, the Coupling-of-Modes model, and the matrix models. While the impulse-model is only a first order model the other models include second order effects, e.g. reflections, dispersion, and charge distribution effects. The influence of diffraction and refraction on the transfer function of a SAW filter can be described by the angular spectrum of straight-crested waves model. A survey of these different models will be given. The simulation of low-loss filters requires flexible analysis tools, which can cope with different geometries and substrates. Operating with a parameter set, which depends only on the substrate crystal and not on the specific geometry of the SAW filter, is advantageous. Due to the high insertion attenuation of conventional transversal filters the requirements on the accuracy of the analysis are focused on S21, whereas for low-loss filters all elements of the S-matrix are important. The comparison of simulations with a P-matrix model, which fulfills the above mentioned prerequisites, and measurements of different types of low-loss filters, e.g. SPUDT, DMS, and transverse-mode coupled resonator filters are presented

70 citations


Journal ArticleDOI
TL;DR: extremely area-efficient designs are presented to implement very large time-constant filters used to process speech and other acoustic signals to reduce significantly the capacitance spread ratios needed in the filter banks.
Abstract: A general scheme for the VLSI implementations of auditory wavelet transforms is proposed using switched-capacitor (SC) circuits. SC circuits are well suited for this application since the dilation constant across different scales of the transform can be precisely implemented and controlled by both the capacitor ratios and the clock frequency. The hardware implementations are made possible by several new circuit designs. Specifically, extremely area-efficient designs are presented to implement very large time-constant filters used to process speech and other acoustic signals. The designs employ a charge differencing technique to reduce significantly the capacitance spread ratios needed in the filter banks. Also, a parasitic-insensitive sum-gain amplifier is designed which samples several inputs at the same phase. The proposed circuits have been fabricated using a 2 /spl mu/m CMOS n-well process with double polysilicon and double metal. In addition, a 32-channel prototype filter bank (each channel is a 6th order transfer function), covering a frequency range from 0.2 to 6.4 kHz which includes 36 biquads, 32 sum-gain amplifiers and a preemphasis highpass filter, is implemented on a 4.6/spl times/6.8 mm/sup 2/ die. The IC measurement results of the proposed circuits and the filter bank show the advantages of such new designs. >

62 citations


Proceedings ArticleDOI
25 Oct 1994
TL;DR: A near-perfect-reconstruction, two-channel hybrid filter bank which introduces 0.00095 dB average deviation from 0 dB distortion and -108 dB average aliasing is developed.
Abstract: This paper presents a novel approach to high-speed, high-resolution analog-to-digital (A/D) conversion using a hybrid filter bank with an array of slower speed A/D converters (ADCs). The hybrid filter bank is a new class of filter bank that employs continuous-time analysis filters to allocate a frequency band to each ADC in the array and discrete-time synthesis filters to reconstruct the digitized signal. The filter bank improves the speed and resolution of the A/D conversion by reducing the effects of mismatches between the ADCs in the array. This paper presents a filter design algorithm which minimizes mean-squared reconstruction error for the M-channel hybrid filter bank. A near-perfect-reconstruction, two-channel hybrid filter bank which introduces 0.00095 dB average deviation from 0 dB distortion and -108 dB average aliasing is developed. >

57 citations


Journal ArticleDOI
TL;DR: In this article, a new configuration of dielectric loaded cavity filters is presented, which combines the superior spurious free performance of TE/sub 01/mode ring D resonators with the advantage of HE/sub 11/ dual-mode D resonator loading.
Abstract: A new configuration of dielectric loaded cavity filters is presented. The filter combines the superior spurious free performance of TE/sub 01/ mode ring dielectric resonators with the advantage of HE/sub 11/ dual-mode dielectric loading. Resonant frequency, field distributions and unloaded Q of each cavity are computed by rigorous mode-matching technique. The fields are used to compute the coupling between two similar cavities by small aperture approximation based on formulae modified by Levy, which are extended to the cases of dissimilar cavities. Design aspects of the filter are discussed. This filter is used to construct an L-band triplexer. Excellent experimental results verify the theory and show the advantage of this type of filter. >

55 citations


Journal ArticleDOI
TL;DR: An active power filter for compensating voltage sags that occur on a weak AC power system is described, and a design procedure based on IEEE/ANSI voltage withstand tolerance (IEEE standard 446-1987) is proposed.
Abstract: An active power filter for compensating voltage sags that occur on a weak AC power system is described. The proposed active power filter is especially suitable in situations where sensitive data processing and other critical loads are to be operated on a weak AC system. The proposed filter is fast acting and simple in design. A design procedure based on IEEE/ANSI voltage withstand tolerance (IEEE standard 446-1987) is proposed. Laboratory tests on a prototype filter show fast response and linear correction characteristics. >

Journal ArticleDOI
B. Hopf1, Ingo Wolff1, Marco Guglielmi
22 May 1994
TL;DR: In this article, a second order active bandpass filter for a fixed center frequency and a tunable one have been developed in a coplanar line technique using negative resistance circuits and operate in the 1.8 GHz band and have a 3 dB bandwidth of 110 MHz.
Abstract: A second order active bandpass filter for a fixed centre frequency and a tunable one have been developed in a coplanar line technique using negative resistance circuits. These filters operate in the 1.8 GHz band and have a 3 dB bandwidth of 110 MHz. The tuning range of the centre frequency is 200 MHz. Each filter is fabricated on a GaAs substrate and occupies an area of 1.5/spl times/1.6 mm/sup 2/ on the wafer including all biasing elements. >

Journal ArticleDOI
TL;DR: By requiring the filter to minimize the average correlation plane energy, this work produces a multiclass rotation invariant (RI) RI-MACE filter, which controls correlation plane sidelobes and improves discrimination against false targets.
Abstract: Advanced correlation filter synthesis algorithms to achieve rotation invariance are described. We use a specified form for the filter as the rotation invariance constraint and derive a general closed-form solution for a multiclass rotation-invariant filter that can recognize a number of different objects. By requiring the filter to minimize the average correlation plane energy, we produce a multiclass rotation invariant (RI) RI-MACE filter, which controls correlation plane sidelobes and improves discrimination against false targets. To improve noise performance, we require the filter to minimize a weighted sum of correlation plane signal and noise energy. Initial test results of all filters are provided. >

Proceedings ArticleDOI
Cormac Herley1
30 May 1994
TL;DR: It is shown that by associating with both analysis and synthesis operators a set of boundary filters, it is possible to make the analysis structure vary arbitrarily in time, and yet reconstruct the input with a similarly time-varying synthesis section.
Abstract: We examine the question of how to construct time-varying filter banks in the most general M-channel non-orthogonal case. We show that by associating with both analysis and synthesis operators a set of boundary filters, it is possible to make the analysis structure vary arbitrarily in time, and yet reconstruct the input with a similarly time-varying synthesis section. There is no redundancy or distortion introduced. This gives a solution to the problem of applying filter banks to finite length signals; it suffices to apply the boundary filters at the beginning and end of the signal segment. This also allows the construction of orthogonal and non-orthogonal bases with essentially any prescribed time and frequency localization, but which, nonetheless, are based on structures with efficient filter bank implementations. >

Patent
31 Aug 1994
TL;DR: In this article, a tracking filter has a tunable filter responsive to an input signal for producing a filtered output signal, a Hilbert transformer for producing an in-phase reference signal and a quadrature phase reference signal from the filter output signal.
Abstract: A tracking filter has a tunable filter responsive to an input signal for producing a filtered output signal, a Hilbert transformer for producing an in-phase reference signal and a quadrature-phase reference signal from the filtered output signal, and a discriminator responsive to the input signal and the in-phase and quadrature-phase reference signals for producing a passband center frequency control signal and a passband width control signal for controlling the passband center frequency and the passband width of the tunable filter. The frequency discriminator performs complex demodulation of the input signal with the in-phase reference signals to produce respective in-phase and quadrature-phase baseband signals which are low-pass filtered. The quadrature-phase baseband signal is divided by the in-phase baseband signal. The quotient is integrated to produce the passband center frequency control signal. Preferably the baseband signals are also filtered by adjustable filters having passband center frequencies and passband widths controlled in response to the passband center frequency control signal and the passband width control signal, respectively. Preferably the tracking filter is a digital filter.

Proceedings ArticleDOI
D. Frey1
30 May 1994
TL;DR: It is shown that log filter topologies are possible which function well at 3.3 volts and are particularly well suited for high frequency applications since they are essentially current mode networks.
Abstract: A very high frequency low voltage active filter is proposed which is based on the "log filters" introduced by Frey (1993). These filters have been shown to be a special case of exponential state space filters. Log filters are particularly well suited for high frequency applications since they are essentially current mode networks. They are also well suited to low power supply operation, not only because of their current-mode nature, but also because there is no overhead associated with linearization, since the intrinsic nonlinearity is an integral part of the design formulation. In this paper it is shown that log filter topologies are possible which function well at 3.3 volts. >

Proceedings ArticleDOI
30 May 1994
TL;DR: A method for making possible the active parallel-mode compensation of on-chip inductor and capacitor losses, and for making both the quality factor and the inductance value electronically tunable is discussed.
Abstract: In this paper we discuss a method for making possible the active parallel-mode compensation of on-chip inductor and capacitor losses, and for making both the quality factor and the inductance value electronically tunable The application of this technique in filters is emphasized throughout, and is demonstrated in a 2nd-order bandpass filter The paper provides analytical results, discusses transistor-level circuits and presents experimental results from a linearity test on a breadboard >

Journal ArticleDOI
TL;DR: In this paper, a novel realization of monotonic Butterworth-type lowpass, highpass, and bandpass optical filters by cascading the all-pole and all-zero resonators is presented.
Abstract: A novel realization of monotonic Butterworth-type lowpass, highpass, and bandpass optical filters (from their electrical digital filter characteristics) by cascading the all-pole and all-zero resonators is presented. A graphical method for fast derivation of the transfer functions, quick inspection of the resonance effects, and important characteristics of any photonic circuits is described. It is shown that incorporation of the optical amplifiers and optical phase modulators into the delay lines of two basic optical resonators, whose pole and zero can be adjusted independently of each other, provides great design flexibility which would otherwise not possible using conventional passive optical resonators. Possible applications of these optical filters as optical pulse equalizers and receiver shaping filters in long-haul coherent lightwave transmission systems are discussed. Possible application of basic resonators comprising of optical phase modulators as tunable optical filters for spectrum analyzers is also considered. >

Journal ArticleDOI
01 Apr 1994
TL;DR: In this article, an outer product expansion method for expanding the multidimensional array as the sum of outer products of 1D arrays (vectors) was proposed, which can reduce the difficult problem of designing a variable 1D digital filter to the easy one that only needs constant 1D filter designs and 1D polynomial approximations.
Abstract: Digital filters with adjustable frequency domain characteristics are referred to as variable digital filters. Variable filters are useful in the applications where the filter characteristics are required to be changeable during the course of signal processing. Especially in real time applications, variable filters are needed to change their coefficients instantaneously such that the real time signal processing can be performed. The present paper proposes a very efficient technique for variable 1D digital filter design. Generally speaking, the variable coefficients of variable digital filters are multidimensional functions of a set of spectral parameters which define the desired frequency domain characteristics. The authors first sample the given variable 1D magnitude specification and use the samples to construct a multidimensional array, then propose an outer product expansion method for expanding the multidimensional array as the sum of outer products of 1D arrays (vectors). Based on the outer product expansion, one can reduce the difficult problem of designing a variable 1D digital filter to the easy one that only needs constant 1D filter designs and 1D polynomial approximations. The technique can obtain variable 1D filters having arbitrary desired magnitude characteristics with a high design accuracy. >

Proceedings ArticleDOI
23 May 1994
TL;DR: In this paper, a two-pole comb-line filter is proposed for portable telephones, where parallel stripline sections of stepped impedance resonators are coupled electromagnetically to form an attenuation pole.
Abstract: A filter named as a stepped impedance comb-line filter is proposed. The parallel stripline sections of stepped impedance resonators are coupled electromagnetically to form an attenuation pole. The design procedure for a two-pole planar filter is derived from an analysis using the even and odd-mode impedances. The experimental filters were constructed by ceramic lamination technique and they exhibited performances suitable for portable telephones. >

Journal ArticleDOI
TL;DR: Several types of new and useful 3D LCR prototype filters are proposed and classified and a technique for implementing the 3D filter transfer functions is proposed that employs 3D differential or 3D integral operators, leading to highly-parallel and modular 3D recursive filters that are efficient in computation.
Abstract: Applications of three-dimensional (3D) LCR prototype networks in the design of 3D recursive filters are reviewed and several types of new and useful 3D LCR prototype filters are proposed and classified. These 3D LCR prototype filters can be used to design 3D recursive filters for the processing of image sequences involving 3D spatio-temporal-domain linear-trajectory (LT) and planar-wave (PW) component signals. Among the new proposed filters, a 3D planar-rejection (PR) filter can be used to reject an undesired spatially-varying or spatially-static background LT component signal; a 3D planar-pass/planar-rejection (PP-PR) filter can be tuned to enhance a desired 3D LT component signal and, at the same time, reject an undesired 3D LT component signal. A technique for implementing the 3D filter transfer functions is proposed that employs 3D differential or 3D integral operators, leading to highly-parallel and modular 3D recursive filter structures that are efficient in computation. A simple design procedure is described and examples of image sequence processing are given. >

Proceedings ArticleDOI
31 Oct 1994
TL;DR: In this paper, a simple quadratic filter was used in place of the linear high-pass filter for contrast enhancement of noise free images, and a further modification to make the overall approach considerably less sensitive to noise is then proposed.
Abstract: The classical unsharp masking method of image contrast enhancement is based on the addition of an amplitude scaled linear highpass filtered version of the image to itself However, the highpass filter also enhances noise components present in the image Some improvement in the quality of the enhancement has been obtained using a fairly simple quadratic filter in place of the linear highpass filter The authors first explain why the linear unsharp masking performs well for contrast enhancement of noise free images A further modification to make the overall approach considerably less sensitive to noise is then proposed A general class of quadratic filters utilizing Weber's law is also introduced and their important properties are discussed The modified unsharp masking scheme together with the proposed class of quadratic filters is shown to provide significant improvement in the quality of enhanced images compared to that obtained using similar approaches >

Journal ArticleDOI
TL;DR: In this paper, the design and implementation of single-ended and fully-differential switched current (SI) biquadratic high-Q bandpass filters to meet the specifications of the dual-tone multiple-frequency (DTMF) system are presented.
Abstract: The design and implementation of single-ended and fully-differential switched current (SI) biquadratic high-Q bandpass filters to meet the specifications of the dual-tone multiple-frequency (DTMF) system are presented. Both designs use the regulated-gate cascode (RGC) dynamic current mirror to obtain center frequency accuracy of 0.1% and a quality factor of 24. Compared to the equivalent switched capacitor (SC) implementation of these filters, the single-ended SI filter requires 30% less area for the same minimum-sized capacitance, power dissipation and performance. >

Proceedings ArticleDOI
J. Princen1
25 Oct 1994
TL;DR: In this paper, an approach to non-uniform filter bank design based on modulated filters and the principle of adjacent channel aliasing cancellation is presented, which is a generalization of psuedo QMF designs to nonuniform channel arrangements.
Abstract: In this paper we present an approach to nonuniform filter bank design based on modulated filters and the principle of adjacent channel aliasing cancellation. The approach is a generalization of psuedo QMF designs to nonuniform channel arrangements and the essential idea is to form nonuniform filter banks from uniform sections joined by 'transition' filters. All channel filters are formed by modulating lowpass prototypes. The approach provides a computationally simple method for designing filter banks with large numbers of channels because of the fact that channel filters are modulated from a few lowpass prototypes and because the lowpass prototype designs can be scaled. The technique can be used to produce integer decimation factor designs directly and excellent rational decimation factor designs by combining channel outputs using an inverse polyphase transform. >

Proceedings ArticleDOI
30 May 1994
TL;DR: A class of approximately linear phase recursive digital filters composed of two allpass sections is introduced, and there exists an analytic formula relating the squared-magnitude response to the passband ripple and the zero locations, making the filter optimization very fast.
Abstract: A class of approximately linear phase recursive digital filters composed of two allpass sections is introduced. The passband response for these filters is equiripple with the maximum number of alternations as for elliptic filters. By slightly widening the passband region and transferring some zeros close to the poles, the poles are forced to move to locations generating an approximately linear phase in the specified passband. For this class of filters, there exists an analytic formula relating the squared-magnitude response to the passband ripple and the zero locations, making the filter optimization very fast. Several examples illustrate that, especially in narrowband applications, these filters are superior to linear-phase non-recursive filters and phase equalized elliptic filters. >

Journal ArticleDOI
TL;DR: In this article, a polarization-insensitive optical bandpass filter in indium phosphide (InP) with a 3 dB bandwidth of 1.5 nm at a center wavelength of 1498 μm is presented.
Abstract: We demonstrate a polarization‐insensitive optical bandpass filter in indium phosphide (InP) with a 3 dB bandwidth of 1.5 nm at a center wavelength of 1.498 μm. The 5‐mm‐long filter is based on a grating‐assisted vertical directional coupler and features a novel double‐periodic coupling grating.

Proceedings ArticleDOI
01 Jan 1994
TL;DR: In this paper, a new class of SAW filters, balanced bridge impedance element filters (BEMF filters), is proposed, which have numerous advantages: low insertion loss, extremely small size and weight, a wide variety of center frequencies and passbands, excellent suppression in the stopband and no external matching circuits.
Abstract: Over the last few years a new generation of Surface Acoustic Wave (SAW) devices with low loss and operating at high frequency have been invented to meet the demand of mobile communication systems. In this work we discuss a new class of SAW filters-balanced bridge impedance element filters,-which have numerous advantages: low insertion loss, extremely small size and weight, a wide variety of center frequencies and passbands, excellent suppression in the stopband and no external matching circuits

Proceedings ArticleDOI
01 Jan 1994
TL;DR: In this article, the L and S band low-loss filters using one-port SAW resonators in a ladder circuit structure were developed. But the insertion loss of the narrow band filter was 6 dB.
Abstract: This paper describes L and S band low-loss filters using one-port SAW resonators in a ladder circuit structure. Four kinds of filters were developed. Three types have a wide frequency band, with fractional bandwidth of about 4%. A 36d y-x LiTaO3 substrate was used for these. The last type of filter has a narrow frequency band, with 0.03% of fractional bandwidth, and used an ST-cut quartz substrate. To design these ladder type SAW filters, several important factors were considered, the static capacitance of IDT, the period of IDT and film thickness. For fabrication, i-line stepper and reactive ion etching was used to delineate fine IDT patterns with line and gap width of 0.4 to 0.7 mm. Minimum insertion losses of 2 dB were obtained for the three wide band filters. The insertion loss of the narrow band filter was 6 dB. The input and output impedance of these filters were 50 O. The filters were mounted in 3 mmt3 mmt1 mm or 3.8 mmt3.8 mmt1.5 mm SMT packages

Journal ArticleDOI
TL;DR: It is shown that the errors in differentiation can be corrected using filters that preserve polynomials up to a given order, and a condition for the validity domain of these filters is derived, involving some characteristics of the filter and of the shape.
Abstract: Reliable derivatives of digital images have always been hard to obtain, especially (but not only) at high orders. We analyze the sources of errors in traditional filters, such as derivatives of the Gaussian, that are used for differentiation. We then study a class of filters which is much more suitable for our purpose, namely filters that preserve polynomials up to a given order. We show that the errors in differentiation can be corrected using these filters. We derive a condition for the validity domain of these filters, involving some characteristics of the filter and of the shape. Our experiments show a very good performance for smooth functions. >

Journal ArticleDOI
TL;DR: The composite wavelet-matched filter as mentioned in this paper is a combination of the wavelet matched filters that yields desired outputs for a given set of training mages, which performs the continuous wavelet transform for edge feature enhancement and the correlation between two wavelet transforms for pattern recognition in a single step.
Abstract: The wavelet-matched filter performs the continuous wavelet transform for edge feature enhancement and the correlation between two wavelet transforms for pattern recognition in a single step. The composite wavelet-matched filter is a combination of the wavelet-matched filters, that yields desired outputs for a given set of training mages. We present the definition, the iterative design algorithm, the quasi-orthogonality of the components, and the optical implementation of the composite wavelet-matched filter. The filter yields a sharp correlation peak at the origin without sidelobe. A comparison between the composite wavelet-matched filter with the conventional composite filter is also given.