Dissertations / Theses on the topic '2-D Signals'

Le présent travail porte sur la localisation incrémentale et absolue d'un robot mobile dans un environnement d'intérieur partiellement modélisé en utilisant la vision monoculaire. L'environnement de navigation du robot est à base de primitives géométriques (segments). Il intègre la notion d'occultation grâce à un découpage de l'espace 2-D navigable en Régions d'Invariance Visuelle. Le modèle de caméra à perspective pleine est obtenu grâce au calibrage par la méthode de Zhang. L'approche adoptée est composée de quatre étapes : acquisition d'une image à partir de la position courante du robot, extraction des primitives observées, mise en correspondance des primitives de l'image avec celles du modèle et calcul de la position et de l'orientation de la caméra. Deux méthodes numériques de calcul de la position et de l'orientation de la caméra grâce à des correspondances de droites sont présentées est adaptées au cas spécifique de la robotique mobile. Enfin, un algorithme de mise en correspondance des segments de l'image avec ceux du modèle est défini. Il est basé sur la recherche dans un arbre d'interprétation. Les Régions d'Invariance Visuelle et la configuration du système sont utilisées pour réduire l'espace des correspondances. Des contraintes géométriques d'ordre un et deux sont définies pour assurer l'élagage rapide de l'arbre. Une nouvelle fonction de vérification de la cohérence globale permet de sélectionner l'hypothèse de correspondance la plus cohérente.

Cette thèse détaille la conception, le développement et l'analyse d'un nouvel outil de caractérisation des textures exploitant les modèles de prédiction linéaire complexe sur les espaces couleur perceptuels séparant l'intensité lumineuse de la partie chromatique. Des modèles multicanaux 2-d causaux et non-causaux ont été utilisés pour l'estimation simultanée des densités spectrales de puissance d'une image " bi-canal ", le premier contenant les valeurs réelles de l'intensité et le deuxième les valeurs complexes de la partie chromatique. Les bonnes performances en terme de biais et de variance de ces estimations ainsi que l'usage d'une distance appropriée entre deux spectres assurent la robustesse et la pertinence de l'approche pour la classification de textures. Une mesure de l'interférence existante entre l'intensité et la partie chromatique à partir de l'analyse spectrale est introduite afin de comparer les transformations associées aux espaces couleur. Des résultats expérimentaux en classification de textures sur différents ensembles de tests, dans différents espaces couleur (RGB, IHLS et L*a*b*) sont présentés et discutés. Ces résultats montrent que la structure spatiale associée à la partie chromatique d'une texture couleur est mieux caractérisée à l'aide de l'espace L*a*b* et de ce fait, cet espace permet d'obtenir les meilleurs résultats pour classifier les textures à l'aide de leur structure spatiale et des modèles de prédiction linéaire. Une méthode bayésienne de segmentation d'images texturées couleur a aussi été développée à partir de l'erreur de prédiction linéaire multicanale. La contribution principale de la méthode réside dans la proposition d'approximations paramétriques robustes pour la distribution de l'erreur de prédiction linéaire multicanale : la distribution de Wishart et une approximation multimodale exploitant les lois de mélanges gaussiennes multivariées. Un autre aspect original de l'approche consiste en la fusion d'un terme d'énergie sur la taille des régions avec l'énergie du modèle de Potts afin de modéliser le champ des labels de classe à l'aide d'un modèle de champ aléatoire possédant une distribution de Gibbs. Ce modèle de champ aléatoire est ainsi utilisé pour régulariser spatialement un champ de labels initial obtenu à partir des différentes approximations de la distribution de l'erreur de prédiction. Des résultats expérimentaux en segmentation d'images texturées couleur synthétiques et d'images satellites hautes résolutions QuickBird et IKONOS ont permis de valider l'application de la méthode aux images fortement texturées. De plus les résultats montrent l'intérêt d'utiliser les approximations de la distribution de l'erreur de prédiction proposées ainsi que le modèle de champ de labels amélioré par le terme d'énergie qui pénalise les petites régions. Les segmentations réalisées dans l'espace L*a*b* sont meilleures que celles obtenues dans les autres espaces couleur (RGB et IHLS) montrant à nouveau la pertinence de caractériser les textures couleur par la prédiction linéaire multicanale complexe à l'aide de cet espace couleur.

<p>Beamforming of ultrasound signals in the presence of clutter, or partial aperture blockage by an acoustic obstacle can lead to reduced visibility of the structures of interest and diminished diagnostic value of the resulting image. We propose new beamforming methods to recover the quality of ultrasound images under such challenging conditions. Of special interest are the signals from large apertures, which are more susceptible to partial blockage, and from commercial matrix arrays that suffer from low sensitivity due to inherent design/hardware limitations. A coherence-based beamforming method designed for suppressing the in vivo clutter, namely Short-lag Spatial Coherence (SLSC) Imaging, is first implemented on a 1-D array to enhance visualization of liver vasculature in 17 human subjects. The SLSC images show statistically significant improvements in vessel contrast and contrast-to-noise ratio over the matched B-mode images. The concept of SLSC imaging is then extended to matrix arrays, and the first in vivo demonstration of volumetric SLSC imaging on a clinical ultrasound system is presented. The effective suppression of clutter via volumetric SLSC imaging indicates it could potentially compensate for the low sensitivity associated with most commercial matrix arrays. The rest of the dissertation assesses image degradation due to elements blocked by ribs in a transthoracic scan. A method to detect the blocked elements is demonstrated using simulated, ex vivo, and in vivo data from the fully-sampled 2-D apertures. The results show that turning off the blocked elements both reduces the near-field clutter and improves visibility of anechoic/hypoechoic targets. Most importantly, the ex vivo data from large synthetic apertures indicates that the adaptive weighing of the non-blocked elements can recover the loss of focus quality due to periodic rib structure, allowing large apertures to realize their full resolution potential in transthoracic ultrasound.</p><br>Dissertation

碩士<br>中原大學<br>電子工程研究所<br>94<br>With the advent of digital television, the digitization of a traditional analog NTSC (National Television System Committee) composite video signal television system is needed. In other words, a video decoder receives digital composite video signals. The separation effect of Y/C Separator in video decoder will affect output image quality seriously. In this paper, we propose a new method to improve the video quality of NTSC composite video signals in television system. Our objective is to solve the cross-chrominance problem caused by conventional luminance (Y) and chrominance (C) Separation effect. Our Y/C separation approach uses 2-D adaptive comb filter separation techniques for static images applications. Simulation results show that it can achieve excellent output video quality than traditional Y/C Separators.

Speech signals possess a rich time-varying spectral content, which makes their analysis a challenging signal processing problem. Developing methods for accurate speech analysis has a direct impact on applications such as speech synthesis, speaker recognition, speech recognition, voice morphing, etc. A widely used tool to visualize the time-varying spectral content is the spectrogram, which represents the spectral content of the signal in the joint time-frequency plane. A spectrogram can be viewed as a collection of several localized spectrotemporal patches. By analyzing the structure of two-dimensional (2-D) patterns in the spectrogram, we propose modeling it using 2-D amplitude-modulated and frequency-modulated (AM-FM) sinusoids. The justification for the 2-D AM-FM model for speech can be provided based on the physical process behind its generation. From a speech production perspective, the AM and FM components correspond to the vocal-tract smooth envelope and excitation signal, respectively. We demonstrate that analyzing speech jointly in time and frequency reveals several important characteristics, which are otherwise not evident either in purely time-domain or frequency-domain analysis. The central problem in this dissertation is 2-D demodulation of a speech spectrogram, which yields 2-D AM and FM components. We advocate the use of the Riesz transform, which is a 2-D extension of the Hilbert transform, to demodulate narrowband and pitch adaptive spectrograms. Interestingly, the 2-D AM and FM components obtained as a result of demodulation have potential benefits for speech analysis. We demonstrate the impact of the proposed modeling technique for vocal tract filter estimation, voiced/unvoiced component separation, pitch tracking, speech synthesis, and periodic/aperiodic decomposition of speech signals. The accuracy of the estimated speech parameters is validated considering the task of speech reconstruction. The first part of the thesis is focused on theoretical developments related to 2-D modeling. We consider prototypical 2-D cosine signals, analyze their Fourier transform properties, solve the problem of demodulation of a 2-D AM-FM cosine signal and extend the model to spectrotemporal patches. Following this, we examine the taxonomy of time-frequency patterns in the FM component, highlighting the salient attributes of different types of phonation in speech. We show that 2-D patterns specific to different speech sounds (voiced/unvoiced) can be captured by computing two novel time-frequency maps from the 2-D FM component: the coherencegram and orientationgram. The usefulness of the maps is demonstrated for the problem of periodic and aperiodic decomposition of speech signals. In the second part, we use the FM component for estimating the source parameters. We show that the FM component is a rich representation of the source signal in 2-D and use it to estimate the speaker’s fundamental frequency (or pitch), speech aperiodicity, and voiced/unvoiced segmentation of the speech signal. We propose novel spectrotemporal features for voiced and unvoiced segmentation of speech. In contrast to time-domain features such as short-time energy, zero crossings, and autocorrelation coefficients, the proposed features are relatively insensitive to local variations of the speech waveform. The FM component is obtained by demodulating the narrowband speech spectrogram, which exhibits high frequency resolution. Consequently, the FM component encodes the speaker’s pitch. Hence, we propose methods for estimating the pitch from the FM component. Another critical component of a speech signal is its aperiodicity. Voiced sounds are quasi-periodic and have a noise component of strength relatively weaker than unvoiced sounds. Utilizing the time-frequency properties of the FM component, we propose methods for the estimation of speech aperiodicity. While the FM component is used to estimate the source parameters, the 2-D AM component models the slowly varying vocal-tract filter. However, estimation of the vocal-tract filter is challenging due to its interaction with the quasi-periodic excitation. Two issues arise in this context: the first one is related to the length of the analysis window used for computing the spectrogram. We argue that a fixed-length analysis window is not ideal for vocal tract estimation. We show that the best results can be obtained by adapting the window length to the speaker’s pitch while computing the spectrogram. Such a spectrogram is referred to as the pitch-adaptive spectrogram. The second issue is related to the processing involved in demodulation, which has the undesirable effect of broadening the formant bandwidths. Hence, we propose a method to compensate for the formant broadening. It is crucial to estimate the optimum formant bandwidths as they determine the shape of the vocal tract filter and govern speech intelligibility during synthesis. The effectiveness of the estimated source and filter parameters is shown by incorporating them in a spectral synthesis model and a neural vocoder for speech reconstruction. For neural vocoder, we use WaveNet, which is a deep generative model for audio generation. By conditioning the model on acoustic features, one can guide WaveNet to produce realistic speech waveforms. We use the Riesz transform-based acoustic features as conditional features in WaveNet vocoder. The quality of generated speech waveforms is evaluated by using objective and subjective measures.

The Fourier transform (spectrum) of a signal is a complex function and is characterized by the magnitude and phase spectra. Phase retrieval is the reconstruction of the phase spectrum from the measurements of the magnitude spectrum. Such problems are encountered in imaging modalities such as X-ray crystallography, frequency-domain optical coherence tomography (FDOCT), quantitative phase microscopy, digital holography, etc., where only the magnitudes of the wavefront are detected by the sensors. The phase retrieval problem is ill-posed in general, since an in nite number of signals can have the same magnitude spectrum. Typical phase retrieval techniques rely on certain prior knowledge about the signal, such as its support or sparsity, to reconstruct the signal. A classical result in phase retrieval is that minimum-phase signals have log-magnitude and phase spectra that satisfy the Hilbert integral equations, thus facilitating exact phase retrieval. In this thesis, we demonstrate that there exist larger classes of signals beyond minimum-phase signals, for which exact phase retrieval is possible. We generalize Hilbert integral equations to 2-D, and also introduce a variant that we call the composite Hilbert transform in the context of 2-D periodic signals. Our first extension pertains to a particular type of parametric modelling of 2-D signals. While 1-D minimum-phase signals have a parametric representation, in terms of poles and zeros, there exists no such 2-D counterpart. We introduce a new class of parametric 2-D signals that possess the exact phase retrieval property, that is, their magnitude spectrum completely characterizes the signal. Starting from the magnitude spectrum, a sequence of non-linear operations lead us to a sum-of-exponentials signal, from which the parameters are computed employing concepts from high-resolution spectral estimation such as the annihilating filter and algebraically coupled matrix-pencil methods. We demonstrate that, for this new class of signals, our method outperforms existing techniques even in the presence of noise. Our second extension is to continuous-domain signals that lie in a principal shift-invariant space spanned by a known basis. Such signals are characterized by the basis combining coefficients. These signals need not be minimum-phase, but certain conditions on the coefficients lead to exact phase retrieval of the continuous-domain signal. In particular, we introduce the concept of causal, delta dominant (CDD) sequences, and show that such signals are characterized by their magnitude spectra. This condition pertains to the time/spatial-domain description of the signal, in contrast to the minimum-phase condition, which is described in the spectral domain. We show that there exist CDD sequences that are not minimum-phase, and vice versa. However, finite-length CDD sequences are always minimum-phase. Our method reconstructs the signal from the magnitude spectrum up to ma-chine precision. We thus have a class of continuous-domain signals that are neither causal nor minimum phase, and yet allow for exact phase retrieval. The shift-invariant structure is applicable to modelling signals encountered in imaging modalities such as FDOCT. We next present an application of 2-D phase retrieval to continuous-domain CDD signals in the context of quantiative phase microscopy. We develop sufficient conditions on the interfering reference wave for exact phase retrieval from magnitude measurements. In particular, we show that when the reference wave is a plane wave with magnitude greater that the intensity of the object wave, and when the carrier frequency is larger than the band-width of the object wave, we can reconstruct the object wave exactly. We demonstrate high-resolution reconstruction of our method on USAF target images. Our final and perhaps the most unifying contribution is in developing Hilbert integral equations for 2-D first-quadrant signals and in introducing the notion of generalized minimum-phase signals for both 1-D and 2-D signals. For 2-D continuous-domain, first-quadrant signals, we establish partial Hilbert transform relations between the real and imaginary parts of the spectrum. In the context of 2-D discrete-domain signals, we show that the partial Hilbert transform does not suffice and introduce the notion of composite Hilbert transform and establish the integral equations. We then introduce four classes of signals (combinations of 1-D/2-D and continuous/discrete-domain) that we call generalized minimum-phase signals, which satisfy corresponding Hilbert integral equations between log-magnitude and phase spectra, hence facilitating exact phase retrieval. This class of generalized minimum-phase signals subsumes the well known class of minimum-phase signals. We further show that, akin to minimum-phase signals, these signals also have stable inverses, which are also generalized minimum-phase signals.

The Fourier transform (spectrum) of a signal is a complex function and is characterized by the magnitude and phase spectra. Phase retrieval is the reconstruction of the phase spectrum from the measurements of the magnitude spectrum. Such problems are encountered in imaging modalities such as X-ray crystallography, frequency-domain optical coherence tomography (FDOCT), quantitative phase microscopy, digital holography, etc., where only the magnitudes of the wavefront are detected by the sensors. The phase retrieval problem is ill-posed in general, since an in nite number of signals can have the same magnitude spectrum. Typical phase retrieval techniques rely on certain prior knowledge about the signal, such as its support or sparsity, to reconstruct the signal. A classical result in phase retrieval is that minimum-phase signals have log-magnitude and phase spectra that satisfy the Hilbert integral equations, thus facilitating exact phase retrieval. In this thesis, we demonstrate that there exist larger classes of signals beyond minimum-phase signals, for which exact phase retrieval is possible. We generalize Hilbert integral equations to 2-D, and also introduce a variant that we call the composite Hilbert transform in the context of 2-D periodic signals. Our first extension pertains to a particular type of parametric modelling of 2-D signals. While 1-D minimum-phase signals have a parametric representation, in terms of poles and zeros, there exists no such 2-D counterpart. We introduce a new class of parametric 2-D signals that possess the exact phase retrieval property, that is, their magnitude spectrum completely characterizes the signal. Starting from the magnitude spectrum, a sequence of non-linear operations lead us to a sum-of-exponentials signal, from which the parameters are computed employing concepts from high-resolution spectral estimation such as the annihilating filter and algebraically coupled matrix-pencil methods. We demonstrate that, for this new class of signals, our method outperforms existing techniques even in the presence of noise. Our second extension is to continuous-domain signals that lie in a principal shift-invariant space spanned by a known basis. Such signals are characterized by the basis combining coefficients. These signals need not be minimum-phase, but certain conditions on the coefficients lead to exact phase retrieval of the continuous-domain signal. In particular, we introduce the concept of causal, delta dominant (CDD) sequences, and show that such signals are characterized by their magnitude spectra. This condition pertains to the time/spatial-domain description of the signal, in contrast to the minimum-phase condition, which is described in the spectral domain. We show that there exist CDD sequences that are not minimum-phase, and vice versa. However, finite-length CDD sequences are always minimum-phase. Our method reconstructs the signal from the magnitude spectrum up to ma-chine precision. We thus have a class of continuous-domain signals that are neither causal nor minimum phase, and yet allow for exact phase retrieval. The shift-invariant structure is applicable to modelling signals encountered in imaging modalities such as FDOCT. We next present an application of 2-D phase retrieval to continuous-domain CDD signals in the context of quantiative phase microscopy. We develop sufficient conditions on the interfering reference wave for exact phase retrieval from magnitude measurements. In particular, we show that when the reference wave is a plane wave with magnitude greater that the intensity of the object wave, and when the carrier frequency is larger than the band-width of the object wave, we can reconstruct the object wave exactly. We demonstrate high-resolution reconstruction of our method on USAF target images. Our final and perhaps the most unifying contribution is in developing Hilbert integral equations for 2-D first-quadrant signals and in introducing the notion of generalized minimum-phase signals for both 1-D and 2-D signals. For 2-D continuous-domain, first-quadrant signals, we establish partial Hilbert transform relations between the real and imaginary parts of the spectrum. In the context of 2-D discrete-domain signals, we show that the partial Hilbert transform does not suffice and introduce the notion of composite Hilbert transform and establish the integral equations. We then introduce four classes of signals (combinations of 1-D/2-D and continuous/discrete-domain) that we call generalized minimum-phase signals, which satisfy corresponding Hilbert integral equations between log-magnitude and phase spectra, hence facilitating exact phase retrieval. This class of generalized minimum-phase signals subsumes the well known class of minimum-phase signals. We further show that, akin to minimum-phase signals, these signals also have stable inverses, which are also generalized minimum-phase signals.

碩士<br>國立交通大學<br>控制工程系<br>85<br>In this thesis, we discuss two-dimensional direction estimation by using a fuzzy neural network(FNN). We can track high speed moving target with highresolutions by FNN for its mapping capacity. Furthermore, the array geometry can be quite free, and fewer sensors are necessary comparing to classicazimuth/ elevation direction finding using uniformly regular array. Also, wedemostrate, in a coherent enviornment, how FNN can outperform conventional eigenstructure-based methods with spatial smoothing scheme in dealing with low angle tracking problem.

Thesis (M.S.)--Florida State University, 2005.<br>Advisor: Dr. Simon Foo, Florida State University, College of Engineering, Dept. of Electrical and Computer Engineering. Title and description from dissertation home page (viewed June 7, 2005). Document formatted into pages; contains xi, 87 pages. Includes bibliographical references.

碩士<br>國立交通大學<br>電信工程系所<br>95<br>The electrocardiogram (ECG) is an important biomedical signal for the diagnosis of heart diseases. Efficicient ECG waveform coding for long-term recording and effective real-time transmission have received constant intensive attention in modern clinical applications. In this thesis, we propose two new ECG waveform coding methods that require reduced memory and provide high compression ratio (CR) performance. The first approach uses a variable sampling rate analog-to-digital converter that adapts to the waveform variation rate. It reduces not only the computational complexity but also the memory requirement for subsequent discrete cosine transform as well. The second approach is based on the observation that ECG signals often exhibit a near-periodic behavior. We first convert the one-dimensional ECG waveform into a two dimensional (2D) array by the Average Magnitude Difference Function (AMDF) method then apply a two dimension time/frequency transform to increase CR as much as possible. The resulting CR is about 21.87 and the percent-root-mean-square (PRD) is 3.25% which is much better than that of the 1-D approach based on adaptive sampling. In order to further improve the performance of the 2-D approach and capture the important part of ECG signals (QRS wave), we employ a sample-dependent multi-rate quatization approach which gives an improved CR of 22.05 and PRD of 2.88%.

碩士<br>國立交通大學<br>電機與控制工程系<br>88<br>The aim of this thesis is to employ signal processing techniques to analyze the spatio-spectral correlation of multi-channel EEG (electroencephalograph) signals. In this thesis, we present two methods, the coherence and the 2-D FFT, to analyze the EEG’s spatial characteristics. Conventional 1-D Fourier transform（FT）cannot directly provide information of the spectral property varying with the EEG electrodes. Coherence analysis provides a technique for estimating the degree of local spatial correlation between two channels. This study was focused on the meditation EEG signals. We utilized the grayscale image to display the result. The display method allows us to easily visualize the intensity and distribution of coherence changes. Alternatively, 2-D FFT provides a tool to illustrate the channel-to-channel variability of the frequency contents of EEG signals. A coefficient called the “synchronization coefficient ( SC )” was proposed and validated by simulation studies. The evaluation approach was then applied to multi-channel EEG signals to monitor the synchronization of spectral property among channels.

碩士<br>國立中興大學<br>電機工程學系<br>87<br>Abstract 2-D semiconductor device simulations are used to study uniform doped GaAs MESFETs in this thesis. The primary function of simulations is to solve the basic governing equations in a self —consistent way and obtain the electrostatic potentials and carrier concentrations, respectively. Thus, several GaAs MESFETs with different structure have been simulated for both small-signal and large-signal behavior. A “software” cold FET method is incorporated into the de-embedding process to extract the extrinsic source and drain resistance. Intrinsic circuit parameters are then converted from the calculated intrinsic Y parameters. Circuit parameters as a function of bias voltages for uniform doped MESFETs are presented. The gate-drain avalanche breakdown was studied in detail by performing 2-D numerical simulations of narrow and wide recessed-gate MESFETs. These simulation demostrated that the breakdown occurs at the drain-side edge of the gate. The relations between device design parameters and circuit parameters can be established by using the approach in the thesis.

碩士<br>國立中山大學<br>電機工程學系研究所<br>96<br>The main purpose of this thesis is to combine modified GML algorithm with 2-D simulated annealing for estimation of signal arrival time in the UWB systems.In a dense multipath environment, the generalized maximum-likelihood (GML) algorithm can be used for the time-of-arrival (TOA) estimation. Nevertheless, the GML algorithm usually takes a long period of time, and sometimes fails to converge. Hence, a modified GML (MGML) algorithm is investigated. Two threshold parameters need to be determined in using the estimation algorithm. One threshold is to decide the arrival time range of estimated path, and the other, an amplitude threshold, is to judge whether the estimated path is true. Generally, the decision rule of thresholds may be based on the minimum error probability, which is defined as the sum of false alarm probability and miss probability. To mitigate the effects from noise and dense multipath interference, and to reduce the computational complexity of the algorithm, a method of threshold settings based on the minimum root mean square error (RMSE) criteria is discussed. In this scheme, the RMSE value for each candidate threshold pair in an appropriate region is computed. Constructing an accurate RMSE table and performing a full-scale grid search of adequate threshold settings can be very time-consuming. A 2-D simulated annealing process is adopted for finding the best pair of thresholds for use in the modified GML algorithm. The simulated annealing, different from the gradient descent, can avoid trapping into a local minimum in finding the best threshold pair. The resulting threshold pair makes the modified GML algorithm become more efficient in estimating the signal arrival time with an automatic search manner. Simulation results show that the proposed scheme can achieve better performance than the grid search approaches in UWB environments.

Στην παρούσα διπλωματική εργασία παρουσιάζεται ο σχεδιασμός και η υλοποίηση ενός καινοτόμου μετατροπέα σήματος (D/A converter ή DAC) με τη δυνατότητα εξωτερικής ρύθμισης (offline calibration) για μετατροπή υψηλής ακρίβειας, η οποία εξασφαλίζει υψηλή γραμμικότητα ανεξαρτήτως της ανοχής των στοιχείων που τον απαρτίζουν. Μόλις ο μετατροπέας ρυθμιστεί κατάλληλα, λειτουργεί αντίστοιχα με ένα DAC, όπου όλα τα στοιχεία του έχουν υποστεί επεξεργασία με λέιζερ (laser trimmed DAC), αλλά χωρίς το υψηλό κόστος κατασκευής που συνεπάγεται η παραπάνω διαδικασία, με αποτέλεσμα να αποτελεί μία ιδανική οικονομική λύση για εφαρμογές που απαιτούν υψηλή ακρίβεια μετατροπής.<br>This diploma thesis presents the design and implementation of an innovative Digital to Analog Converter (DAC) with the capability of offline external calibration for accurate measurements, which guarantees high linearity regardless of the mismatch of its components. Once the converter has been configured, it can attain the same linearity performance as a laser trimmed DAC, but without the high manufacturing costs involved in the laser etching process, making it an ideal low-cost solution for high accuracy applications.