Search

Philosophy should be understood with its accumulative structure. Thus, when one strives to understand a philosopher’s thoughts, he/she should not isolate the philosopher from the previous and contemporary theories in his/her era; and should take into account this accumulative and continuous structure. In this context, Kant’s, Bergson’s, and Iqbal’s understandings of time seem to have continuity in themselves, even if they might be seen as having incompatible points. Kant’s understanding of time can be considered in two periods as pre-Critical and Critical. In the former, Kant accepts the own-reality and existence of time itself, outside of the human mind. But he also sows the seed of an understanding of time as a prior intuition to all sensations, while he is still in his pre-critical period. Hence, his focus seems to have shifted to a subject-centred approach. In his critical period, subject-centrality becomes more obvious and Kant claims that time is prior to any externality. According to him, time locates things in simultaneity and succession for the perception of mind as a sensible intuition. Bergson, on the other hand, clearly exploits Kant, even though he criticizes Kant in many aspects. Bergson’s understanding of time is comprised of two components: Pure duration and homogenous time. Pure duration is affected by the Kantian conception of time in the sense of being subject-centred. It is the time that each consciousness has individually as a combination of one’s past and present in a whole; and it is, in its essence, heterogeneous, unorderly successive, and indivisible. Homogenous time has its roots, again, in Kant’s thoughts in the sense of being serial and simultaneous. It is the impersonal common ground for individuals on which pure durations can work in a harmony. When it comes to Iqbal, he benefits from both Kant’s time as a form of sensible intuition and Bergson’s pure duration. Iqbal, by using both of these concepts of time, reconstructs the Divine Time in Islamic thought, and thus, freewill. By means of pure duration and creativity, mechanical understanding of the universe is refused by Bergson and Iqbal. By doing so, Iqbal allows freewill to permeate through pure duration of the God, namely the Divine Time, and to penetrate into pure durations of all egos. Throughout this article, we mainly intend to retrace Iqbal’s reconstruction of freewill by having use of the concept of pure duration, and the Divine Time as pure duration of the God., Felsefe, kümülatif yapısı ile ele alınmalıdır. Bu yüzden, bir filozofun düşünceleri anlaşılmak istendiğinde, o kendi çağındaki mevcut ve geçmiş teorilerden soyutlanmamalı ve bu kümülatif ve devamlılık arz eden yapı dikkate alınarak incelenmelidir. Bu bağlamda, Kant, Bergson ve İkbal’in zaman anlayışları, bazı uyumsuz noktalara sahip gibi anlaşılabilseler de, dikkatle incelendiğinde birbirleri arasında bir devamlılığın bulunduğu göze çarpar. Kant’ın zaman anlayışı, Kritik öncesi ve Kritik dönemi olmak üzere iki dönemde incelenebilir. Kritik öncesi döneminde Kant, zamanın insan zihninin dışında kendinde bir gerçekliğe ve varlığa sahip olduğunu kabul eder. Fakat Kant, zamanı bütün duyuları önceleyen bir görü olarak anlamasının tohumlarını da hala Kritik öncesi dönemde iken eker. Bu doğrultuda, onun odağı özneyi merkeze alan bir tutuma doğru ilerler görünür. Kritik döneminde özne merkezci konumu daha da belirginleşir ve Kant, zamanın bütün dışsallıkları öncelediğini iddia eder. Ona göre zaman, duyulur bir görü olarak, eşyayı zihnin algılayabilmesi için eşzamanlılık ve ardışıklık içinde konumlandırır. Diğer taraftan Bergson, Kant’ı pek çok açıdan eleştirmekle beraber onun düşüncelerinden açık bir şekilde faydalanır. Bergson’un zaman anlayışı iki bileşenden oluşur: Salt süre ve homojen zaman. Salt süre, özne-merkezci olması bakımından üzerinde Kant’ın düşünce pratiğinin etkisinin görünür olduğu bir kavramsallaştırmadır. Bu, her bir bilincin, kişinin geçmiş ve şimdisini bir bütünde birleştirerek bireysel olarak sahip olduğu ve özünde heterojen, sırasız bir şekilde ardışık ve bölünemez zamandır. Homojen zaman ise sıralı ve eşzamanlı olması bakımından köklerini yine Kant’ta bulur. Homojen zaman, salt sürelerin uyum içinde çalışmasını sağlayan, bireyler için ortak zemini teşkil eden zamandır. Bu iki filozofun düşünceleri doğrultusunda İkbal’in zaman teorisi incelendiğinde, onun hem duyulabilir görünün bir formu olan Kant’ın zamanından hem de Bergson’un salt süresinden faydalandığı ortaya çıkar. İkbal, bu iki zaman anlayışını kullanarak İslam düşüncesinde İlahi Zaman’ı ve dolayısıyla da özgür iradeyi yeniden inşa eder. Salt süre ve yaratıcılık açısından, evrene yönelik mekanik bir anlayış Bergson ve İkbal tarafından reddedilir. Böylece İkbal, özgür iradenin Tanrı’nın salt süresi, yani İlahi Zaman, aracılığı ile yayılmasına ve tüm benliklere ait salt sürelere nüfuz etmesine izin verir. Biz, bu makale aracılığı ile, İkbal’in salt süre mefhumunu ve Tanrı’ya ait salt süre olarak İlahi Zaman’ı kullanarak özgür irade anlayışını yeniden inşa etmesinin köklerine gitmek niyetindeyiz.

Bu çalışmada Türkmen edebiyatının önde gelen isimlerinden Hıdır Deryayev’in Ikbal isimli romanı (birinci cilt) Türkiye Türkçesine aktarılmış ve dil yönünden incelenmiştir. Çalışmamız temel olarak Giriş, Dil İncelemesi, Metinler, Dizinler ve Sonuç olmak üzere beş ana bölümden oluşmaktadır. Giriş kısmında XX yüzyıl’dan bağımsızlık dönemine kadar Türkmen Edebiyatının tarihi kısaca anlatılmıştır. Hıdır Deryayev’in hayatı, eserleri ve incelememize konu olan metin ele alınmıştır. Dil İncelemesi bölümünde eser Ses Bilgisi ve Şekil Bilgisi alt başlıklarında ayrıntılı bir biçimde incelenmeye çalışılmıştır. Örnek cümlelerin aktarılmış şekilleri de verilmiştir. Metin bölümünde eserin transkripsiyonu ve Türkiye Türkçesine aktarması verilmiştir. Dizinler kısımında söz dizini ve özel adlar dizini bulunmaktadır. Sonuç bölümünde tüm bu çalışmaların neticesinde elde ettiğimiz bulgular maddeler halinde değerlendirilmiştir., The given study presents linguistic analysis and translation into Turkish of the first chapter of Hidir Deryayev’s novel, which was one of the first works in Turkmen literature. The dissertation is structured in five main chapters: Introduction, Linguistic analysis, Texts and Conclusion. Introduction part briefly describes the history of Turkmen literature from the beginning of 20th century till the independence period. There is also aimed to study Hidir Deryayev’s biography, works and texts which are the main part of our investigation. There is made an attempt to analyze phonetic and morphologic structures of this work, which are seperately titled. It also includes the samples of the translated sentences. Textual part has transcription and Turkish variant of translation of the work. The index section is alphabetically organized and contains phrase and proper noun indexation. In conclusion we listed all the results of analysis we have reached.

Doktora Tezi, Çalışmamız 20. yy. da İslam siyasi düşüncesine yeni bir dinamizm ve anlayış kazandıran M. İkbal'in siyaset felsefesini konu almaktadır. İkbal, İslam dünyasını içine düştüğü esaretten ve krizden kurtarmaya çalışarak Batı emperyalizmine karşı güçlü, gelişmiş, yüksek maneviyatlı, İslam ilkelerine bağlı, benliğini (şahsiyet) kazanmış bir ideal birlik toplum oluşturmak ister. Bu toplumu oluşturan bireyler Allah'a yaklaşarak özgürlüğe kavuşacak ve kendisini sınırlayan tüm maddi bağlardan kurtulacaktır. Bu bireylerin tek rehberi Kur'ân ve Hz. Peygamberin yüksek ahlakı ve şahsiyetidir. Böylece bireyler Kur'ân'ı içselleştirecek, Kâbe'yi manevi kardeşliğin sembolü ve yeryüzünü Müslümanların yurdu olarak benimseyecek, kaderciliği ve taklitçiliği kökten reddecektir. Ayrıca bu toplumun bireyleri güçlü, yaratıcı, özgür, dinamik, çalışkan, mücadeleci ve her türlü gelişmeye, değişmeye ve modernliğe açık bireyler olmalıdır. Bu sebeple İkbal, toplumdan ziyade toplumu oluşturan bireyler üzerine yoğunlaşır. İkbal'in öngördüğü insan modeli, kalbi ve ruhu diri, yüksek şahsiyet sahibi, vatan mefhumundan bağımsız, köleliği, ideolojik milliyetçiliği reddeden ve dünyada olup bitenlere karşı kayıtsız kalmayan bir insan modelidir. Söz konusu niteliklere sahip bireylerden oluşan topluluklar birleşerek ideal devleti meydana getirecektir. Bu devletin idaresi ise tek kişinin elinde değil, toplumun elindedir yani bu idare, Cumhuriyet sistemidir. Bu sistemde halk yönetime aktif olarak katılmalıdır. Bu Cumhuriyetler birleşerek İslam birliğini veya milli devleti oluşturmalıdırlar. Çünkü Müslümanlar parçalanamaz tek millettir. Bu millet şuuru ile hareket edilmeli, milli ahlak geliştirilmeli ve topluma sağlıklı nesiller yetiştiren kadınlar iyi bir eğitimle donatılmalıdır., Our study is about the political philosophy of Muhammed Iqbal who gave a new dynamism and understanding of Islamic political thought in the 20th century. Iqbal wants to create an ideal society that strong, developed, highly spiritualized, depended on the principles of Islam, and self-identity against Western imperialism by trying to free the Islamic world from its captivity and crisis. The individuals who make up this society will liberate themselves by getting close to Allah and get rid of all the material connection that limit themselves. The only guide for these people is the Qur'an and the moral superiority and personality of the Prophet. Thus, people will internalize the Qur'an and adopt the Kaaba as the symbol of spiritual brotherhood and the earth as the home of Muslims, and will radically reject fatalism and imitation. In addition, individuals of this society should be strong, creative, free, dynamic, hardworking, challenging, and open to all kinds of development, change and modernity. For this reason, Iqbal focuses on individuals who make society rather than society. The human model predicted by Iqbal is a model in which is alive heart and soul, has a strong personality, is independent of the notion of the motherland, denial of slavery and ideological nationalism, and not indifferent to what is happening in the world. The communities of individuals with these qualifications will form the ideal state by uniting. The administration of this state is not in the hands of a single person, but in the hands of society, that is, this administration is the Republic system. In this system, the public should actively participate in the administration. These republics should form the Islamic Union or the national state by uniting. Because Muslims are the only nation that cannot disintegrate. It should be acted with this national consciousness, national morality must be developed, and women who bring up reliable generations to society should be equipped with a good education.

Tez (yüksek lisans) -- Ondokuz Mayıs Üniversitesi, 2006 Libra Kayıt No: 17075 "Muhammed İkbal'de Tanrı Anlayışı" adını taşıyan ve iki ana bölümden oluşan çalışmamızın birinci bölümünde İkbal'in Tanrı'nın varlığına ilişkin kanıtları eleştirel olarak ele almasını ve değerlendirmesini tartıştık.Bu bölümde İkbal'in özellikle ontolojik , kozmolojik ve teknolojik kanıtları zayıf bulduğunu ve Tanrının varlığı lehinde kullanılabilecek kanıtlar olarak değerlendirmediğini gözlemledik.Bununla birlikte İkbal'in Tanrı-evren ilişkisi içinde yararlı bir kanıt olarak dinsel deneyimi kabul ettiğini ve onun gerektirdiği dini epistemolojiyi ayrıntılı olarak tartışmaya çalıştık.Özellikle İkbal'in dinsel deneyimle kimliksiz bir evrensel ilkeye değil, kimliği olan bir zat fikrine ulaşmasının önemi üzerinde durduk.Tez çalışmamızın ikinci bölümünü oluşturan Tanrı'nın mahiyeti ve Tanrı-evren ilişkisinde ise İkbal'in önem afettiği benlik fikri etrafında Tanrı'nın aşkın ve içkin yönü üzerinde durmaya çalıştık.İkbalde öne çıkan bu çift kutuplu organik birliğin İkbal'in felsefesinde önemli bir yere sahip olan, birlik içinde farklılığın vurgulanması açısından ne kadar önemli olduğu üzerinde durduk.Bu bölümde Tanrının içkin mahiyetini açıklar nitelikte olan yaratma ve bilmeyi genel hatları ile konumuz içerisinde tartıştık ve Tanrı-evren ilişkisini bir bütün şeklinde süreççi bakış açısıyla ele almaya gayret gösterdik.Çalışmamız neticesinde batılı panenteistlerden farklı olarak panenteizm konusunda İkbal'in de önemli bir yere sahip olduğunu ve İkbal'in özellikle süreç düşüncesiyle İslam kelamına getirmiş olduğu düşüncelerin kendi bağlamlarında yenilikçi bir öz taşıdığını göstermeye çalıştık.

In this paper, we introduce a new noise robust representation of speech signal obtained by locating points of potential importance in the spectrogram, and parameterizing the activity of time-frequency pattern around those points. These features are referred to as Spectro-Temporal Activity Pattern (STAP) features. The suitability of these features for noise robust speech recognition is examined for a particular parameterization scheme where spectral peaks are chosen as points of potential importance. The activity in the time-frequency patterns around these points are parameterized by measuring the dynamics of the patterns along both time and frequency axes. As the spectral peaks are considered to constitute an important and robust cue for speech recognition, this representation is expected to yield a robust performance. An interesting result of the study is that inspite of using a relatively less amount of information from the speech signal, STAP features are able to achieve a reasonable recognition performance in clean speech, when compared to the state-of-the-art features. In addition, STAP features produce a significantly better performance in high noise conditions. An entropy based combination technique in tandem frame-work to combine STAP features with standard features yields a system which is more robust in all conditions.

In this paper, we introduce a new class of noise robust acoustic features derived from a new measure of autocorrelation, and explicitly exploiting the phase variation of the speech signal frame over time. This family of features, referred to as ``Phase AutoCorrelation'' (PAC) features, include PAC spectrum and PAC MFCC, among others. In regular autocorrelation based features, the correlation between two signal segments (signal vectors), separated by a particular time interval $k$, is calculated as a dot product of these two vectors. In our proposed PAC approach, the angle between the two vectors is used as a measure of correlation. Since dot product is usually more affected by noise than the angle, it is expected that PAC-features will be more robust to noise. This is indeed significantly confirmed by the experimental results presented in this paper. The experiments were conducted on the Numbers 95 database, on which ``stationary'' (car) and ``non-stationary'' (factory) Noisex 92 noises were added with varying SNR. In most of the cases, without any specific tuning, PAC-MFCC features perform better.

Recently, a nonlinear transformation of autocorrelation coefficients named Phase AutoCorrelation (PAC) coefficients has been considered for feature extraction \cite{ikbal03}. PAC based features show improved robustness to additive noise as a result of two operations, performed during the computation of PAC, namely energy normalization and inverse cosine transformation. In spite of the improved robustness achieved for noisy speech, these two operations lead to some degradation in recognition performance for clean speech. In this paper, we try to alleviate this problem, first by introducing the energy information back into the PAC based features, and second by studying alternatives to inverse cosine function. Simply appending the frame energy as an additional coefficient in the PAC features has resulted in noticeable improvement in the performance for clean speech. Study of alternatives to inverse cosine transformation leads to a conclusion that linear transformation is the best for clean speech, while nonlinear functions help to improve robustness in noise.

In this paper, we present an entropy based method to combine tandem representations of the recently proposed Phase AutoCorrelation (PAC) based features and Mel-Frequency Cepstral Coefficients (MFCC) features. PAC based features, derived from a nonlinear transformation of autocorrelation coefficients and shown to be noise robust, improve their robustness to additive noise in their tandem representation. On the other hand, MFCC features in their tandem representation show a significant improvement in recognition performance on clean speech. An entropy based combination method investigated in this paper adaptively gives a higher weighting to the representation of MFCC features in clean speech and to the representation of PAC based features in noisy speech, thus yielding a robust recognition performance in all conditions.

In this paper, we present an HMM/ANN based algorithm to estimate the spectral peak locations. This algorithm makes use of distinct time-frequency (TF) patterns in the spectrogram for estimating the peak locations. Such a use of TF patterns is expected to impose temporal constraints during the peak estimation task, thereby yielding a smoother estimate of the peaks over time. Additionally, the algorithm uses an ergodic topology for the HMM/ANN, thus allowing an estimation of a varying number of peak locations over time. The usefulness of the proposed algorithm is evaluated in the framework of a recently introduced noise robust feature called the spectro-temporal activity pattern (STAP) feature. Interestingly, the recently introduced phase autocorrelation (PAC) spectrum, with enhanced spectral peaks and smoothed spectral valleys, turns out to be more appropriate for this algorithm than the regular spectrum.

Methods to improve noise robustness of speech recognition systems often result in degradation of recognition performance for clean speech. Recently proposed phase autocorrelation (PAC) based features (S. Ikbal et al., Proc. ICASSP-03, p.II-133-6, 2003; Proc. IEEE ASRU 2003 Workshop, 2003), while showing noticeable improvement in noise robustness, also suffer from this drawback. We try to alleviate this problem by using the PAC based features along with regular speech features in a multi-stream framework. The multi-stream system uses the entropy of the posterior probability distribution, computed during recognition, as a confidence measure to combine evidence from different feature streams adaptively (Misra, H. et al., Proc. ICASSP-03, p.II-741-4, 2003). Experimental results obtained on OGI Numbers95 database and Noisex92 noise database show that such a system yields the best possible recognition performance in all conditions. Actually, the combination always performs better than the best performing stream for all the conditions.

In this paper, we present an HMM2 based method for speaker normalization. Introduced as an extension of Hidden Markov Model (HMM), HMM2 differentiates itself from the regular HMM in terms of the emission density modeling, which is done by a set of state-dependent HMMs working in the feature vector space. The emission modeling HMM aims at maximizing the likelihood through optimal alignment of its states across the feature components. This property makes it potentially useful to speaker normalization, when applied to spectrum. With the alignment information we get, it is possible to normalize the speaker related variations through piecewise linear warping of frequency axis of the spectrum. In our case, (emission modeling) HMM based spectral warping is employed in the feature extraction block of regular HMM framework for normalizing the speaker related variabilities. After a brief description of HMM2, we present the general approach towards HMM2-based speaker normalization and show, through preliminary experiments, the pertinence of the approach.

State-of-the-art Automatic Speech Recognition (ASR) systems make extensive use of Hidden Markov Models (HMMs), characterized by flexible statistical modeling, powerful optimization (training) techniques and efficient recognition algorithms. When allowed by the software implementation, their flexibility can also be fully exploited in research, by testing various topologies, acoustic units, parameterization schemes, etc. Unfortunately, these HMM systems still suffer from an excessive sensitivity to the variability generally observed in real acoustic environments, including speaker, channel and noise characteristics. In an attempt to tackle this problem, IDIAP recently introduced a new form of HMM, referred to as HMM2, exhibiting numerous potential advantages, which could result in improved robustness of current speech recognition systems. HMM2 can be described as a mixture of HMMs where the HMM emission probabilities (usually estimated by Gaussian Mixtures or a neural network) are themselves estimated by state-specific HMMs working along the acoustic features. Among other properties, it is believed that such HMM2 approach could better model the time/frequency speech flow, including better modeling of the feature correlation. After a brief reminder of the HMM theory, this report first introduces the theoretical basis of HMM2, including their parameterization schemes and the estimation of their parameters through a generalized form of the Expectation-Maximization (EM) training algorithm. It is also the goal of the present report to describe the functionalities and specifications of a new software able to handle, in a flexible way, different forms of HMM and HMM2 topologies and training schemes.

In general, entropy gives us a measure of the number of bits required to represent some information. When applied to probability mass function (PMF), entropy can also be used to measure the ``peakiness'' of a distribution. In this paper, we propose using the entropy of short time Fourier transform spectrum, normalised as PMF, as an additional feature for automatic speech recognition (ASR). It is indeed expected that a peaky spectrum, representation of clear formant structure in the case of voiced sounds, will have low entropy, while a flatter spectrum corresponding to non-speech or noisy regions will have higher entropy. Extending this reasoning further, we introduce the idea of multi-band/multi-resolution entropy feature where we divide the spectrum into equal size sub-bands and compute entropy in each sub-band. The results presented in this paper show that multi-band entropy features used in conjunction with normal cepstral features improve the performance of ASR system.

Robustness against external noise is an important requirement for automatic speech recognition (ASR) systems, when it comes to deploying them for practical applications. This thesis proposes and evaluates new feature-based approaches for improving the ASR noise robustness. These approaches are based on nonlinear transformations that, when applied to the spectrum or feature, aim to emphasize the part of the speech that is relatively more invariant to noise and/or deemphasize the part that is more sensitive to noise. Spectral peaks constitute high signal-to-noise ratio part of the speech. Thus an efficient parameterization of the components only from the peak locations is expected to improve the noise robustness. An evaluation of this requires estimation of the peak locations. Two methods proposed in this thesis for the peak estimation task are: 1) frequency-based dynamic programming (DP) algorithm, that uses the spectral slope values of single time frame, and 2) HMM/ANN based algorithm, that uses distinct time-frequency (TF) patterns in the spectrogram (thus imposing temporal constraints during the peak estimation). The learning of the distinct TF patterns in an unsupervised manner makes the HMM/ANN based algorithm sensitive to energy fluctuations in the TF patterns, which is not the case with frequency-based DP algorithm. For an efficient parameterization of spectral components around the peak locations, parameters describing activity pattern (energy surface) within local TF patterns around the spectral peaks are computed and used as features. These features, referred to as spectro-temporal activity pattern (STAP) features, show improved noise robustness, however they are inferior to the standard features in clean speech. The main reason for this is the complete masking of the non-peak regions in the spectrum, which also carry significant information required for clean speech recognition. This leads to a development of a new approach that utilizes a soft-masking procedure instead of discarding the non-peak spectral components completely. In this approach, referred to as phase autocorrelation (PAC) approach, the noise robustness is actually addressed in the autocorrelation domain (time-domain Fourier equivalent of the power spectral domain). It uses phase (i.e., angle) variation of the signal vector over time as a measure of correlation, as opposed to the regular autocorrelation which uses dot product. This alternative measure of autocorrelation is referred to as PAC, and is motivated by the fact that angle gets less disturbed by the additive disturbances than the dot product. Interestingly, the use of PAC has an effect of emphasizing the peaks and smoothing out the valleys, in the spectral domain, without explicitly estimating the peak locations. PAC features exhibit improved noise robustness. However, even the soft masking strategy tends to degrade the clean speech recognition performance. This points to the fact that externally designed transformations, which do not take a complete account of underlying complexity of the speech signal, may not be able to improve the robustness without hurting the clean speech recognition. A better approach in this case will be to learn the transformation from the speech data itself in a data-driven manner, compromising between improving the noise robustness while keeping the clean performance intact. An existing data-driven approach called TANDEM is analyzed to validate this. In TANDEM approach, a multi-layer perceptron (MLP) used to perform a data-driven transformation of the input features, learns the transformation by getting trained in a supervised, discriminative mode, with phoneme labels as output classes. Such a training makes the MLP to perform a nonlinear discriminant analysis in the input feature space and thus makes it to learn a transformation that projects the input features onto a sub-space of maximum class discriminatory information. This projection is able to suppress the noise related variability, while keeping the speech discriminatory information intact. An experimental evaluation of the TANDEM approach shows that it is effective in improving the noise robustness. Interestingly, TANDEM approach is able to further improves the noise robustness of the STAP and PAC features, and also improve their clean speech recognition performance. The analysis of noise robustness of TANDEM has also lead to another interesting aspect of it namely, using it as an integration tool for adaptively combining multiple feature streams. The validity of the various noise robust approaches developed in this thesis is shown by evaluating them on OGI Numbers95 database added with noises from Noisex92, and also with Aurora-2 database. A combination of robust features developed in this thesis along with standard features, in a TANDEM framework, result in a system that is reasonably robust in all conditions.

This paper presents the theoretical basis and preliminary experimental results of a new HMM model, referred to as HMM2, which can be considered as a mixture of HMMs. In this new model, the emission probabilities of the temporal (primary) HMM are estimated through secondary, state specific, HMMs working in the acoustic feature space. Thus, while the primary HMM is performing the usual time warping and integration, the secondary HMMs are responsible for extracting/modeling the possible feature dependencies, while performing frequency warping and integration. Such a model has several potential advantages, such as a more flexible modeling of the time/frequency structure of the speech signal. When working with spectral features, such a system can also perform nonlinear spectral warping, effectively implementing a form of nonlinear vocal tract normalization. Furthermore, it will be shown that HMM2 can be used to extract noise robust features, supposed to be related to formant regions, which can be used as extra features for traditional HMM recognizers to improve their performance. These issues are evaluated in the present paper, and different experimental results are reported on the Numbers95 database.

Recently, entropy measures at different stages of recognition have been used in automatic speech recognition (ASR) task. In a recent paper, we proposed that formant positions of a spectrum can be captured by multi-resolution spectral entropy feature. In this paper, we suggest modifications to the spectral entropy feature extraction approach and compute entropy contribution from each sub-band to the total entropy of the normalized spectrum. Further, we explore the ideas of overlapping sub-bands and the time derivatives of the spectral entropy feature. The modified feature is robust to additive wide-band noise and performs well at low SNRs. In the last, in the frame work of TANDEM, we show that the system using combined entropy and PLP features works better than the baseline PLP feature for additive wide-band noise at different SNRs.