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Matched frequency responses are a fundamental starting point for a variety ofimplementations for microphone arrays. In this report, two methods for frequencyresponse-calibration of a pre-assembled microphone array are presented andevaluated. This is done by extracting the deviation in frequency responses of themicrophones in relation to a selected reference microphone, using a swept sine asa stimulus signal and an inverse filter. The swept sine includes all frequencieswithin the bandwidth of human speech. This allows for a full frequency responsemeasurements from all microphones using a single recording.Using the swept sine, the deviation in frequency response between the microphonescan be obtained. This deviation represents the scaling factor that all microphonesmust be calibrated with to match the reference microphone. Applying the scalingfactors on the recorded stimulus signal shows an improvement for both implementedmethods, and where one method matches the frequency response of the microphoneswith high accuracy.Once the scaling factors of the various microphones is obtained, it can be usedto calibrate other recorded signals. This leads to an minor improvement formatching the frequency responses, as it has been shown that the differencesin frequency response between the microphones is signal-dependent and variesbetween recordings. The response differences between the microphones dependson the design of the array, speaker, room and the acoustic frequency dispersionthat occurs with sound waves. This makes it difficult to calibrate the frequencyresponses of the microphones without appropriate equipment because the responseof the microphones is noticeably affected by these other factors. Proposals to addressthese problems are discussed in the report as future work. / Matchade frekvenssvar är en grundläggande utgångspunkt för ett flertal implementationer för mikrofonarrayer. I denna rapport presenteras och utvärderas tvåmetoder för frekvenssvarskalibrering för en förmonterad mikrofonarray. Detta görsgenom att extrahera avvikelsen i frekvenssvar hos alla mikrofoner i förhållandetill en vald referensmikrofon. Frekvenssvaren tas fram med hjälp av ettsinussvep som stimulanssignal och ett inverterat filter. Sinussvepet inkluderar helafrekvensbredden för mänskligt tal och möjliggör att mikrofonernas fulla frekvenssvarkan analyseras från en enda inspelning.Med hjälp av sinussvepet kan avvikelsen i frekvenssvar mellan mikrofonerna erhållas.Denna avvikelse representerar den skalningsfaktor alla mikrofoner måste kalibrerasefter för att matcha referensmikrofonen. Genom att applicera faktorerna på deninspelade stimulussignalen ses en förbättring för båda implementerade metoderna,där en metod matchar mikrofonernas frekvenssvar med hög noggrannhet.När skalningsfaktorn för de olika mikrofonerna har erhållits kan den användas föratt kalibrera andra inspelade signaler. Detta leder till en liten förbättring i att matchafrekvenssvaren, då det har visat sig att skillnader mellan mikrofonernas frekvenssvarär signalberoende och varierar mellan inspelningar. Skillnader i frekvenssvar mellanmikrofonerna beror på ljudets utbredning i rummet, utformningen av arrayen,högtalaren och den akustiska frekvensspridningen som uppstår hos ljudvågor. Dettagör det svårt att kalibrera frekvenssvaren hos mikrofonerna utan lämplig utrustningeftersom mikrofonernas respons märkbart påverkas av dessa andra faktorer. Förslagför att kringgå dessa problem diskuteras i rapporten och tas upp som framtidaarbete.

Syftet med att mäta vibrationer och rekyler i ett padelrack i detta arbete är att utveckla en prototyp som kan användas som träningsredskap för att minska risken för skador. En vanlig skada som drabbar padelspelare är tennisarmbåge, som enligt studier tros uppkomma genom upprepad exponering av mikrotrauman som vibrationer och rekyler. Genom att utföra en litteraturstudie i ämnet har systemkrav för ett sensorbaserat system definierats. Systemet som mäter vibrationer och rekyler har monterats i handtaget på padelracket. Två olika testmiljöer har utvecklats för att möjliggöra kontrollerade tester. För att identifiera och analysera slag använder systemet frekvensanalyser, korrelationstester och positionsförändring. Vid utveckling av metoden för identifiering av träffpunkt delades racket upp i fem olika zoner. Resultatet indikerar att träffar i två av zonerna ger upphov till mindre mängd vibrationer jämfört med de övriga zonerna. Resultatet för identifiering av träffzon varierar mellan testmiljöerna och enbart identifiering av en zon kan anses vara fungerande i båda fallen. Systemet identifierade träffzonen korrekt i 18 av 25 slag i den ena testmiljön och 9 av 25 i den andra. För att förbättra identifieringen av träffzon behövs flera analyser och korrelationtester utformas. En slutsats för det här examensarbetet är att det här arbetet kan användas som grund för vidare utveckling av ett sensorbaserat system för att identifiera träffzonen och kvantifiera vibrationer i ett padelrack. / The purpose of measuring vibrations and recoils in a padel racket in this thesis is to develop a prototype that can be used as a training equipment to reduce the risk of injury. A common injury for padel players is tennis elbow, studies show that the cause of this injury are microtraumas from vibrations and recoils. Through a literature study in the subject, system demands for a sensor-based system have been defined. The system that has been used to measure vibrations and recoils have been attached to the bottom of the handle on the padel racket. To achieve controlled tests two different test environments have been developed. To identify and analyze impacts the system utilizes frequency analysis, correlation tests and displacement tracking. For identification of the impact area the racket was divided into five zones. The result indicates, that two of the impact zones generate less vibrations than the others. The result also shows that identification of impact zone varies between the test environments and that only the sweet spot can be identified in both cases. The system identified the impact zone correctly in 18 out of 25 strokes in one test environment and 9 out of 25 in the other. To further improve the methods for identification of the impact zone more analyses and correlations tests are required. One conclusion for this thesis is that it can be used as a platform for further development of a sensor-based system that can correctly identify impacts in all zones and quantify the resulting vibrations.

Η διαμόρφωση με πολύπλεξη συχνότητας ορθογωνίων φερουσών (Orthogonal Frequency Division Multiplexing - OFDM) έχει εδραιωθεί ως μία από τις επικρατέστερες μεθόδους διαμόρφωσης για την υψηλού ρυθμού μετάδοση πληροφορίας μέσω ασύρματων μέσων. Σε ένα σύστημα OFDM, ένα από τα βασικότερα και υπολογιστικά πολυπλοκότερα τμήματα είναι ο υπολογισμούς του Ταχύ Μετασχηματισμού Fourier. Αντικείμενο της εργασίας αυτής είναι η μελέτη της χρήσης εναλλακτικής αριθμητικής για την υλοποίηση κυκλωμάτων FFT. Τυπικά, τέτοιου είδους κυκλώματα υλοποιούνται χρησιμοποιώντας κάποια γραμμική αναπαράσταση σταθερής υποδιαστολής. Στη βιβλιογραφία έχουν προταθεί υλοποιήσεις του FFT με χρήση του Λογαριθμικού Συστήματος Αρίθμησης (Logarithmic Numbering System – LNS) και έχουν αναφερθεί κέρδη για συγκεκριμένους παράγοντες όπως το σφάλμα κβαντισμού, η επιφάνεια ολοκλήρωσης και η κατανάλωση ισχύος. Η αποδοτικότητα αυτών των λύσεων ερευνάται για τη συγκεκριμένη περίπτωση της εφαρμογής του FFT σε OFDM modems. Εστιάζοντας στην περίπτωση του FFT 64 σημείων για OFDM modem για ασύρματα δίκτυα 802.11a, μία από τις πλέον επιτυχημένες αρχιτεκτονικές που έχουν προταθεί για την υλοποίηση του, στηρίζεται στη λογική του FFT γραμμής – στήλης και παρουσιάζει έναν τρόπο πραγματοποίησης του υπολογισμού χωρίς κανένα ψηφιακό πολλαπλασιαστή. Με το βασικό πλεονέκτημα της λογαριθμικής αναπαράστασης να είναι η απλοποίηση των κυκλωμάτων πολλαπλασιασμού (με ταυτόχρονη όμως αύξηση του κόστους για την πραγματοποίηση προσθέσεων), δείχνεται ότι τελικά η υλοποίηση ενός FFT αμιγώς σε LNS δεν είναι προτιμητέα. Αν και η αρχιτεκτονική του FFT γραμμής – στήλης μπορεί να προσφέρει υψηλή απόδοση με χαμηλό κόστος υλοποίησης, παρουσιάζει μια σειρά από αδυναμίες, που σχετίζονται κυρίως με τη χρήση ειδικών κυκλωμάτων για την εκτέλεση των πολλαπλασιασμών με τις σταθερές που εμφανίζονται στον FFT (twiddle factors). Για την αντιμετώπιση αυτών των περιορισμών προτείνεται η εισαγωγή του LNS σε κάποια τμήματα του κυκλώματος του FFT, οδηγώντας έτσι στη δημιουργία ενός συστήματος μικτής αναπαράστασης. Σε τέτοιου είδους υβριδικά συστήματα τίθενται δύο βασικά ζητήματα. Το πρώτο αφορά τον ορισμό της ισοδυναμίας μεταξύ των διαφορετικών αναπαραστάσεων και το δεύτερο τον αποδοτικό τρόπο υλοποίησης των κυκλωμάτων μετατροπής από το ένα αριθμητικό σύστημα στο άλλο. Τυπικά, τα κριτήρια ισοδυναμίας που επιλέγονται είναι αυστηρά μαθηματικά ορισμένα, όπως για παράδειγμα ο Λόγος Σήματος προς Θόρυβο (Signal-to-Noise Ratio - SNR) ή το Μέσο Σχετικό Σφάλμα Αναπαράστασης (Average Relative Representation Error – ARRE). Στη συγκεκριμένη εργασία ακολουθείται μια λιγότερο δεσμευτική προσέγγιση, ορίζοντας την ισοδυναμία δύο αναπαραστάσεων με βάση την τελική απόδοση του συστήματος OFDM όσον αφορά το ρυθμό λαθών στο δέκτη (Bit Error Rate - BER). Με βάση αυτή τη λογική, αποδεικνύεται ότι μπορούν να χρησιμοποιηθούν αναπαραστάσεις πολύ μικρού μεγέθους λέξης και οι προσεγγίσεις που χρειάζεται να γίνουν κατά τις μετατροπές μεταξύ των δύο συστημάτων δεν είναι ανάγκη να είναι ιδιαίτερα ακριβείς. Έτσι, τα σχετικά κυκλώματα μπορούν να υλοποιηθούν αποδοτικά και με μικρό κόστος. Η υλοποίηση δύο συστημάτων για τον FFT 64 σημείων, ένα βασισμένο αποκλειστικά σε γραμμική αναπαράσταση σταθερής υποδιαστολής και ένα υβριδικό που χρησιμοποιεί γραμμική και λογαριθμική αναπαράσταση, δείχνει ότι χωρίς διαφορές όσον αφορά το BER και την καθυστέρηση (delay), η υβριδική προσέγγιση απαιτεί μικρότερη επιφάνεια ολοκλήρωσης και παρουσιάζει σημαντικά χαμηλότερη κατανάλωση ισχύος. / Orthogonal Frequency Division Multiplexing (OFDM) has been established as one of the most prevalent methods for high data rate transmission through wireless channels. In an OFDM communication system, one of the fundamental and most computationally intensive parts is the computation of the Fast Fourier Transform (FFT). The subject of this thesis is to investigate the use of alternative arithmetic representation systems for the implementation of FFT circuits. Typically, these circuits are implemented using linear fixed-point representations. In literature, implementations of the FFT using the Logarithmic Numbering System (LNS) have been proposed and significant gains in quantization errors, chip area and power consumption have been reported. The effectiveness of these proposals in the case of the FFT for OFDM systems is investigated. Focusing on the case of the 64-point FFT for an OFDM modem for an 802.11a wireless network, one of the most efficient architectures proposed is based on the concept of row-column FFT and presents a way of implementing the computation without using any digital (non-fixed input) multiplier. The most important feature of the LNS representation is the fact that multiplication operations turn to mere additions, thus there are significant implementation gains. On the downside though, addition in LNS is very expensive. Combining the aforementioned, it is shown that the implementation of the whole FFT computation in LNS is not a preferable solution. Although the row-column FFT architecture may offer high performance and low implementation cost, it presents a number of deficiencies mainly due to the fact that special purpose circuits are used to perform the multiplications with the complex constants (twiddle factors) that appear in the computation. In order to alleviate these deficiencies, it is proposed to use the LNS representation in some parts of the FFT circuit, thus forming a hybrid-representation system. In hybrid-representation systems two major issues are raised. The first one is how to define equivalence between the arithmetic representation systems used and the second one is related to the cost of the circuits required to perform the conversions between the numbers of the different arithmetic systems. Typically, the equivalence criterion used is mathematically defined and metrics like the Signal-to-Noise Ratio (SNR) or Average Relative Representation Error (ARRE) are commonly used. In this report, a less restrictive metric is used: two arithmetic representations are defined to be equal if the Bit Error Rate (BER) performance of the overall OFDM system is equal. Using this approach, it is shown that short word-length representations may be used and the conversions between the linear and logarithmic systems need not be very accurate. This results in great simplification of the conversion process and the respected circuits can be implemented with low cost. For comparison, two 64-point FFT systems have been implemented, one using a linear fixed-point 2’s complement representation and one using both linear and LNS representation. Without any differences in BER performance and circuit delay, the hybrid-representation system requires less chip area and consumes significantly lower power.

Cognitive Radio (CR) has received tremendous research attention over the past decade, both in the academia and industry, as it is envisioned as a promising solution to the problem of spectrum scarcity. ACR is a device that senses the spectrum for occupancy by licensed users(also called as primary users), and transmits its data only when the spectrum is sensed to be available. For the efficient utilization of the spectrum while also guaranteeing adequate protection to the licensed user from harmful interference, the CR should be able to sense the spectrum for primary occupancy quickly as well as accurately. This makes Spectrum Sensing(SS) one of the where the goal is to test whether the primary user is inactive(the null or noise-only hypothesis), or not (the alternate or signal-present hypothesis). Computational simplicity, robustness to uncertainties in the knowledge of various noise, signal, and fading parameters, and ability to handle interference or other source of non-Gaussian noise are some of the desirable features of a SS unit in a CR. In many practical applications, CR devices can exploit known structure in the primary signal. IntheIEEE802.22CR standard, the primary signal is a wideband signal, but with a strong narrowband pilot component. In other applications, such as military communications, and blue tooth, the primary signal uses a Frequency Hopping (FH)transmission. These applications can significantly benefit from detection schemes that are tailored for detecting the corresponding primary signals. This thesis develops novel detection schemes and rigorous performance analysis of these primary signals in the presence of fading. For example, in the case of wideband primary signals with a strong narrowband pilot, this thesis answers the further question of whether to use the entire wideband for signal detection, or whether to filter out the pilot signal and use narrowband signal detection. The question is interesting because the fading characteristics of wideband and narrowband signals are fundamentally different. Due to this, it is not obvious which detection scheme will perform better in practical fading environments. At another end of the gamut of SS algorithms, when the CR has no knowledge of the structure or statistics of the primary signal, and when the noise variance is known, Energy Detection (ED) is known to be optimal for SS. However, the performance of the ED is not robust to uncertainties in the noise statistics or under different possible primary signal models. In this case, a natural way to pose the SS problem is as a Goodness-of-Fit Test (GoFT), where the idea is to either accept or reject the noise-only hypothesis. This thesis designs and studies the performance of GoFTs when the noise statistics can even be non-Gaussian, and with heavy tails. Also, the techniques are extended to the cooperative SS scenario where multiple CR nodes record observations using multiple antennas and perform decentralized detection. In this thesis, we study all the issues listed above by considering both single and multiple CR nodes, and evaluating their performance in terms of(a)probability of detection error,(b) sensing-throughput trade off, and(c)probability of rejecting the null-hypothesis. We propose various SS strategies, compare their performance against existing techniques, and discuss their relative advantages and performance tradeoffs. The main contributions of this thesis are as follows: The question of whether to use pilot-based narrowband sensing or wideband sensing is answered using a novel, analytically tractable metric proposed in this thesis called the error exponent with a confidence level. Under a Bayesian framework, obtaining closed form expressions for the optimal detection threshold is difficult. Near-optimal detection thresholds are obtained for most of the commonly encountered fading models. Foran FH primary, using the Fast Fourier Transform (FFT) Averaging Ratio(FAR) algorithm, the sensing-through put trade off are derived in closed form. A GoFT technique based on the statistics of the number of zero-crossings in the observations is proposed, which is robust to uncertainties in the noise statistics, and outperforms existing GoFT-based SS techniques. A multi-dimensional GoFT based on stochastic distances is studied, which pro¬vides better performance compared to some of the existing techniques. A special case, i.e., a test based on the Kullback-Leibler distance is shown to be robust to some uncertainties in the noise process. All of the theoretical results are validated using Monte Carlo simulations. In the case of FH-SS, an implementation of SS using the FAR algorithm on a commercially off-the ¬shelf platform is presented, and the performance recorded using the hardware is shown to corroborate well with the theoretical and simulation-based results. The results in this thesis thus provide a bouquet of SS algorithms that could be useful under different CRSS scenarios.

The aim of the master’s thesis is to acquaint the reader with Discrete Fourier Transform DFT and its introduction to spectral analysis descrete time signals. Furthermore it describes efficient computation of the DFT using the algorithm Fast Fourier Transform FFT and effects that appear in the DFT spectral analysis, the effect of the length of the DFT, the effect of the length of the segment of the analysed signal and the leakage. Next is explained the issue of the complex representation of real bandpass signals in the baseband, called the complex envelope of signals. This represenation uses the Hilbert Transform and the analytic signal. The thesis also describes the application library Real Time Toolbox of the software Matlab/Simulink, that uses the data acquition card AD622 allows to connect and process real signals in real time. In Matlab/Simulink with use this facilities is create the laboratory lesson, that simulating the complex represenation of real bandpass signals in real time.

In the last decade, a considerable growth has been added to the volume of the credit risk derivatives market. This growth has been followed by the current financial market turbulence. These two periods have outlined how significant and important are the credit derivatives market and its products. Modelling-wise, this growth has parallelised by more complicated and assembled credit derivatives products such as mth to default Credit Default Swaps (CDS), m out of n (CDS) and collateralised debt obligation (CDO). In this thesis, the Lévy process has been proposed to generalise and overcome the Credit Risk derivatives standard pricing model's limitations, i.e. Gaussian Factor Copula Model. One of the most important drawbacks is that it has a lack of tail dependence or, in other words, it needs more skewed correlation. However, by the Lévy Factor Copula Model, the microscopic approach of exploring this factor copula models has been developed and standardised to incorporate an endless number of distribution alternatives those admits the Lévy process. Since the Lévy process could include a variety of processes structural assumptions from pure jumps to continuous stochastic, then those distributions who admit this process could represent asymmetry and fat tails as they could characterise symmetry and normal tails. As a consequence they could capture both high and low events¿ probabilities. Subsequently, other techniques those could enhance the skewness of its correlation and be incorporated within the Lévy Factor Copula Model has been proposed, i.e. the 'Stochastic Correlated Lévy Factor Copula Model' and 'Lévy Random Factor Loading Copula Model'. Then the Lévy process has been applied through a number of proposed Pricing Basket CDS&CDO by Lévy Factor Copula and its skewed versions and evaluated by V-FFT limiting and mixture cases of the Lévy Skew Alpha-Stable distribution and Generalized Hyperbolic distribution. Numerically, the characteristic functions of the mth to default CDS's and (n/m) th to default CDS's number of defaults, the CDO's cumulative loss, and loss given default are evaluated by semi-explicit techniques, i.e. via the DFT's Fast form (FFT) and the proposed Very Fast form (VFFT). This technique through its fast and very fast forms reduce the computational complexity from O(N2) to, respectively, O(N log2 N ) and O(N ).

In the last decade, a considerable growth has been added to the volume of the credit risk derivatives market. This growth has been followed by the current financial market turbulence. These two periods have outlined how significant and important are the credit derivatives market and its products. Modelling-wise, this growth has parallelised by more complicated and assembled credit derivatives products such as mth to default Credit Default Swaps (CDS), m out of n (CDS) and collateralised debt obligation (CDO). In this thesis, the Lévy process has been proposed to generalise and overcome the Credit Risk derivatives standard pricing model's limitations, i.e. Gaussian Factor Copula Model. One of the most important drawbacks is that it has a lack of tail dependence or, in other words, it needs more skewed correlation. However, by the Lévy Factor Copula Model, the microscopic approach of exploring this factor copula models has been developed and standardised to incorporate an endless number of distribution alternatives those admits the Lévy process. Since the Lévy process could include a variety of processes structural assumptions from pure jumps to continuous stochastic, then those distributions who admit this process could represent asymmetry and fat tails as they could characterise symmetry and normal tails. As a consequence they could capture both high and low events' probabilities. Subsequently, other techniques those could enhance the skewness of its correlation and be incorporated within the Lévy Factor Copula Model has been proposed, i.e. the 'Stochastic Correlated Lévy Factor Copula Model' and 'Lévy Random Factor Loading Copula Model'. Then the Lévy process has been applied through a number of proposed Pricing Basket CDS&CDO by Lévy Factor Copula and its skewed versions and evaluated by V-FFT limiting and mixture cases of the Lévy Skew Alpha-Stable distribution and Generalized Hyperbolic distribution. Numerically, the characteristic functions of the mth to default CDS's and (n/m) th to default CDS's number of defaults, the CDO's cumulative loss, and loss given default are evaluated by semi-explicit techniques, i.e. via the DFT's Fast form (FFT) and the proposed Very Fast form (VFFT). This technique through its fast and very fast forms reduce the computational complexity from O(N2) to, respectively, O(N log2 N ) and O(N ).

Este trabalho tem seu foco na monitoração dos processos de usinagem das máquinas ferramentas sem a utilização de sensores dedicados à medição direta das grandezas mecânicas envolvidas no processo de usinagem em si. Assim sendo, optou-se por um método de medição indireta utilizando um estimador de potência e torque baseado nas grandezas elétricas na entrada de energia do motor de indução da máquina ferramenta. O núcleo central do trabalho consiste na medição de processos de usinagem utilizando um dinamômetro de alta precisão próprio para máquina ferramenta para obter os valores médios e os modos de vibração do processo máquina ferramenta-usinagem e fazer a confrontação com os mesmos dados obtidos pelo estimador de torque. A pesquisa realizada utilizou ferramentas clássicas de processamento de sinais, como é o caso da FFT, assim como duas poderosas ferramentas atuais, a transformada de wavelet (WT) e a transformada de Hilbert-Huang (HHT). Em adição foi utilizado um processo de otimização para a determinação dos parâmetros do motor de indução on-line baseado em uma metaheurística denominada busca de harmonia (Harmony Search HS) / This work focuses on monitoring the machining processes in machine tools without the use of dedicated transducers to directly measure mechanicals quantities of the machining process. The approached method used the option of measuring the power and torque through a estimator based in the electrical quantities in the input of the induction motor used by machine tool. The core of the work consists in the measuring the mechanical processes of machining using a high precision dynamometer specified to machine tool to get the average values of mechanical quantities and the vibration modes of the set machine tool-machining process, the objective is to compare the same data group got from dynamometer and estimator. The research data was based on classical analysis tool such as Fourier transform (FFT) and on modern powerful tools such as wavelet transforms (WT) and Hilbert-Huang transform (HHT). To refine the measuring process of average values of torque and power using the induction motor a method to estimates the motor parameters was added based on an optimization method named harmony search (HS).

Este trabalho tem seu foco na monitoração dos processos de usinagem das máquinas ferramentas sem a utilização de sensores dedicados à medição direta das grandezas mecânicas envolvidas no processo de usinagem em si. Assim sendo, optou-se por um método de medição indireta utilizando um estimador de potência e torque baseado nas grandezas elétricas na entrada de energia do motor de indução da máquina ferramenta. O núcleo central do trabalho consiste na medição de processos de usinagem utilizando um dinamômetro de alta precisão próprio para máquina ferramenta para obter os valores médios e os modos de vibração do processo máquina ferramenta-usinagem e fazer a confrontação com os mesmos dados obtidos pelo estimador de torque. A pesquisa realizada utilizou ferramentas clássicas de processamento de sinais, como é o caso da FFT, assim como duas poderosas ferramentas atuais, a transformada de wavelet (WT) e a transformada de Hilbert-Huang (HHT). Em adição foi utilizado um processo de otimização para a determinação dos parâmetros do motor de indução on-line baseado em uma metaheurística denominada busca de harmonia (Harmony Search HS) / This work focuses on monitoring the machining processes in machine tools without the use of dedicated transducers to directly measure mechanicals quantities of the machining process. The approached method used the option of measuring the power and torque through a estimator based in the electrical quantities in the input of the induction motor used by machine tool. The core of the work consists in the measuring the mechanical processes of machining using a high precision dynamometer specified to machine tool to get the average values of mechanical quantities and the vibration modes of the set machine tool-machining process, the objective is to compare the same data group got from dynamometer and estimator. The research data was based on classical analysis tool such as Fourier transform (FFT) and on modern powerful tools such as wavelet transforms (WT) and Hilbert-Huang transform (HHT). To refine the measuring process of average values of torque and power using the induction motor a method to estimates the motor parameters was added based on an optimization method named harmony search (HS).