Authentication of recordings is an important task in forensic sciences. When processing audio or video material, some tasks might be related to determining whether or not the material has been edited or falsified in any way, or in other cases, to determine at what point in time a recording was made. The transition from analog to digital media has provided a solid foundation for the process of determining recording times by using the frequency variations in the electrical network, when interferences from the network are present in the investigated recording. This thesis describes a method of how to record the frequency of the electrical network in order to establish a reference database, evaluates several methods to isolate and extract the disturbances from recordings as well as suggests methods of how to search the database in order to locate the time of a recording. It is concluded, that each of the methods suggested has both advantages and disadvantages, depending on the state of the examined recording. Tests are also conducted in order to determine, whether or not, battery powered recording equipment is susceptible to recording the disturbances, or harmonics thereof, from electromagnetic fields near conducting wire or other electrical equipment. It is found that the fundamental frequency disturbance is usually difficult to detect, but also, that it is not uncommon that harmonics can be present in the recordings from the battery powered devices tested. Included in this thesis are also the results of the development of a graphical user interface for Matlab, where some of the features include the possibility to filter sound files, estimate frequency patterns and perform database searches, as well as the evaluation of a frequency analysis software. Both intended to serve as an aid for locating and extracting the disturbances of interest, as well as for finding the corresponding frequency patterns in the established database.

The knee joint is the most commonly injured joint in the body. Clinical methods used at present for the diagnosis of cartilage pathology in the knee are invasive in nature. Analysis of vibration signals emitted by the knee joint has the potential for the development of a non-invasive procedure for the diagnosis of knee pathology. By Short Time Fourier Transform (STFT) and calculating root mean square (RMS) value, via One Way ANOVA at last, to demonstrate whether the two analysis methods are valid in this work. The method was tested on 14 male volunteers from NSYSU (7 players of in-line skating and 7 normal schoolmates). By analyzing the signals extracted from the players, finding difference of them, and distinguishing whether they are healthy. In conclusion, if the knee joint ligament is unusual, the frequency of signal is higher than 50 Hz; if not, the frequency is lower than 10 Hz. On the other hand, the RMS value of signal has no distinct region among the testers, so could not be used to analyze the signals. The results should be able to take as the reference for the diagnosis of knee joint non-invasively in clinical medicine.

This project includes an overview of different processing methods phonograms. It focuses primarily on time - frequency analysis carried out using Fast Fourier Transform (STFT). The main essence is to evaluate the time - frequency analysis of recorded motor vehicle, driving at different options, together with an analysis of driver activity in these variants. Based on the results of the analysis deals with the creation of synthetic audio signals of motor vehicle records. Further addresses the creation of the program for acoustic simulation engine is running smoothly when driving a car. Processing recorded signals and their evaluation is transferred using Matlab 7.7.0 ( R2008 )

Υλοποίηση ενός επεξεργαστή διακριτών ηχητικών σημάτων, με χρήση μεθόδων STFT. Ο επεξεργαστής έχει την ικανότητα να διαχωρίζει τα μεταβατικά φαινόμενα και εφαρμόζει διαφορετικού τύπου επεξεργασία σε αυτά, από ότι στον υπόλοιπο όγκο του σήματος εισόδου. / Implementation of a processor of discrete audio signals, using STFT (overlap-add) methods. This processor can successfully detect transients in the input signal and apply a separate filter to them.

<p style="text-align: justify;">In this doctoral dissertation several integral transforms are discussed.The first one is the Short time Fourier transform (STFT). We present continuity theorems for the STFT and its adjoint on the test function space <em>K</em>₁(ℝⁿ) and the topological tensor product <em>K</em>₁(ℝⁿ) &otimes; <em>U</em>(<strong>ℂ</strong>ⁿ), where <em>U</em>(<strong>ℂ</strong>ⁿ) is the space of entirerapidly decreasing functions in any horizontal band of&nbsp;<strong>ℂ</strong>ⁿ. We then use such continuity results to develop a framework for the STFT on K&#39;₁(ℝⁿ). Also, we devote one section to the characterization of <em>K</em>&rsquo;₁(ℝⁿ) and related spaces via modulation spaces. We also obtain various Tauberian theorems for the short-time Fourier transform.</p><p style="text-align: justify;">Part of the thesis is dedicated to the ridgelet and the Radon transform. We define and study the ridgelet transform of (Lizorkin) distributions and we show that the ridgelet transform and the ridgelet synthesis operator can be extended as continuous mappings <em>R</em>_{<em>&psi;&nbsp;</em>}: <em>S</em>&rsquo;₀(ℝⁿ) &rarr; <em>S</em>&rsquo;(<strong>Y</strong>ⁿ⁺¹) and <em>R^t</em>_{<span style="vertical-align: sub;">&psi;</span>}: <em>S</em>&rsquo;(<strong>Y</strong>ⁿ⁺¹) &rarr; <em>S</em>&rsquo;₀(ℝⁿ). We then use our results to develop a distributional framework for the ridgelet transform that is, we treat the ridgelet transform on <em>S</em>&rsquo;₀(ℝⁿ) via a duality approach. Then, the continuity theorems for the ridgelet transform are applied to discuss the continuity of the Radon transform on these spaces and their duals. Finally, we deal with some Abelian and Tauberian theorems relating the quasiasymptotic behavior of distributions with the quasiasymptotics of the its Radon and ridgelet transform.</p><p style="text-align: justify;">The last chapter is dedicated to the MRA of M-exponential distributions. We study the convergence of multiresolution expansions in various test function and distribution spaces and we discuss the pointwise convergence of multiresolution expansions to the distributional point values of a distribution. We also provide a characterization of the quasiasymptotic behavior in terms of multiresolution expansions and give an MRA sufficient condition for the existence of &alpha;-density points of positive measures.</p> / <p>U ovoj doktorskoj disertaciji razmotreno je nekoliko integralnih transformacija. Prva je short time Fourier transform (STFT). Date su i dokazane teoreme o neprekidnosti STFT i njena sinteza na prostoru test funkcije <em>K</em>₁(ℝⁿ) i na prostoru <em>K</em>₁(ℝⁿ) &otimes; <em>U</em>(ℂⁿ), gde je&nbsp;<em>U</em>(ℂⁿ) prostor od celih brzo opadajućih funkcija u proizvoljnom horizontalnom opsegu na ℂⁿ. Onda, ovi rezultati neprekidnosti su iskori&scaron;teni za razvijanje teorije STFT na prostoru <em>K</em>&rsquo;₁(ℝⁿ). Jedno poglavlje je posvećeno karakterizaciji&nbsp;<em>K</em>&rsquo;₁(ℝⁿ) sa srodnih modulaciskih prostora. Dokazani su i različiti Tauberovi rezultata za STFT. Deo teze je posvećen na ridglet i Radon transformacije. Ridgelet transformacija je definisana na (Lizorkin) distribucije i pokazano je da ridgelet transformacija i njen operator sinteze mogu da se pro&scaron;ire kako neprekidna preslikava <em>R</em>_&psi; : <em>S</em>&rsquo;₀(ℝⁿ) &rarr; <em>S</em>&rsquo;(<strong>Y</strong>ⁿ⁺¹) and <em>R</em>^t_&Psi;: <em>S</em>&rsquo;(<strong>Y</strong>ⁿ⁺¹) &rarr; <em>S</em>&rsquo;₀(ℝⁿ).&nbsp;Ridgelet transformacija na <em>S</em>&rsquo;₀(ℝⁿ) je data preko dualnog pristupa. Na&scaron;e teoreme neprekidnosti ridgelet transformacije su primenjene u dokazivanju neprekidnosti Radonove transformacije na Lizorkin test prostorima i njihovim dualima. Na kraju, dajemo Abelovih i Tauberovih teorema koji daju veze izmedju kvaziasimptotike distribucija i kvaziasimptotike rigdelet i Radonovog transfomaciju.<br />Zadnje poglavje je posveceno multirezolucijskog analizu M - eksponencijalnih distrubucije. Proucavamo konvergenciju multirezolucijkog razvoja u razlicitih prostori test funkcije i distribucije i razmotrena je tackasta konvergencija multirezolucijkog razvoju u tacku u distributivnog smislu. Obezbedjena je i karakterizacija kvaziasimptotike u pogled multirezolucijskog razvoju i dat dovoljni uslov za postojanje &alpha;-tacka gustine za pozitivne mere.</p>

Fingerprints are the oldest and most used form of biometric identification. A critical step is reliable extract minutiae from the fingerprint images. However fingerprint images are rarely of perfect quality, they may be degraded and corrupted due to natural variations in skin and sensing conditions. Thus, image enhancement techniques are necessary prior to minutiae extraction. This work includes implementation of three techniques for fingerprint image enhancement, minutiae extraction and consturction of fingerprint reading device. Experiments are realized with two sets of fingerprints to evaluate the performance of implemented techniques.

Denna rapport omfattar ett arbete kring att förbättra signalbehandling och målföljning av en förbränningsfrekvens i en androidapplikation för effektberäkning hos accelererande fordon. Den ursprungliga applikationen är utvecklad på i3tex AB och det var även där som arbetet utfördes. Effektberäkningen görs genom att först spela in ljudet i kupén under ett accelerationsförlopp, där inspelningen signalbehandlas och förbränningsfrekvensen målföljs, sedan sker transformering från frekvensdomänen till hastighetsdomänen, varpå effekten beräknas via multiplikation av fordonets vikt, hastighet och acceleration. Problemet med den ursprungliga implementationen av målföljningen var att algoritmen inte var tillräckligt robust mot lågt signal/brus-förhållande (snr). För att göra systemet mer robust utvecklades flermålsföljning med Kalmanfilter, där ett poängsystem bestämmer vilken av målföljarna som mest troligt har följt förbränningsfrekvensen. Den nya algoritmen presterar betydligt bättre än den ursprungliga i avseende på rmse, men är betydligt mer resurskrävande. Genom optimering av hur signalbehandlingen görs, såsom längd och typ av fönsterfunktioner och andra parametrar för korttidsfouriertransformen (stft), är exekveringstiden för hela analysen marginellt snabbare och betydligt snabbare på en androidenhet med respektive utan stöd för hårdvaruaccelererade flyttalsoperationer. Det visade sig även att, trots att inte hårdvaruspecifikationerna för Android, cdd, specificerar inspelningar av frekvenser under 100 Hz är det möjligt på alla testade androidtelefoner och med tillräckligt gott resultat för att genomföra frekvensföljning enligt ovan.

In this thesis we examine properties of Gelfand-Shilov spaces Ssσ and Pilipović spaces Σsσ. These are spaces of smooth functions which, along with their Fourier transforms, decay sub-exponentially. Results for the two types of spaces relating to Fourier transforms, analyticity of functions, triviality of the spaces and short-time Fourier transforms are explored. It is determined that Σsσ is nontrivial if and only if s+σ&gt;1, and that results for Ssσ when s+σ≥1 can generally be found to have corresponding counterparts for Σsσ when s+σ&gt;1.

M. Tech. (Department of Metallurgical Engineering, Faculty of Engineering and Technology), Vaal University of Technology. / To meet the ever-increasing demand for maintenance of gear systems, industrial companies have traditionally depended on the shutdown of the machines before processing the fault diagnosis. Nowadays, online monitoring has proven to be effective in terms of machine state analysis and fault prediction. However, the application of such a technique in the analysis of combined multiple nonlinear faults is still a subject of research. The vibration signature of a coexisting nonlinear crack and pit in two-stage gear system is unknown, it can be regarded as one of the most difficult problems to extract and diagnose. Additionally, incorporating both a crack and a pit into numerical models is a time-consuming process that demands a breadth of mechanical understanding. Diagnostics of faulty gears, on the other hand, can be performed in the time and frequency domain or in the Time-Frequency domain, depending on the complexity of the vibration. Non-linear and non-stationary phenomena (Features) occur when repeated pitting and cracking faults occur, reducing the reliability of standard signal processing methods (Gear displacement and Fast Fourier Transform). This thesis solves each of these shortcomings by developing an eight-degree-of-freedom (DOF) gear model with a breathing crack and multiple pitted gear teeth. The identified spur-gear model enabled the investigation of the crack and pitting signatures and their effect on the ensuing vibrations independently of the action of other system components. Additionally, when pitting and cracking coexist, the study was conducted to determine the influence of such a failure on the transmission system. Theoretical results indicated that the presence of pitting and crack in the tooth of the gear resulted in a decrease in mesh stiffness. Additionally, the influence of the breathing pitting and crack results in material fatigue, which results in the generation of a random term in the vibration signal. To corroborate the acquired results, several experimental tests on a spur-gear test rig with a defined pit and crack size range were undertaken under a variety of conditions. In comparison to the presented methodologies, theoretical and experimental results indicate that 3D Frequency-RPM analysis is the most sensitive and resilient method for the early detection and identification of pit and crack faults. Furthermore, when crack or pit faults are studied individually, the STFT analysis yields interesting results. The feature analysis revealed that, when using the Time-Frequency technique, the crack and pit combination in a two-stage gear system is a priori more efficient than the other options.

Extracting the Electric Network Frequency (ENF) fluctuations from an audio recording and comparing it to a reference database is a new technology intended to perform forensic digital audio authentication. The objective of this thesis is to implement and design a range of programs and algorithms for capturing and extracting ENF signals. The developed C-program combined with a probe can be used to build the reference database. Our implementation of the Short-Time Fourier Transform method is intended for the ENF extraction of longer signals while our novel proposed use of the Autoregressive parametric method and our implementation of the zero-crossing approach tackle the case of shorter recordings. A Graphical User Interface (GUI) was developed to facilitate the process of extracting the ENF fluctuations. The whole process is tested and evaluated for various scenarios ranging from long to short recordings.