The wavelet transform technique has been frequently used in time-frequency analysis as a relatively new concept. Compared to the traditional technique Short-time Fourier Transform (STFT), which is theoretically based on the Fourier transform, the wavelet transform has its advantage on better locality in time and frequency domain, but not significant as the solutions in spectrum. Wavelet transform has dynamic ‘window functions’ to represent time-frequency positions of raw signals, and can get better resolutions in time-frequency analysis. In this report, we shall first briefly introduce fuzzy sets and related concepts. And then we will evaluate their similarities and differences by not only the theoretic comparisons between STFT and wavelet transform, but also the process of the de-nosing to a noisy recorded signal.

Thesis (M.S.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / We address the problem of efficiently computing, over narrow frequency bands, the short-time Fourier transform (STFT) and approximations to the STFT. This problem is important for the design of signal understanding systems that have to efficiently carry out STFT reprocessing of signals in order to examine detailed features of signal components that have already been located within narrow frequency bands. In the computation of the exact STFT we use an "overlap pruning" approach (Covell et al. 1992) for exploiting the commonality of computations between successive slices of the STFT with unity decimation interval. We have also extended this approach to the STFT with non-unity decimation intervals and combined it with a frequency pruning method (Sreenivas et al. 1980) to provide additional computational savings. In the computation of approximations to the STFT we use an algorithm (Khan et al. 1988) for efficiently computing Taylor series approximations over narrow frequency bands. Through examples involving real data we demonstrate the feasibility of using the approximated STFT to obtain more accurate estimates of the center frequency of spectral peaks, and to resolve multiple peaks that have been smeared due to the use of short window lengths. The efficiency of all the algorithms we have investigated is less than 0(N log N) multiplications per STFT slice and can be as small as O(N) multiplications per STFT slice in certain cases. Consequently, all the algorithms compare favourably with the standard FFT implementation of the STFT which requires O(N log N) multiplications per slice. All the algorithms considered in this thesis were implemented in software and tested on synthetic and real sound signals. / 2999-01-01

Our thesis work focuses on Frequency-domain Blind Source Separation (BSS) in which the received mixed signals are converted into the frequency domain and Independent Component Analysis (ICA) is applied to instantaneous mixtures at each frequency bin. Computational complexity is also reduced by using this method. We also investigate the famous problem associated with Frequency-Domain Blind Source Separation using ICA referred to as the Permutation and Scaling ambiguities, using methods proposed by some researchers. This is our main target in this project; to solve the permutation and scaling ambiguities in real time applications / Gozie: modebelu2001@yahoo.com Anayo: ezeudea@yahoo.com

In this thesis we study the short-time Fourier transform. The short-time Fourier transform of a function f(x) is obtained by restricting our function to a short time segment and take the Fourier transform of this restriction. This method gives information locally of f in both time and frequency simultaneously.To get a smooth frequency localization one wants to use a smooth window, whichmeans that the windows will overlap. The continuous short-time Fourier transform is not appropriate for practical purpose, therefore we want a discrete representation of f. Using Gabor theory, we can write a function f as a linear combination of time- and frequency shifts of a fixed window function g with integer parameters a; b > 0. We show that if the window function g has compact support, then g generates a Gabor frame G(g; a; b). We also show that for such a g there exists a dual frame such that both G(g; a; b) and its dual frame has compact support and decay fast in the Fourier domain. Based on [2], we show that B-splines generates a pair of Gabor frames.

Incorporating information from the short-time phase spectrum into a feature set for automatic speech recognition (ASR) may possibly serve to improve recognition accuracy. Currently, however, it is common practice to discard this information in favour of features that are derived purely from the short-time magnitude spectrum. There are two reasons for this: 1) the results of some well-known human listening experiments have indicated that the short-time phase spectrum conveys a negligible amount of intelligibility at the small window durations of 20-40 ms used for ASR spectral analysis, and 2) using the short-time phase spectrum directly for ASR has proven di?cult from a signal processing viewpoint, due to phase-wrapping and other problems. In this thesis, we explore the possibility of using short-time phase spectrum information for ASR by considering the two points mentioned above. To address the ?rst point, we conduct our own set of human listening experiments. Contrary to previous studies, our results indicate that the short-time phase spectrum can indeed contribute signi?cantly to speech intelligibility over small window durations of 20-40 ms. Also, the results of these listening experiments, in addition to some ASR experiments, indicate that at least part of this intelligibility may be supplementary to that provided by the short-time magnitude spectrum. To address the second point (i.e., the signal processing di?culties), it may be necessary to transform the short-time phase spectrum into a more physically meaningful representation from which useful features could possibly be extracted. Speci?cally, we investigate the frequency-derivative (or group delay function, GDF) and the time-derivative (or instantaneous frequency distribution, IFD) as potential candidates for this intermediate representation. We have performed various experiments which show that the GDF and IFD may be useful for ASR. We conduct several ASR experiments to test a feature set derived from the GDF. We ?nd that, in most cases, these features perform worse than the standard MFCC features. Therefore, we suggest that a short-time phase spectrum feature set may ultimately be derived from a concatenation of information from both the GDF and IFD representations. For best performance, the feature set may also need to be concatenated with short-time magnitude spectrum information. Further to addressing the two aforementioned points, we also discuss a number of other speech applications in which the short-time phase spectrum has proven to be very useful. We believe that an appreciation for how the short-time phase spectrum has been used for other tasks, in addition to the results of our research, will provoke fellow researchers to also investigate its potential for use in ASR.

In this thesis we use pulse shaping system to generate pulse train. Using empirical mode decomposition(EMD) and short-time Fourier transform(STFT) to analyze the signal of terahertz radiation. we use pulse shaping system to modulate the amplitude and phase of light which provide for pulse train generation. Compare with other method, first, our method will improve the stability of time delay control. Second this method is easier to control the time delay and number of pulse in the pulse train. In the past, people find the occur time of high frequency by observed the time domain of terahertz radiation directly, but if the occur time near the time of the peak power of terahertz radiation, we can¡¦t find out the occur time of high frequency. Using STFT can find out the relationship between intensity and time, but if the modes in signal have different width of frequency STFT have to use different time window to get the best frequency resolution and time resolution. However the time window with different width will have different frequency resolution, and the relationship between intensity and time will change with different frequency resolution, therefore using different frequency resolution will get different result, so we need a new signal analysis method. To solve this problem we use EMD to decompose different mode in the signal of terahertz radiation into different intrinsic mode function(IMF), and analyze the signal of terahertz by STFT to find the occur time of high frequency of terahertz radiation. Because the modes are separated in to different IMF, we can use STFT with the same time window. We expect this method applied to narrow-band frequency-tunable THz wave generation will be better.

This article studies ambient noise in the surf zone that was simulated by piston-type wavemaker in the tank. The experiment analyzed the bubbles of breaking wave by using a hydrophone to receive the acoustic signal, and the images of bubbles were recorded by a digital video camera to observe distribution of bubbles. The tank is in College of Marine Sciences, National Sun Yat-sen University, the dimensions of water tank are 35 m ¡Ñ1 m ¡Ñ1.2 m, and the slope of the simulated seabed is 1:5. The studied parameters of ambient noise generates by breaking wave bubbles were wave height, period, and water depth. Short-time Fourier Transform was applied to obtain the acoustic spectrum of bubbles, MATLAB programs were used to calculate mean sound pressure level, and determine number of bubbles. Bubbles with resonant frequency from 0.5 to 10 kHz were studied, counted from peaks in the spectrum. The number of bubbles generated by breaking waves could be estimated by bubbles energy distributions. The sound pressure level of ambient noise was highly related to the wave height and period, with correlation coefficient 0.7. The results were compared with other studies of ambient noise in the surf.

The aim of this thesis is to determine the horse’s gait types using the acceleration values measured from the horse. A measurement was taken in Gävletravet, a total of five Nanotrak sensors were used, four on the different parts of the horse, and one on the hand of the horse’s driver, a car was driven parallel to the horse and the motions of the horse was recorded by a camera in order to synchronize with the data measured by the sensors, a total of four videos were recorded. The software to process the data was Matlab R2010b, and the methods to analyze them were Fast Fourier Transform (FFT), Short Time Fourier Transform (STFT), and Least Squares (LS). Different window functions were tried when applying the STFT, and the Hanning window was the best to smooth the curves, different window sizes (or data length) were also tried, the data length of 512 was found to be the most proper value. The methods for classification of horse’s gaits included amplitude, ratio, and LS. The method of amplitude worked well for the first three videos except for the last one, and performed better than the other two. The method of ratio was more reliable, but the results were not satisfactory. The method of LS gave bad results, so it was not trustworthy. More measurements and more analysis needed to be done in the future to find a proper way to automatic determine the horse’s gaits, and the use of modern technology will be very popular in other fields like animal science.

In this report, studies on interharmonics from three different measurement sites are performed. The first site is a wind park with three turbines, where the measurements are performed at the point of common coupling of these three. The second site is a network which consists of a PV inverter and two types of EV chargers – a DC charger or an AC charger. Measurements are performed with three different set-ups in this site – only AC charger connected, only DC charger connected, and AC charger and PV inverter connected simultaneously. The third site where measurements were made is a microgrid using frequency control in order to signal how the microgrid should operate at the moment. The interharmonic analysis was conducted using desynchronized processing technique (DP) and Sliding-Window Estimation of Signal Parameters via Rotational Invariance Techniques (SlidingWindow ESPRIT or SWESPRIT). The result from the wind park is that closely and evenly spaced interharmonics can be seen when the current suddenly increases (could be fast variations in wind speed). It is however uncertain if these interharmonics are caused by spectral leakage or not since SWESPRIT estimates the fundamental frequency to vary drastically when wind speed varies. It is observed that the SWESPRIT estimation of fundamental frequency could be caused by sudden changes in phase angle as the current varies. Further investigation and analysis are needed. The result from the measurements on the site with EV chargers and a PV inverter is that eight distinct patterns can be observed. Some patterns appear to come from the upstream grid, while some appear to be caused by either one of the EV chargers or the PV inverter, or interaction between them. Further studies are needed. The result from the microgrid measurements is that two distinct patterns at high frequencies (above 1000 Hz) can be observed during grid connected mode and island mode, respectively. During transitions between grid connection and island mode or vice versa, the fundamental frequency varies drastically, and it is therefore hard to analyse potential interharmonics and draw inferences. Further studies are needed. Advantages and disadvantages, as well as ideas for improvements, of the two applied signal processing methods are discussed throughout the different case-studies.

The main subject of this work represents the time-frequency signal analysis. Firstly, it intends to provide the most essential theoretical background with focus on the continuous wavelet transform, where also a comparison of the key features with its close relative the short-time Fourier transform is performed. Afterwards, there follows a demonstration of the purpose with a practical example. The particular aim is to create a phase vocoder solution for modifying the length of a sound record duration and pitch shifting. Here, in this place, the functional principles, design, procedure of assembling, outputs and achieved results are well documented.