This work focuses on efficient, joint time-frequency analysis of time series data. Joint time-frequency analysis is based on the sliding window. There are two major contributions of this thesis. Firstly, we haveThis work focuses on efficient, joint time-frequency analysis of time series data. Joint time-frequency analysis is based on the sliding window. There are two major contributions of this thesis. Firstly, we have introduced a notion of “aggregate spectrogram (AS)” which is a unimodal distribution at each time instant. The AS is extremely useful and computationally efficient when we are interested in a few spectral features and not the entire spectrum. Properties/characteristics of the AS have been listed. A para- metric method, based on a second order autoregressive model of the signal, for the construction of the AS, has been described. Of all the existing spectral estimation tools, the AS has the least computational complexity. Based on the AS, instan- taneous frequency estimation for multicomponent signals with equal amplitudes has been achieved. The AS does not require Goertzel filters in dual tone multi frequency detection applications. The AS finds many potential application. A few examples are voice activity detection, edge detection, motion vector estimation etc. Secondly, the problem of estimating the instantaneous frequency and band- width for multicomponent signals with time varying amplitudes has been solved by employing a new peak detection algorithm. The algorithm has been shown to outperform existing algorithms when the frequencies and amplitudes of the multi- component noisy signals are time-varying. Other contributions of the thesis include: low computational cost algorithms for the sliding discrete Fourier transform, and algorithms for its extension to spectral interpolation through zero padding and window padding. A low cost, optimized iii split-radix FFT architecture for zero-padded signals is also proposed. The Wiener-Khintchine theorem (WKT) yields better spectral estimates of Gaussian signals as compared to the discrete Fourier transform (DFT). Higher order spectra find utility in case of additive colored noise or the signals are non- Gaussian. Due to high computational complexities, the WKT and higher order spectra are avoided in the sliding window based spectral analysis. We have devel- oped recursive forms of the WKT, bispectrum and trispectrum whose computa- tional complexities have reduced to linear, quadratic and cubic orders, respectively introduced a notion of “aggregate spectrogram (AS)” which is a unimodal distribution at each time instant. The AS is extremely useful and computationally efficient when we are interested in a few spectral features and not the entire spectrum. Properties/characteristics of the AS have been listed. A para- metric method, based on a second order autoregressive model of the signal, for the construction of the AS, has been described. Of all the existing spectral estimation tools, the AS has the least computational complexity. Based on the AS, instan- taneous frequency estimation for multicomponent signals with equal amplitudes has been achieved. The AS does not require Goertzel filters in dual tone multi frequency detection applications. The AS finds many potential application. A few examples are voice activity detection, edge detection, motion vector estimation etc. Secondly, the problem of estimating the instantaneous frequency and band- width for multicomponent signals with time varying amplitudes has been solved by employing a new peak detection algorithm. The algorithm has been shown to outperform existing algorithms when the frequencies and amplitudes of the multi- component noisy signals are time-varying. Other contributions of the thesis include: low computational cost algorithms for the sliding discrete Fourier transform, and algorithms for its extension to spectral interpolation through zero padding and window padding. A low cost, optimized split-radix FFT architecture for zero-padded signals is also proposed. The Wiener-Khintchine theorem (WKT) yields better spectral estimates of Gaussian signals as compared to the discrete Fourier transform (DFT). Higher order spectra find utility in case of additive colored noise or the signals are non- Gaussian. Due to high computational complexities, the WKT and higher order spectra are avoided in the sliding window based spectral analysis. We have devel- oped recursive forms of the WKT, bispectrum and trispectrum whose computa- tional complexities have reduced to linear, quadratic and cubic orders, respectively
درد کا حد سے گزرنا ہے دوا ہو جانا نحمدہ ونصلی علی رسولہ الکریم امّا بعد فاعوذ بااللہ من الشیطن الرجیم بسم اللہ الرحمن الرحیم معزز اسا تذہ کرام اور میرے ہم مکتب ساتھیو!السلام علیکم! آج مجھے جس موضوع پر گفتگو کرنی ہے وہ ہے:’’درد کا حد سے گزرنا ہے دوا ہو جانا ‘‘ جنابِ صدر! دکھ درد، تکلیف ہم معنی الفاظ ہیں، زندگی میں ہر شخص کوکسی نہ کسی موقع پر رنج وغم اور دکھ و تکلیف سے واسطہ پڑتا ہے خوشیاں روٹھ جاتی ہیں، رنج و الم کے بادل گھٹائیں بن کر برسنا شروع ہو جاتے ہیں گھر کے آنگن میں نوید ومسرت کی چاندنی بکھیرنے والا قمر گہنا جاتا ہے۔ صدرِ ذی وقار! زندگی کے نشیب وفراز سے انسان ہمکنارر ہتا ہے۔ افراط و تفریط کا سلسلہ شروع رہتا ہے، کامیاب انسان وہ ہے جوایسے حالات میں مستقل مزاج رہتا ہے ان بوقلمونیوں سے اس کے پائے استقلال میں لغزش نہیں آتی اور یوں اس کی زندگی کی گاڑی رواں دواں رہتی ہے۔بقول غالبؔ رنج سے خوگر ہوا انساں تو مٹ جاتا ہے رنج مشکلیں اتنی پڑیں مجھ پر کہ آساں ہو گئیں صدرِ محترم! جب کوئی چیز حد سے بڑھ جاتی ہے، اپنی انتہا کو پہنچ جاتی ہے تو اس کا وجود عنقا ہو جاتاہے اس کی حیثیت بدل جاتی ہے اس کے نفع نقصان کا تصور تبدیل ہو جاتا ہے۔ اس کے مضر اثرات مصلح ہو جاتے ہیں اس میں یکسر تبدیلی آجاتی ہے اور ایّام کے ساتھ ساتھ وہ قصہ پارینہ بن جاتی ہے۔ محترم سامعین! رات اپنی انتہا کو پہنچتی ہے تو بادِ نسیم صبح کے حیات بخش جھونکوں سے آشنا ہے۔ دن اپنی بلندیوں کومس کرتا ہے تو قمر کی برووت بھری چاندنی قلب و ذہن کی طراوت کا باعث بنتی...
Temporary pools are relatively small water bodies with limited resources and are seasonally available. These freshwater bodies are rich source of microbial and planktonic lifeObjective: This survey was conducted to find out the presence of rotifers in temporary pools formed inJallo Park established in 1978 and explore their density and diversityMethods: Sample collection was done from ten pools with the help of a planktonic mesh. The counting was performed with a Sedgwick- Rafter chamber. Diversity indices like Shannon Weaver index etc. Were applied Results: In present study 27 rotifer species belonging to 14 genera were identified. The highest diversity and density was shown by Brachionus and Lecane. There was even distribution in each pool. Results of ANOVA showed statistically significant difference in population density and diversityConclusions: This study has presented a guideline to find out rotifer diversity which could be present in any water reservoir like temporary pool.
This qualitative study, where I was involved as a researcher and mentor, with two primary school mathematics teachers, who were in the beginning of their first year, describes the mentoring process in a particular setting. I conducted the study with the research participants in their classrooms during seven-week fieldwork. The data comes from semi-structured interviews (pre and post fieldwork), descriptive and reflective field notes, audiotape transcripts and teachers' journals. I played different roles such as: a support teacher, demonstrator/teacher and a critical friend. The findings of the study show that in a context like Pakistan, where teachers often enter the teaching profession without any professional training, need support not only in pedagogy and classroom management, but also in subject matter content as well. In the context of the mentor-mentee relationship, support from an experienced teacher seemed to enable them to address the challenges that they face. The study further sheds light on a mentor-mentee relationship and the roles that a school based mentor plays in supporting beginning teachers. Mentoring, in the untrained beginning teachers' context seems to be more enactive and supportive relationship rather than an advisory one, but the question still remains whether or not schools can afford to have mentors for professional development of the beginning teachers.