ڈاكٹر فضل الرحمن (م۱۹۸۸ء) کے آرا ء كا ایجابی اور سلبى پہلو

The government of General Ayub Khan (Former President of Pakistan) established an Institution in 1960, in the name of Idarah Tahqeeqat Islami (Islamic Research Institute). Dr, Fazlur Rahman, was the visiting professor at the institute remained on the rank of director of the year 1961 to 768 in seven years. And later, he serves as an advisor to the Islamic Ideology council. The writer who was published by the Institute of Islamic Research was the first editor of "Fikr-o - Nazar”. The scholars were considered as 'expertise of logic and philosophy' as 'interpretation of the Qur'an'. It is mentioned in the various verses of the Prophet (peace and blessings of Allah be upon him). The slaughtering of zakat in 'zakat' animal slaughtering 'basic laws and family planning' matters of marriage and Sunnah, such as the month of revelation, and their opinions have earned great reputation. And because of which they were accused of denying the heavenly nature of the Qur'an. Therefore, the first step towards Islamic thinking regarding the Islamic idea was to put an eye on Islamic law and religious beliefs on Islam. According to their plan, the difference between the Quranic verses and the verses and the laws of the law, is the difference. Regarding the meanings, his axis received: The beginning of the tradition and the meaning of 'the law of the law' is the word and the law. Islamic Laws' Principles Concernedly speaking about issues like Fiqh and Qa'as and al-Azai speak.

Adaptive Estimation Using State-Space Methods

This thesis focuses on the development of new variants of adaptive filters. Built around state-space framework, the proposed filters are especially suitable for applications like tracking, output feedback control and recursive spectrum estimation. They operate without prior knowledge of process and observation noise statistics and exhibit good stability properties. The development in this thesis can broadly be classified into state- space least mean square (SSLMS) and finite memory least-squares filters. SSLMS is a generalization of the well-known least mean square (LMS) filter. Incorporating linear time-varying state-space model of the underlying environment, SSLMS exhibits marked improvement in its tracking performance over the standard LMS. An extension of SSLMS is SSLMS with adaptive memory (SSLMSWAM). SSLMSWAM iteratively tunes the step-size parameter by stochastic gradient method in an attempt to yield its most appropriate value. This filter is useful for situations where a suitable value of step-size parameter is difficult to obtain beforehand. Recursive nature of an adaptive filter brings with it stability issues. The concept of finite memory (or receding horizon) for an adaptive filter is appealing because it ensures stability. This motivates the development of finite memory filters, both for iiiunforced and forced systems. Finite impulse response (FIR) adaptive filter, built around structure of an unforced system, uses weighted observations on a finite interval. Uniform weighting of the observations results in rectangular RLS (RRLS). Additional flexibility is achieved by developing an adaptive memory variant of FIR adaptive filter. Similar to SSLMSWAM, the data window size is iteratively tuned so as to minimize the prediction error. For the forced system case, a useful solution in the form of receding horizon state observer is obtained. It finds utility in output feedback control of linear time-varying systems. An insight into convergence properties of finite memory based filters is provided by the convergence analyses. Spectrum update with the arrival of new data is a desirable feature in real-time spectrum estimation applications. The mathematical equivalence of RRLS resonator bank and recursive discrete Fourier transform (DFT) gives the rationale for using the newly developed filters for recursive spectrum estimation. A symmetric windowed variant of RRLS called ‘truncated exponential RLS (TERLS)’ is useful for reducing spectral leakage. Same is true for an SSLMS resonator, which has an attractive feature that spectral side levels and main lobe width may be reduced simultaneously by reducing the step-size parameter. The higher order resonator (HOR), constructed from several SSLMS resonators, exhibits close resemblance to an ideal (rectangular) frequency bin, thus minimizing spectral leakage and increasing resolution.