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Over the last decade or so, wavelets have had a growing impact on signal processing theory and practice, both because of their unifying role and their successes in applications. Filter banks, which lie at the heart of wavelet-based algorithms, have become standard signal processing operators, used routinely in applications ranging from compression to modems. The contributions of wavelets have often been in the subtle interplay between discrete-time and continuous-time signal processing. The purpose of this article is to look at recent wavelet advances from a signal processing perspective. In particular, approximation results are reviewed, and the implication on compression algorithms is discussed. New constructions and open problems are also addressed. Finding a good basis to solve aproblem dates at least back to Fourier and his investigation of the heat equation. The series proposed by Fourier has several distinguishing features: The series is able to represent any finite energy function on an interval. The basis functions are eigenfunctions of linear shift invariant systems or, in other words, Fourier series diagonalize linear, shift invariant operators.

The present article consists of three sections. The first section considers some dimensions of the discussion on ‘rights’ in the framework of religious thought with the centrality of jurisprudence, and distinguishes four types of rights, defining each of them. This section aims at specifying the central point of the subject of this study. In the framework of jurisprudence, rights – as opposed to obligations – contain benefits for a Muslim, and they have been mentioned inside Shariʿa in a variety of direct or indirect forms through legal or non-legal languages. Sometimes, such rights have not been mentioned in Shariʿa. The latter type constitutes of rights that we may cause them to be confirmed by Shariʿa through some certain mechanisms. In the second section of this study, the nature of the theory of Ibāḥa (literally, ‘permissibility’) and important arguments in this regard have been considered. Our purpose in entering this section was clarifying the mechanisms of confirmation of right of the fourth type. The last section of the article is dedicated to the political results of the theory of ibāḥa from the viewpoint of political rights. In this section, we have discussed in detail that by accepting the theory of ibāḥa, the way is paved for harmonizing the religious world with other worldly realms.