In this paper, we derive the impulse response of a fractional second order filter of the form ðs2þasþbÞ g, where a; b 0 and g40. The asymptotic properties of the impulse responses are obtained. Moreover, based on the derived analytical impulse response, we show how to perform the discretization of the above fractional second order filter. Finally, a number of illustrated examples in time and fr...

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Compressed images may be decompressed for devices using di erent resolutions. Full decompression and rescaling in space domain is a very expensive method. We studied downscaled inverses where the image is decompressed partially and a reduced inverse transform is used to recover the image. We studied the design of fast inverses, for a given forward transform. General solutions are presented for ...

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In this study, a synthesis tool using a novel multirate folding technique, which handles each FIR filter in a multirate DSP system as a single node, is developed. A new architecture is presented for the multiplierless realization of a fold of multirate FIR filters. This synthesizer fully exploits the redundancies (i.e. "idle" and "missing" cycles) and common terms in multirate systems without s...

We study in a constructive manner some problems of topology related to the set Irr of irrational reals. The constructive approach requires a strong notion of an irrational number ; constructively, a real number is irrational if it is clearly different from any rational number. We show that the set Irr is one-to-one with the set Dfc of infinite developments in continued fraction (dfc). We define...

The H2-optimal controller for systems with preview, in which the knowledge of external input is available in advance for the controller, is derived. The single input case is first considered and solved by transforming the problem into a non-standard LQR problem. It turns out that the extensions to multiple inputs and multiple preview times cases are straightforward. In every case considered, th...