ADAPTIVE SIGNAL PROCESSING THROUGH STOCHASTIC APPROXIMATION*

One of the problems in signal processing is estimating the impulse response function of an unknown system. The well-known Wiener filter theory has been a powerful method in attacking this problem. In comparison, the use of stochastic approximation method as an adaptive signal processor is relatively new. This adaptive scheme can often be described by a recursive equation in which the estimated impulse response parameters are adjusted according to the gradient of a predetermined error function. This paper illustrates by means of simple examples the application of stochastic approximation method as a single-channel adaptive processor. Under some conditions the expected value of its weight sequence converges to the corresponding Wiener optimum filter when the least-mean-square error criterion is used.     

Cyanit und Sillimanit in moldanubischen Granuliten

Zusammenfassung Der Cyanit tritt immer nur in biotitfreien Granuliten auf; in den biotitreicheren kommt Sillimanit vor. Der Cyanit gehört einer frühen Kristallisationsphase im polymetamorphen Ablauf der Granulitgenese an und ist immer älter als der Sillimanit. Cyanit kann sich direkt in Sillimanit umwandeln, meistens jedoch wächst der Sillimanit unabhängig von Cyanit. Die Fe-Gehalte beider Aluminiumsilikate werden angegeben und die Granulitgenese kurz diskutiert.

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Kyanite and sillimanite in moldanubian granulites

Summary Kyanite always occurs in granulites free from any biotite; in micaceous granulite kyanite is replaced by sillimanite. Kyanite belongs to an early phase of crystallization with in the polymetamorphic genesis of the granulite complexes, and is therefore older than sillimanite. Sillimanite may grow directly out of kyanite, in most cases, however, sillimanite appears to grow independently from kyanite. The iron-contents of both aluminium-silicates are indicated and the genesis of the granulites is shortly discussed.

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Mit 8 Abbildungen

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Herrn Prof. DDr.H. Wieseneder zum 65. Geburtstag gewidmet.     

Modelling waving crops in a wind tunnel

Analysis of movie films of a field of barley, combined with observations of the motions of individual plants, show that single stalks oscillate at a well-defined natural frequency even when stimulated by turbulent winds. Treating single stalks as resonant cantilevers allows the use of standard engineering methods to determine their elastic properties. Armed with these values, the application of similarity analysis to the equation of motion of a single stalk leads to criteria for aeroelastic modelling of wheat plants in the wind tunnel. A representative value for the spacing of stalks in a small section of model wheat field was calculated by referring to published data on momentum absorption in a variety of real and model canopies. Preliminary measurements of first and second moments of velocity in the model appear to confirm the importance of including elastic properties in wind-tunnel simulations of airflow in flexible crops.