A new method of realizing linear, time-invariant digital filters is developed and demonstrated. The result is based on the convolution integral. It is assumed that the specifications of the filter are known and from these, an appropriate analog filter is chosen. The properties of this filter are then retained by digital filter after transformation. The behaviour of lowpass, highpass bandpass and bandstop digital filters is investigated in both the frequency and time domains, for both cascade and parallel structure is superior for lowpass and bandpass digital filters, and that the cascade structure is superior for high pass and bandstop digital filters. / Thesis / Master of Engineering (ME)

In this thesis, a highly selective broadband hybrid bandpass filter operating between 0.4-2.0 GHz with a stopband up to 7 GHz is designed and analyzed. The realization is carried out by hybrid method, which combines both lumped and distributed element filters. In this approach, two separate filters, which are lumped highpass with 0.4 GHz corner frequency and distributed stripline lowpass with 2 GHz corner frequency, are combined to get the bandpass filter that has a passband in between 0.4 to 2.0 GHz. The usage of the lumped elements for the highpass filter resulted in a great size reduction compared to distributed element approach. The design software FILPRO&trade / is used to synthesize the trial filters. More than forty filters are synthesized, and among them, the ones that have better properties are chosen for further processes. Optimization, modeling and electromagnetic simulations of the selected lumped and distributed filters are carried out on the software GENESYS&trade / . Distributed filters are also simulated using the software SONNET&trade / . After the simulations, all of the simulated filters are realized and measured, and the level of consistency with the simulations is observed. According to the results of the measurements, the filter combination that has the best combination of low insertion loss, small dimensions, high stopband attenuation and low spur levels is selected for the final bandpass filter structure and a few variants are examined to get the final structure.

The goal of this project is to perform a pre-study for taking a step toward implementing CT-scanners into medical transportation, and to answer the following questions. Can a miniaturized CT-scanner be created from lower end hardware without compromising image quality? Which image filters are optimal to obtain the clearest, least noisy images from the created CT-scanner? To answer these questions, a literature study is performed and the study shows that a highpass filter combined with flat field correction and a contrast enhancing filter is the most efficient way to increase the image detail in an X-ray image. The image filter is created in MATLAB and the CT-scanner software is created with Python. This project concludes that it is possible with the right hardware and software implementations, to create a miniature CT-scanner as images of both organic and inorganic objects are taken, filtered and their internal structure displayed.

Diese Arbeit beschäftigt sich sowohl mit der experimentell motivierten Fragestellung nach der Kontrolle der Einzelzellaktivität kortikaler Neurone sowie mit der theoretischen Beschreibung der neuronalen Dynamik und ihrer Transfereigenschaften anhand einfacher Neuronenmodelle. Hierfür werden in-vivo Daten, die mit Hilfe der juxtazellulären Stimulation mit weißem bandpass limitiertem Gaußschem Rauschen erhoben wurden, verwendet. Mit Parameterfits einfacher Neuronenmodelle werden die experimentell ermittelten Pulszugstatistiken sowie die präzisen Zeitpunkte der einzelnen Aktionspotentiale quantitativ reproduziert. Diese Untersuchungen zeigen, dass mit dynamischen Rauschstimuli in juxtazellulärer Stimulation verlässlich und reproduzierbar Pulszüge in einzelnen kortikalen Neuronen hervorgerufen werden können. Weiterhin offenbart die Analyse der Daten die Eigenschaft der untersuchten Neurone frequenzunabhängig, bishin zu Vielfachen der Feuerrate des Neurons, Information über Signalkomponenten zu transferieren. Diese Eigenschaft steht im Widerspruch zum Verhalten der einfachsten (und populärsten) integrate-and-fire Modelle, die die Zelle ohne Auflösung ihrer räumlichen Struktur näherungsweise beschreiben. Die Erweiterung solcher Ein-Kompartiment Modelle auf ein Zwei-Kompartiment Modell und die damit eingeführte Unterscheidung zwischen Soma und Dendrit ermöglicht es, für einzelne Neuronen sämtliche experimentell erhobenen Statistiken, einschließlich des Hochfrequenz- Transfers, quantitativ zu reproduzieren. Zusätzlich zu den obigen Untersuchungen wird eine Methode vorgestellt, um, anhand von Input-Output Statistiken konkreter Neurone, Gaußsche Stimuli zu berechnen, die in der jeweiligen Zelle einen vorgeschriebenen Pulszug hervorrufen. In Experimenten und Simulationen wird gezeigt, dass diese vorgeschriebenen Pulszüge mit einer Verlässlichkeit erzeugt werden können, die in etwa der intrinsischen Verlässlichkeit des untersuchten Neurons entspricht. / This work elaborates on the question to which extent experimental control about the activity of single cortical neurons can be achieved and deals with the theoretical description of the neuronal dynamics. To this end, in-vivo data that have been recorded from juxtacellular experiments in cortical neurons are used. By means of parameter optimization, simple neuron models are fitted in order to quantitatively reproduce the measured spike train statistics and specific action potential timings. The analysis reveals that dynamic noise-stimuli can be used in juxtacellular stimulation to reliably generate reproducible spike trains in single cortical neurons. The analysis also reveals that the cells show a marked broadband coding of information, up to frequencies that are multiples of the firing rate of the respective neuron. This is in contrast to what is known for the simplest (and most popular) integrate-and-fire models, for which the cellular dynamics are described by a single space-independent variable. The extension of these one-compartment models to two-compartment models introduces a spatially distinction between soma and dendrite and we could show that for particular neurons it is sufficient to quantitatively reproduce all experimentally measured spike-train and input-output statistics, including the highfrequency information-transfer. Therefore, the effect of the spatial structure can be an important (structural) mechanism that can have influence on the neuronal dynamics. Additionally to the above considerations, by means of input-output statistics of particular neurons, we propose a method to compute Gaussian stimuli that are supposed to evoke prescribed spike trains in the respective neuron. Using experiments and simulations, we show that the prescribed spike trains can be evoked with a reliability that is comparable to the intrinsic reliability of the neuron under investigation.