Basic Concepts in Digital Signal Processing for by Frank Scherbaum

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By Frank Scherbaum

Digital sign processing has develop into a growing number of an essential component of observational seismology. whereas it bargains unparalleled energy in extracting details from seismic signs, it comes on the cost of getting to benefit numerous new abilities. facing electronic seismic info calls for at the very least a simple knowing of electronic sign processing. Taking the calculation of precise flooring movement because the guiding challenge, this path covers the elemental conception of linear platforms, the layout and research of easy electronic filters, the impression of sampling and A/D conversion and an creation to spectral research of electronic signs. It encompasses a variety of examples and workouts that may be reproduced utilizing the PITSA software program package deal (Scherbaum and Johnson 1993) or related programs.

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We will start out by looking at the differences that makes to our tools for the analysis of systems. 1 shows how the different concepts we have been using to describe the RC-filter have to be formally extended in order to describe general LTI systems. 1) we can see it as a special case of an Nth order LTI system N k=O dk L dk Ctkd-/-y(t) + ~ 15k~-x (t) = 0. 1 how the other concepts are extended to the general case. 5 we have seen that for a system with a single pole, the impulse response could be left-sided or right-sided depending on the region of convergence considered.

The Whittaker reconstruction) is also done by low pass filtering. The Whittaker reconstruction simply takes out all frequencies above the Nyquist frequency. 5 Hz and a discretization frequency of 10 Hz? Try to infer the rule for calculating the alias frequency for a given signal frequency and a given digitization frequency. Hint: The Nyquist frequency is also referred to as the folding frequency. Think of the frequency band as a foldable band which is folded at multiples of the Nyquist frequency.

Fsp is proportional to the elongation (x r = X m - X o measured within t ~ refea'enoe frame x which is attached to the seismometer frame). If the spring is elongated (x r < 0), the force ]:sp will be positive (pointing upwards). 2) • The dashpot - - Finally, the frictional force f / i s acting on the mass. It is propor- tional to the velocity "~m(t) with which the mass is moved with respect to the dashpot. As with the elongation of the spring, this quantity is best described within the reference frame x which is attached to the frame of the seismometer.

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