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Institute for Measurement Technology
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Statistical signal processing by means of cyclostationary processes and higher order spectra

Andreas Winkler


With the computers of today becoming more and more powerful, we get great possibilities in signal processing. It is possible to complete more complex computational tasks ina for the appropriate application reasonable time and to apply better and more extensive mathematical methods.
Many conventional signal-processing methods treat random signals as if they were statistically stationary, that is, as if the parameters of the underlying physical mechanisms that generate those signals do not vary with time. But for most man-made signals (especially in communication and transmission technology) and even natural happenings (just think about climate- and weather data or biomedicine), some parameters do vary periodically with time. That's why we deal with the theories of cyclic stationary processes and higher order spectra. With the cyclic autocorrelation function as an extension of the usual autocorrelation function as well as with the spectral correlation density as an extension of the usual power spectral density it is for example possible to properly separate two signals, which almost share the same spectral band. As a further example, with higher order spectra it is possible to detect phase coupling of components in a signal. Of course there exist much more applications for these theories.
This student project deals with the theory and the development of accordant algorithms plus some particular applications, which are showcased.

October 21, 2009

Figure 1: With the cyclic autocorrelationfunction it is possible to detect correltation of frequency shifted components of a signal. Here the CACF of a pure cosine is shown. Figure 2: The number of observed sunspots over time are a typical example for a natural cyclostationary process.