Abstract
This final chapter presents exercises on most of the techniques discussed in the book, including filter design and filtering implementation, stationary and non-stationary spectral analysis, etc.
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- 1.
Note that since we assigned a value of T_s to our synthetic data, we can express frequencies in analog terms, as we would do in the real world.
- 2.
Actually these functions also serve to compute the cross-correlation and cross-covariance between two records.
- 3.
Angular frequencies here are in \((-\pi ,\pi ]\). There is no particular reason for this choice, which is perfectly equivalent to the usual one \([-\pi ,\pi )\).
- 4.
We could decide to always include the c.l. used for the scalogram in this set of four probability values and avoid the calculation of global_signif. However, we prefer to keep the choice of the additional c.l. values for the GWS separate from the choice made for the scalogram. At the same time, it is evident that if we used the 95 % for the scalogram, for instance, we must also use it for the GWS. So, global_signif is directly related to the choice made for the scalogram significance test, while glob_sign is completely free for what concerns the probability levels.
- 5.
The function can be used also for wavelets packets.
- 6.
In the most general case, the threshold or the set of level-dependent thresholds could be made time-dependent, to handle non-stationary variance noise models. In that case, the signal’s model would still be \(x[n] = s[n] + \sigma _e e[n]\), but the noise standard deviation \(\sigma _e\) should be allowed to vary with time, because there are several different variance values on several time intervals. The values as well as the intervals could then be found by wvarchg. We will not go deeper into these more advanced de-noising techniques.
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Alessio, S.M. (2016). Exercises with Matlab. In: Digital Signal Processing and Spectral Analysis for Scientists. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-25468-5_16
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