diff --git a/content/GA_2_3/Analysis.ipynb b/content/GA_2_3/Analysis.ipynb index cd85ab9987540b7dc914ec8e936648d7d95b767c..67cfdaa4b4056ed694d3d1ec2f7c52e35e7b68de 100644 --- a/content/GA_2_3/Analysis.ipynb +++ b/content/GA_2_3/Analysis.ipynb @@ -571,7 +571,7 @@ "source": [ "### Detrending\n", "\n", - "In this project the signal of interest is the damped, harmonic motion of the cantilever-beam. In addition the measurements may contain (unwanted) effects of the sensor (think of an offset, due to imperfect manufacturing and/or prior calibration, or a drift over time, for instance due to temperature changes in the electronics during the experiment). By detrending we mean to remove such effects, prior to our spectral analysis, so that we can start with a nice, zero mean signal. A-priori detrending is good practice and generally yields a cleaner spectrum.\n", + "In this project the signal of interest is the damped, harmonic motion of the cantilever-beam. In addition the measurements may contain (unwanted) effects of the sensor (think of an offset, due to imperfect manufacturing and/or prior calibration, or a drift over time, for instance due to temperature changes in the electronics during the experiment). By detrending we mean to remove such effects, prior to our spectral analysis, so that we can start with a nice, zero mean signal. A-priori detrending is good practice and generally yields a cleaner spectrum. Next week (week 2.4 on Time Series Analysis) we cover the subject of removing unwanted effects from the signal in more detail, as to obtain a so-called **stationary** signal, meaning that the properties or characteristics of the signal (such as the mean) do not change over time, and, we provide practical means to “stationarize†a given or measured signal.\n", "\n", "There are built-in functions in Python to remove such an offset and/or trend (and you're free to use them). But, earlier in the MUDE, in week 1.3, you learned about least-squares parameter estimation, and that's what you can apply to do the detrending (and actually built-in functions just apply the very same principle). Next week, on Time Series Analysis, you will actually be covering (again) the estimation of a trend in a time series of measurements.\n", "As a re-cap for week 1.3: when a series of observations $y_1, …, y_m$ (in our case with $m=N$) is supposed or expected to exhibit a functional linear trend (a straight line in terms of a graph), this can be modelled as\n",