The Moving Average - High Pass Filter
Learn how a correctly plotted moving average can be inverted to reveal high frequency components of a signal.
Inversion Excursion
We saw in previous articles of this series how only a correctly plotted moving average can be used as a low pass filter for time series extraction of periodic components. Now, let’s take it to the next level by inverting that moving average - throwing away the low passed data and retaining only components shorter in period than the cutoff of the moving average (period). Since in our work we have both the low pass filtered time series (via the application of the centred moving average) and the original signal time series (be that a test signal as above or financial time series) we can perform the operation easily.
Below is how it is done, via the help of some pseudo code. Note carefully that the subtraction performed to reveal the higher frequency components not present in the low pass filter can only be done if the original signal and low pass filtered signal are correctly a…