# Explanation of fundamental filtering's consequences on signal

Can anyone explain why exactly an "Overshooting" phenomena is observed when the fundamental harmonic is removed as seen on the figures? Is it technically right to call this "overshooting" at all ? If not, how is it referred to ?

Signals in time-domain:

Spectra:

• Can you kindly label your plots. Also add more background to understand the context. Aug 16, 2017 at 11:41
• I'm not sure about overshooting phenomena, but if you remove a single frequency from a signal (with notch-stop filter) or apply a filter with sharp cut-off you will observe a ringing in your filtered signal. Aug 16, 2017 at 12:21
• The Green curve, is the same as the blue one, but lacks the first harmonic. The spectra are respectively shown. Aug 17, 2017 at 9:05
• i don't really see any overshoot. i would just call this a "missing fundamental". Mar 20, 2018 at 23:20

As already mentioned by @Fat32 in the comments to your question what you're observing is not commonly referred to as overshoot.

As there are no units on both plots comparing the results in both figures is somewhat difficult. The following assumes that the horizontal axes in both plots are just the indices of either the time or frequency domain values (otherwise the graphs cannot be directly related without additional information and/or do not make sense).

The exact effects of what you're observing will generally depend on the frequency, amplitude and relative phase of the harmonics present in your signal.

A rough visual comparison of the green and blue lines in the first plot indicates that indeed the first harmonic has been removed. The difference between the green and blue lines is roughly a sine wave (phase zero) that fits into the window (i.e. no difference at the start, end and 1/2 of the window; largest difference at roughly 1/4 and 3/4 of the window).

Note that if the amplitude and/or phase of the first harmonic are different the time domain signal, resulting after subtraction of the first harmonic, will probably look completely different.

• The first graph displays the time domain signals. x axis : time, y axis: u(t). The seond graph is the abs of the FFT of both signals. Would you please tell me how to explain the effect of the first harmonic loss on the time domain signal? Aug 28, 2017 at 20:40
• What effects do you observe that are not addressed in the above answer? What kind of explanation are you looking for that is not in the above answer? Aug 29, 2017 at 18:41

I assume you used a filter to remove the harmonic. What you see in the second plot is the stop band ripple of this filter. If you extended the time signal beyond the orginal length, you would also see a slight smudging, also caused by the filter. This smudging would be extreme, if you just manually set the frequency bin of the harmonic to zero, as this corresponds to a convolution with a very broad si-like function. If you want to go into detail, get a standard text book about signal processing, like "Signals, Systems and Inference" by Alan Oppenheim.