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so i basically have a low pass filtering that is filtering a square wave and giving me in output :
As far as i know the square wave can be made with the sum of multiple sine waves
So the over/undershoot i have is due to the frequencies that are not being filtered.
The triangle wave i have is this one, i want to know if the same logic can be used to understand the output of the filter
No, you're not seeing the Gibbs phenomenon on your triangle wave (although it would happen, if it were slower and had a period that's an integer fraction of your sampling rate).
What it appears that you've done is to generate a sine wave that is quite fast with respect to your sampling rate. That is why it doesn't appear to be a perfect triangle wave. Moreover, it is not a low-order integer ratio of your sampling rate (i.e., it's not exactly 2/7, but it appears to be close). Because the ratio isn't exact, you're generating aliases of the higher-order harmonics -- this is why your "triangle" wave appears to be riding on a sine wave.
Your low-pass filter, acting in sampled-time, is filtering out the rapidly-moving "triangle" part, and passing the low-frequency sinusoidal, which is genuinely there as a consequence of the aliasing.
Since the fundamental sine wave is actually 27% higher than the square wave, it is easy to induce ringing from impedance mismatch and block filters that simply truncate harmonics.
One example is by eliminating all above 5f of a squarewave, namely only 1f, 3f and 5f, you can see that the fundamental 1f is greater than the squarewave peak by 27% and ringing appears. That would be a "brick LP filter" just above 5f with 1f = 222 Hz and LPF =1kHz.
A low pass filter with under-damped qualities or Q> 0.707 is what you have. However it is possible to eliminate the ringing by low Q filters <0.7. It is possible to choose a Bessel or Elliptical Filter and Cauer Filters to suppress this harmonic ringing. High order maximally flat Group Delay filters or linear phase shift also have this property of reducing overshoot. These are chosen due to their flat group delay or more linear phase shift properties. ( I will avoid the details here)
Here are 2 examples of 1kHz LPF's . See that the Chebychev filter is more like a brick wall filter such as used to show a 250 Hz square wave with only 1f 3f 5f and cutoff at 1kHz will have ringing or overshoot.
Any questions?
" if the same logic can be used to understand the output of the filter" same logic ?
It is a principal of harmonic attenuation or ratio in -dB per octave and also phase shift as some other measurement.
Your sine has triangles that are ~ approx 19x f of the sine wave or 2,4,8,16 approximately 4 octaves at -6dB/octave per order filter so one can expect >-24dB per order filter of suppression of the big triangles.
