TL; DR A high-pass filter? The first and second derivatives could be easily enough described with first and second-order feedback filters, respectively, but once you start fitting that stuff into DSP terminology, then you might as well make a low-order high-pass filter that has the characteristics you desire.
If you're looking for the time of the peak, I've had a lot of luck by taking the time (or index) of samples weighted by their values. This produces surprisingly high accuracy. I'm sure very mathy person will tell me why that is mathematically inaccurate, and some other mathy person will probably tell them that it is approximately correct to some precision criteria... On Jul 25, 2016 2:01 PM, "Paul Stoffregen" <p...@pjrc.com> wrote: > Does anyone have any suggestions or references for an efficient algorithm > to find the peak of a bandwidth limited signal? > > If I just look only at the numerical values of the samples (yeah, that's > what I've been doing), when a signal is close to an integer division of Fs, > even collecting data over many cycles tends to miss the phases of the > waveform containing the peaks. For example: > > Image also available here: https://forum.pjrc.com/threads > /35478-Problems-Plotting-Filter-Response?p=110442&viewfull=1#post110442 > > The only solution I'm imagining would involve expensive upsampling and > filtering. Even then, if I multiply the sample rate by 16 or more and the > filter is good enough, I still might not get a sample right at the peak. > > Is there a better way? > > _______________________________________________ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp >
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