What resampling is being used here? – DSP and Plug-in Development Forum
You can try to estimate the sidelobes and then based an educated guess based on that, but this spectrum is quite noisy (a test signal would be better) and logarithmic frequency scale makes it very hard to see what’s going on at the high frequencies.
That said, linear interpolation gives a little over 24dB attenuation at the peak of first side-lobe and if you eyeball about 24dB up from the top of the 10kHz bump, we’re pretty close to the spectrum at ~3kHz so based on this plot alone I’d guess linear. Catmull-Rom should perform a little bit better than this, but I guess some other cubic is theoretically possible too… but like probably it’s just linear.
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