this filtering was performed using the well-known formulas from robert bristow-johnson's biquad cookbook.. code's right in there (IIRC the signs for the bandpass y coefficients need to be flipped..)
actually using them will probably be aggravating unless you have a background in audio processing or IIR filtering or otherwise are oriented with the fourier theoremgenerally these filters (the state variable is another trivial algorithm) have a phase effect as well as a frequency dependent attenuation (dspguide.com mentioned above provides a thorough background here) but not always.
what they would allow you to do to images is apply a wide effect at low computation. the actual process (after the coefficients are calculated) uses a few buffer variables to record the last two states of the input (x[n], x[n-1], x[n-2]) and output (y[n], y[n-1], y[n-2]) and a scalar for each.. so the computation would look like this:
y[n] = a0*x[n] + a1*x[n-1] + a2*x[n-2] + b1*y[n-1] + b2*y[n-2];
y[n-2] = y[n-1]; y[n-1] = y[n];
this can often be reduced by a few multiplies as often a0 and a2 are the same coefficient or similar.
in this image, the first frame compares the original signal (a bandlimited triangle wave.. similar to terrain lol) to the 2nd order highpass filter from the cookbook.. the phase distortion is endemic to the filter, it is relative to the wavelength in one direction or the other.. and of course audio/1d filtering is an *extensive* field.. zero-phase filters exist, SINC filters (dspguide) would probably do fascinating things with images..
in the 2nd frame, i recorded the 'audio' and reversed it and filtered it again.. this would be synonymous to running the biquad in one direction along a row of pixels, then running it in the other direction.
in the third frame, i've scaled the output to resemble the input. i'm not particularly anxious to prove any point about the utility of IIR filters, only demonstrating them for those who wish to explore them
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