Hello just had a quick question, would applying a bandpass filter to an image,and then doing a pointwise squaring of the image be considered a linear operation? if its possible to please provide an explanation that would be amazing!
2026-03-27 16:21:59.1774628519
Is a bandpass filter followed by a pointwise squaring considered a linear operation?
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A band pass filter is a linear operator, so in order for both steps to be linear you would need for pointwise squaring to be a linear operator on the range of the band pass filter (i.e., all values mapped to by the band pass filter). In order for pointwise squaring to be a linear operator it would be linear pointwise, requiring $(x+y)^2 = x^2+y^2$ for all $x$, $y$ possible as matrix elements resulting from a band pass filter. This is only true if $x=y=0$, i.e., if the band pass maps every signal to zero.