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I have a binary 2D image that consists of 95% black pixels with a few white pixels scattered about, and I want to convolve it with a 2D gaussian kernel. I'm hoping to exploit its sparsity to improve the efficiency of the blurring.

For simplicity, lets consider my signal to be 1-dimensional. Since the signal is just a superposition of a relatively small number of shifted Kronecker deltas, is there a shortcut for computing it's discrete Fourier transform?

(Apologies in advance for asking a probably obvious question, I'm a lowly computer scientist, not a math major :-) ).

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    This question would fit nicely at [dsp.stackexchange.com](http://dsp.stackexchange.com/)2012-01-16

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