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I'm a pure novice in signal processing but I'm writing a paper that needs to be expressed in the SP way. The question is, I want to express an N-dimensional datum goes through N one-dimensional filters, each along a different dimension of the datum. The simplest example is applying Gaussian blur filter on a 2-D image. You can separate the 2-D Gaussian filter into 2 1-D Gaussian filter and apply it along each dimension of the 2-D image one after the other. But my question is, is there an elegant notation to express such operation?

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  • $\begingroup$ How about "N-dimensional filterbank"? $\endgroup$ – Max Jan 17 at 9:35
  • $\begingroup$ I mean, how do you write it in math? Is it just like A*f1*f2*f3*f4...*fn ? $\endgroup$ – cyfex Jan 17 at 13:01
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...my question is, is there an elegant notation to express such operation?

If you know that these operations are to act on orthogonal dimensions, you can define their 1D version and then use indexing to express the order by which the function is applied to the multidimensional signal.

But if you are working with multidimensional signals over an orthogonal vector basis throughout, you can simply specify this in the beginning and use (for example) $\mathcal{F}(x)$ throughout, to denote a multidimensional discrete Fourier transform.

Hope this helps (?)

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