# The notation to express a datum filtered by arbitray number of one-dimensional filters?

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?

• How about "N-dimensional filterbank"? – Max Jan 17 at 9:35
• I mean, how do you write it in math? Is it just like A*f1*f2*f3*f4...*fn ? – cyfex Jan 17 at 13:01

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.