Mathematically none, as #Richard Gloaguen explained very well above. In terms of interpretitation, of course one will show gain versus frequency (gain x Hz), the other will show gain along 'spatial frequency', which is the inverse of distance (gain x 1/cm or gain x 1/m).
A digital signal having independ variable as time are temporal signal. If indepent variable is not time it is spatial signal . Short time temporal signal can stored and can be taken as spatial signal
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The concepts of spatial and temporal coherence are important in discussing the phase characteristics of imaging systems. In general, the concept of coherence is related to the stability, or predictability, of phase.
Spatial coherence describes the correlation between signals at different points in space. Temporal coherence describes the correlation or predictable relationship between signals observed at different moments in time.
With a same filter, there can be one difference: the data input to it. Let try with a simple example.
Think about a video sequence which comprises of frames or pictures. Ex: http://www.iitk.ac.in/mwn/images/Video_Sequence.jpg
Imagine that you stack enough frames together without leaving any space between; this results in a cube or a 3-d signal. A frame - spatial layer is one face of the cube. The temporal layer is perpendicular to the spatial one.
2-d spatial filtering happens across the spatial layer or frame. 2-d filtering in temporal direction happens across the temporal layer.
concerning for example the field of turbulence and specifically the large eddy simulation, temporal and spatial filtering depends on the discretization of the Navier-Stokes equation. Any discrete form, implicitly introduces a built-in filtering at the time-step and mesh size.
In general, the mathematical form of a transfer function does not depend on the spatial or temporal variable, it is often a convolution product.