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E- - .. - - - ~ .. ~ -.. -1s ... - - c) -- ~ r -T- - - R r '<- Fig. 12. 57) k= _ /=_ Assume that Q=Fro defines the non-separable normalized frequency, and x(n) describes a signal defined on a rectangular grid of samples, for which Do are the original sampling posit ions. e-jnTDTll . 60) define the mapping of the non-rectangular system onto the system with a rectangular grid of periodic continuations of the spectrum. The sampling conditions can now be described separately in the single dimensions.

Aliasing in liJ3 only effects wrong interpretation of motion in the case of progressive sampling. In movies, this is well-known as the "stage coach effect", where the wheels of the vehicle seem to move slowly, stand still or sometimes turn backwards. v=-S/2T v=0 Ol, r- - - - I I' - - - - 1- I I ~I @I L.. _ _ _ I - - 1 I I . I~ I I I _ _ _ J I I I. T. l 1 I J Fig. 16. Effect of alias, vertical motion of an interlaced-sampled sinusoid Fig. 16 shows the effect for the case of interlace sampling of the same signal.

26) Quincunx mapping: [-li 0]. F= D- =FT=[li0 -li]. 27) qui. Hexagonal mapping: Dh~=[~ Y~l F=[~ ~J D-I=FT=[~~ -~J F-I=DT=[~ ~] Rotational mapping, clockwise by an angle tp : l These conditions apply in general for arbitrary numberof dimensions. 28) 30 2 Signals and Sampling D ro' =[ cosrp sinrp] . =F ; -smrp cos e . :~--+ ~l . f}........... • f, ~ : ~l i-: .......... 29) -sinrp] . sm e - iP · r, r fo do r fo 00, e) 00, Fig. 4. 21) from the determinant of the transformation matrix. The shear mapping in principle allows re-defining the angular orientation of two-dimensional signals, while the horizontal spectral characteristics are retained (in case where only the vertical axis is sheared) .