Affine theorem for the Hartley transform of an image

Many well-known theorems for the two-dimensional (2D) Hartley transform are encapsulated in the affine theorem which is presented here and illustrated by example. The mode of presentation permits ready visualization of the effect on the spectral makeup when an object is subjected to a particular distortion as specified by the six disposable parameters of the affine coordinate transformation and of the effects of progressive distortion. By contrast, 2D Fourier transform pairs for images do not lend themselves to visualization in the same way. Affine transformations possess considerable flexibility and generality of a useful kind that arises from the property that a single 2D spectral component transforms into another single component