To find the impulse response of the DMO operator in the different transform
domains, we keep the impulse location *m*,*h*, and *t* fixed.
The impulse response of the DMO operator is spread along
the intersection of a cylinder satisfying equation (1) and a radial
plane
satisfying (2). Logarithmic stretching of the time axis
transforms the
linear plane of slope *h*/*t* into a curved surface with

(8) |

The Impulse response after Fourier transform is located on the same
semicircles in all frequency planes.
The amplitude along the semicircle varies according to the complex factor
of equation (7)^{}.
I spread out the impulse along the circle defined by equation
(1), conducting a 2D convolution. The convolution operator varies
only with offset, but is midpoint independent. The convolution is identical
on all frequency planes:

(9) |

11/18/1997