We consider the bilinear Fourier integral operatorS(f, g)(x) =ZRdZRdei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,on modulation spaces. Our aim is to indicate this operator is well defined onS(Rd) and shall show the relationship between the bilinear operator and BFIO onmodulation spaces.

We now start considering discrete–time signals. A discrete–time signal is a function (real or complex valued) whose argument runs over the integers, rather than over the real line. We shall use square brackets, as in x[n], for discrete–time signals and round parentheses, as in x(t), for continuous–time signals. This is the notation used in EECE 359 and EECE 369. Discrete–time signals arise in t...

Various studies indicate the existence of non-Fourier visual mechanisms that can extract non-luminance cues (e.g., contrast modulation) as well as a Fourier mechanism that deals with luminance variation only. We compared the pattern discrimination performance of the non-Fourier mechanism with that of the Fourier mechanism by using orientation discrimination and spatial-frequency discrimination ...

Typically, image motion analysis in the frequency domain is performed according to the Motion From Fourier Coeecients, or MFFC principle. However , this principle excludes a class of motion that does not generate power spectra containing the origin of the frequency domain, which is usually referred to as Non-Fourier motion. This type of motion includes phenomena relevant to motion analysis such...