ABSTRACT
There are many ways that one can normalize the Fourier transform. Here we will take these definitions for the Fourier Transform (FT) and its inverse transform (INVFT):
I f( t ) = F(t) = £ f Z F(x)e~ixtdx, the FT. \F (x ) = f(x ) = /_°^ f( t )e ixtdt, the INVFT,
300 Rosenblatt
Although the notation is the same for these two different formulas, the convention of using lower case and upper case for the functions will be kept throughout these remarks, and so there should be no confusion between the two transforms. A band-limited signal / (i.e. band-limited function) is one whose inverse Fourier transform has compact support. We will fix the notation that such a signal has no frequencies outside [—27ra , 2nw] when its inverse Fourier transform F has support contained in [—2ttw, 2ttw].
