Re: comp.dsp - a FAQ

Not so. You derive the Fourier relationships by taking
a single function of time, and determining the magnitude
of a multitude of frequency components, and the 1/(2*PI)
is part of those magnitude determinations.

You do not derive from taking a function of frequency and
ending up with a multitude of time-based components.

David Kirkland wrote:
> Since you can sample either in time or frequency and derive the sampling
> theorem either way it is really inconsequential where the 2*pi factor
> comes in.
>
> Of course you should just work with in w and then your equations are
> symmetrical.
>
> Cheers,
> David
> Polymath wrote:
> > It is a frequent error to move the scaling when one considers
> > the derivation of the Fourier equations starting out from
> > what makes up the initial f(t). In particular, the factor
> > of 1/(2*PI) belongs in the frequency spectrum.
> >
> > dbell wrote:
> >
> >>The published scaling on Fourier transforms runs from a) all scaling on
> >>the forward transform, to b) the sqrt of the scaling applied to both
> >>the forward and inverse transforms, to c) all applied to the inverse
> >>transform. Seems to be a function of your field (mathematics, physics,
> >>different engineering disciplines). The scaling can be shifted between
> >>forward and inverse transforms in the definitions. Knowing the
> >>definition being used, and consistency, makes them all work.
> >
> >

.

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