FFT rounding errors in fixed vs floating point

In article 
<9836d57e-fe91-4120-8651-8992040a64fc@f18g2000yqd.googlegroups.com>,
 robert bristow-johnson <rbj@audioimagination.com> wrote:

> On Jan 30, 9:38&#4294967295;pm, "bharat pathak" <bharat@n_o_s_p_a_m.arithos.com>
> wrote:
> > My thought process is it will depend on number of points used for FFT.
> > So best way is to measure the SNR after the FFT is done and see it is
> > able to measure 24 bit input numbers. Else fractional bits needs to be
> > increased.
> 
> there are closed form expressions for the additive error for both
> fixed and float.  i think they are in Oppenhiem and Schafer, but i
> don't have my copy handy at the moment
> 
> r b-j

Thanks for the reference.  I previously found Oppenheim and Schafer to 
be difficult to understand because they so rarely focus on specific 
implementations, but rather tend to stay in the theoretical mathematical 
realm for most of the book.  But, it seems that they do get into 
specific implementations.

You're probably thinking about section 9.7 Effects of Finite Register 
Length, p. 661 in the Second Edition.  I really wish they started with 
the final answer and then moved on to the proof, but I'm sure if I study 
that section long enough then I'll be able to boil it down to a simple 
formula.

Brian Willoughby
Sound Consulting