From: Timothy Newsham <newsham@wiliki.eng.hawaii.edu>
Date: Thu, 22 Apr 93 11:42:26 PDT
To: hughes@soda.berkeley.edu (Eric Hughes)
Subject: Re: non-cypher related question on audio analysis
In-Reply-To: <9304221700.AA00422@soda.berkeley.edu>
Message-ID: <9304221842.AA08140@toad.com>
MIME-Version: 1.0
Content-Type: text/plain


> 
> After you know something, remember this: The FIR filter is the same
> mathematically as a FFT, multiplication by a filter window function,
> and an inverse FFT.  As I recall, you can process multiple FIR's in
> parallel.

you can do two FFT's by using the fact that:

  FFT( x(t) + j y(t) ) =  Z(w)

then X(l) = 1/2 ( Z(l) + Z*(N-l))
and  Y(l) = 1/2j (Zl) - Z*(N-l)) 

Where x(t) <-> X(w)
      y(t) <-> Y(w)

N is the length of both arrays
j is sqrt(-1)
Z* is the conjugate of Z (a+jb <-> a-jb )