> Date: Tue, 09 Dec 2003 07:48:47 -0600 > From: Jeff Brower <> > Subject: Re: Real Symmetric FFT > > Andor Bariska- > > > the source code for the Real FFT can be downloaded from ADI. It > > implements a real N-point FFT using a N/2-point complex FFT, plus > > some signal reassembling. > > > > If the input signal is however real _and_ symmetric (as is the case > > for a linear-phase frequency response), additional speed-up can be > > achieved as compared to the Real FFT, because the resulting imaginary > > part does not have to be calculated. > > Just curious, but how can a real signal in time domain be symmetric? > Since it has no imaginary component, symmetric w.r.t. to what? To > midpoint in analysis framesize? > To amplitude? > > Jeff Brower > system engineer > Signalogic > Hi Jeff, I do not think it really does matter if a real signal in time domain is/isn't symmetric. The problem is an abstract math problem. It has been attended: ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Subroutine RQEFT( X, N, M, S, C, Nmax2 ) c c A real quarter wave even (QE) symmetric sequence of length N=2**M c has the form c X(0),X(1),...,X(N/2-1),X(N/2-1),...,X(1),X(0) c c While the array X must have length N, only the first N/2 elements c are accessed. c c S - array of sin() table initialized to length Nmax2>=2*N by FFTI c C - array of cos() table initialized to length Nmax2>=2*N by FFTI c c This routine requires approximately N*M+N floating point operations. c c The output from this routine will agree with the forward FFT (RFFTF) c applied to the real sequence c X(0),X(1),....,X(N/2-1),X(N/2-1),...,X(1),X(0). c c c Steve Kifowit, November 1997 c c Reference: c Paul N. Swarztrauber, Symmetric FFTs, Mathematics of Computation, c 47 (1986), pp. 323-346. c cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc Regards, Andrew -- |