Normalised Cross-correlation FFT
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From: dlh on 16 Mar 2010 08:07 Hi, I have implemented cross-correlation using FFT's. Is it possible to to normalised cross-correlation with FFT's? If so, how? Sorry if it is a basic question - but I haven't found a solution. Thanks in advance..
From: Rune Allnor on 16 Mar 2010 08:14 On 16 Mar, 13:07, "dlh" <danhordern(a)n_o_s_p_a_m.hotmail.com> wrote: > Hi, > > I have implemented cross-correlation using FFT's. Is > it possible to to normalised cross-correlation with FFT's? > > If so, how? Sorry if it is a basic question - but I haven't > found a solution. Apart from keeping a sharp eye on the various scaling constants involved in the FFT and correlation estimator, you might want to scale the input data to unit norm: xx = x/norm(x); yy = y/norm(y); and then compute the correlation between xx and yy. Rune
From: Dirk Bell on 16 Mar 2010 10:13 On Mar 16, 8:14 am, Rune Allnor <all...(a)tele.ntnu.no> wrote: > On 16 Mar, 13:07, "dlh" <danhordern(a)n_o_s_p_a_m.hotmail.com> wrote: > > > Hi, > > > I have implemented cross-correlation using FFT's. Is > > it possible to to normalised cross-correlation with FFT's? > > > If so, how? Sorry if it is a basic question - but I haven't > > found a solution. > > Apart from keeping a sharp eye on the various scaling constants > involved in the FFT and correlation estimator, you might want > to scale the input data to unit norm: > > xx = x/norm(x); > yy = y/norm(y); > > and then compute the correlation between xx and yy. > > Rune That makes the assumption that all of each signal is involved in the calculation for each offset. Often not true. Dirk
From: Rune Allnor on 16 Mar 2010 10:58 On 16 Mar, 15:13, Dirk Bell <bellda2...(a)cox.net> wrote: > On Mar 16, 8:14 am, Rune Allnor <all...(a)tele.ntnu.no> wrote: > > > > > > > On 16 Mar, 13:07, "dlh" <danhordern(a)n_o_s_p_a_m.hotmail.com> wrote: > > > > Hi, > > > > I have implemented cross-correlation using FFT's. Is > > > it possible to to normalised cross-correlation with FFT's? > > > > If so, how? Sorry if it is a basic question - but I haven't > > > found a solution. > > > Apart from keeping a sharp eye on the various scaling constants > > involved in the FFT and correlation estimator, you might want > > to scale the input data to unit norm: > > > xx = x/norm(x); > > yy = y/norm(y); > > > and then compute the correlation between xx and yy. > > > Rune > > That makes the assumption that all of each signal is involved in the > calculation for each offset. Often not true. Sure. But if you want to use the FFT to compute the normalized correlation, there aren't too many alternatives. Rune
From: steve on 16 Mar 2010 11:42
On Mar 16, 8:07 am, "dlh" <danhordern(a)n_o_s_p_a_m.hotmail.com> wrote: > Hi, > > I have implemented cross-correlation using FFT's. Is > it possible to to normalised cross-correlation with FFT's? > > If so, how? Sorry if it is a basic question - but I haven't > found a solution. > > Thanks in advance.. you just encountered one of several limitations of using FFT for CC, promises so much, then disappointment :) |