Forums

autocorrelation

Started by John McDermick January 3, 2011
On Jan 4, 1:21=A0pm, dvsarwate <dvsarw...@yahoo.com> wrote:
> On Jan 4, 11:09=A0am, Clay <c...@claysturner.com> wrote: > > > > > a=3D(sqrt(3)-j)/2 and b=3D(sqrt(3)+j)/2 > > > and the auto correlation of {a,b} is {1,1,1} > > This must be using a different definition > of autocorrelation than the usual one for > complex-valued sequences, viz., > > R_{x}(k) =3D sum x_i . (x_{i+k})* > > where * means complex conjugation and > i+k is taken modulo the length of the sequence > (for periodic autocorrelation). > > With x =3D (a, b) where a and b are as specified > by Clay, we have that |a| =3D |b| =3D 1, and so > R_{x}(0) =3D |a|^2 + |b|^2 =3D 2, not 1. =A0The periodic > autocorrelation *does* have value 1 for offset 1 > (that is, R_{x}(1) =3D 1) as stated by Clay (and > verified by the OP?) but the in-phase value is 2. > > Tim Wescott's assertion that the autocorrelation > function has a strict maximum at t =3D 0 is correct > (except for the trivial case which Vladimir > Vassilevsky pointed out and the OP rejected). > It *is* possible for a signal to have *all* the > nonzero-offset (i.e., out-of-phase) periodic > autocorrelation values to be the same (though > different from the zero-offset (or in-phase) value). > The well-known PN sequences with their > "thumb-tack" autocorrelation functions are the > classic example of this kind of signal. =A0Young > folks who have seen only push-pins used on > bulletin boards may have trouble with this last > statement.... > > Hope this helps > > Dilip Sarwate
Thanks Dilip, For pointing out my error. My brain is still not in gear after a flu ridden vacation. But I'm on the mend. Clay