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## autocorrelation

**From**: |
Francesco Potorti` |

**Subject**: |
autocorrelation |

**Date**: |
Thu, 27 Apr 1995 16:55 +0100 (MET) |

I wrote:
I need to compute the autocorrelation of vectors. I started with the
following experiment:
kk=[2,3,4,5]
kk =
2 3 4 5
fftconv(kk,kk)
ans =
4 12 25 44 46 40 25
I would have expected
10 23 38 54 38 23 10
instead. What am I doing wrong?
Vinayak Dutt helped me find the answer, with this explanation:
fft convolution is a periodic convolution which will give this aliasing
problems if you try to compute linear convolution.
if you want to compute linear convolution, pad the vectors to
M+N-1 (where M and N are the lengths of the two vectors to
convolve) with zeros and then use the fft method.
for autocorrelation, just pad to twice the length with zeros.
Here are the two small function I wrote to compute the autocorrelation
and autocovariance of a sequence of data:
------------------------------autocov.oct----------------------------
function A = autoconv(x)
A = [x, zeros(1, length(x))];
A = fftconv(A, fliplr(A));
A = A(2*length(x) : 3*length(x)-1);
endfunction
function A = autocov(x)
A = [x, zeros(1, length(x))];
A = fftconv(A, fliplr(A));
A = A(2*length(x) : 3*length(x)-1) / sumsq(x);
endfunction
---------------------------------------------------------------------
Now:
autoconv([2,3,4,5])
ans =
54 38 23 10
autocov([2,3,4,5])
ans =
1.00000 0.70370 0.42593 0.18519
Cmments welcome and solicited.
--
Francesco Potorti` | address@hidden (Internet)
| 39369::pot (DECnet)
| +39-50-593203 (voice) 589354(fax)

**autocorrelation**, *Francesco Potorti`*, `1995/04/27`
**autocorrelation**,
*Francesco Potorti`* **<=**