User`s guide

Autocorrelation
5-29
5Autocorrelation
Purpose Compute the autocorrelation of a vector input.
Library Statistics
Description The Autocorrelation block computes the autocorrelation of each column
(channel) in an M-by-N input matrix u. Matrix inputs must be frame-based.
The result, y, is a frame-based (l+1)-by-N matrix whose jth column has
elements
where
∗ denotes the complex conjugate, and l represents the maximum lag.
Note that y
1,j
is the zero-lag element in the jth column. When All positive lags
is selected, l=M. Otherwise, l is specified as a nonnegative integer by the
Maximum positive lag parameter.
Input u is zero when indexed outside of its valid range. When the input is real,
the output is real; otherwise, the output is complex. If the input is a
sample-based vector (row, column, or 1-D), the output is sample-based, with
the same shape as the input and length l+1. The Autocorrelation block does not
accept a sample-based full-dimension matrix input.
The
Scaling parameter controls the scaling that is applied to the output. The
following options are available:
•
None – Generates the raw autocorrelation, y
i,j
, without normalization.
•
Biased – Generates the biased estimate of the autocorrelation.
•Unbiased – Generates the unbiased estimate of the autocorrelation.
•
Unity at zero-lag – Normalizes the estimate of the autocorrelation for each
channel so that the zero-lag sum is identically 1.
y
ij,
u
kj,
*
u
ki1–+()j,
1 il1+()≤≤
k 1=
M
∑
=
y
ij,
biased
y
ij,
M
--------=
y
ij,
unbiased
y
ij,
Mi–
-------------=
y
1 j,
1=