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Estimate delay(s) between signals

`D = finddelay(X,Y)`

D = finddelay(...,maxlag)

`D = finddelay(X,Y)`

, where `X`

and `Y`

are
row or column vectors, returns an estimate of the delay `D`

between `X`

and `Y`

,
where `X`

serves as the reference vector. If `Y`

is
delayed with respect to `X`

, then `D`

is
positive. If `Y`

is advanced with respect to `X`

,
then `D`

is negative. Delays in `X`

and `Y`

can
be introduced by prepending zeros.

`X`

and `Y`

need not be exact
delayed copies of each other, as `finddelay(X,Y)`

returns
an estimate of the delay via cross-correlation. However this estimated
delay has a useful meaning only if there is sufficient correlation
between delayed versions of `X`

and `Y`

.
Also, if several delays are possible, as in the case of periodic signals,
the delay with the smallest absolute value is returned. In the case
that both a positive and a negative delay with the same absolute value
are possible, the positive delay is returned.

`D = finddelay(X,Y)`

, where `X`

is
a matrix of size *M _{X}*-by-

`Y`

is a
matrix of size `D`

of
estimated delays between each column of `X`

and the
corresponding column of `Y`

. With this usage the
number of columns of `X`

must be equal to the number
of columns of `Y`

(i.e., `D = finddelay(...,maxlag)`

,
uses `maxlag`

as the maximum correlation window size
used to find the estimated delay(s) between `X`

and `Y`

.
The usage of `maxlag`

is detailed in the table below.

By default, `maxlag`

is equal to max(*L _{X}*,

`X`

and `Y`

, respectively), max(`maxlag`

is
input as `[]`

, it is replaced by the default value.
If any element of `maxlag`

is negative, it is replaced
by its absolute value. If any element of `maxlag`

is
not integer-valued, or is complex, `Inf`

, or `NaN`

,
then `finddelay`

returns an error.The calculation of the vector of estimated delays, `D`

,
depends on `X`

, `Y`

, and `maxlag`

as
shown in the following table.

`maxlag` | `X` | `Y` | `D` is calculated by... |
---|---|---|---|

Integer-valued scalar | Row or column vector or matrix | Row or column vector or matrix | Cross-correlating the columns of `X` and `Y` over
a range of lags –`maxlag` :`maxlag` . |

Integer-valued row or column vector | Row or column vector of length L ≥ 1_{X} | Matrix of size M-by-_{Y}N (_{Y}M > 1, _{Y}N > 1)_{Y} | Cross-correlating `X` and column j of `Y` over
a range of lags –`maxlag` (j):`maxlag` (j),
for j = 1:N. _{Y} |

Integer-valued row or column vector | Matrix of size M-by-_{X}N (_{X}M > 1, _{X}N > 1)_{X} | Row or column vector of length L ≥ 1_{Y} | Cross-correlating column j of `X` and `Y` over
a range of lags –`maxlag` (j):`maxlag` (j),
for j = 1:N. _{X} |

Integer-valued row or column vector | Matrix of size M-by-_{X}N (_{X}M > 1, _{X}N > 1)_{X} | Matrix of size Mby-_{Y}-N (_{Y}M > 1, _{Y}N = _{Y}N > 1)_{X} | Cross-correlating column j of `X` and
column j of `Y` over a range of
lags –`maxlag` (j):`maxlag` (j),
for j = 1:N._{Y} |

`X`

as Multiple ChannelsIf you wish to treat a row vector `X`

of length *L _{X}* as
comprising one sample from

`X`

so
that it appears as a matrix. Then each column of `X`

will
be considered a channel.For example, `X = [1 1 1 1]`

is considered
a single channel comprising four samples. To treat it as four different
channels, each channel comprising one sample, define a new matrix `Xm`

:

Xm = [1 1 1 1; 0 0 0 0];

Each column of `Xm`

corresponds to a single
channel, each one containing the samples `1`

and `0`

.

The `finddelay`

function uses the `xcorr`

function to determine the cross-correlation between each
pair of signals at all possible lags specified by the user. The normalized
cross-correlation between each pair of signals is then calculated. The estimated
delay is given by the negative of the lag for which the normalized
cross-correlation has the largest absolute value.

If more than one lag leads to the largest absolute value of the cross-correlation, such as in the case of periodic signals, the delay is chosen as the negative of the smallest (in absolute value) of such lags.

Pairs of signals need not be exact delayed copies of each other. However, the estimated delay has a useful meaning only if there is sufficient correlation between at least one pair of the delayed signals.

`alignsignals`

| `dtw`

| `edr`

| `findsignal`

| `xcorr`