Distance between signals using dynamic time warping

stretches
two vectors, `dist`

= dtw(`x`

,`y`

)`x`

and `y`

, onto
a common set of instants such that `dist`

, the
sum of the Euclidean distances between corresponding points, is smallest.
To stretch the inputs, `dtw`

repeats each element
of `x`

and `y`

as many times
as necessary. If `x`

and `y`

are
matrices, then `dist`

stretches them by repeating
their columns. In that case, `x`

and `y`

must
have the same number of rows.

`[`

returns
the common set of instants, or `dist`

,`ix`

,`iy`

]
= dtw(`x`

,`y`

)*warping path*,
such that `x`

(`ix`

) and `y`

(`iy`

)
have the smallest possible `dist`

between them.

The vectors `ix`

and `iy`

have
the same length. Each contains a monotonically increasing sequence
in which the indices to the elements of the corresponding signal, `x`

or `y`

,
are repeated the necessary number of times.

When `x`

and `y`

are matrices, `ix`

and `iy`

are
such that `x`

`(:,ix)`

and `y`

`(:,iy)`

are
minimally separated.

`dtw(___)`

without output arguments
plots the original and aligned signals.

If the signals are real vectors, the function displays the two original signals on a subplot and the aligned signals in a subplot below the first one.

If the signals are complex vectors, the function displays the original and aligned signals in three-dimensional plots.

If the signals are real matrices, the function uses

`imagesc`

to display the original and aligned signals.If the signals are complex matrices, the function plots their real and imaginary parts in the top and bottom half of each image.

[1] Paliwal, K. K., Anant Agarwal,
and Sarvajit S. Sinha. "A Modification over Sakoe and Chiba’s Dynamic Time Warping
Algorithm for Isolated Word Recognition." *Signal Processing*. Vol.
4, 1982, pp. 329–333.

[2] Sakoe, Hiroaki, and Seibi Chiba. "Dynamic Programming Algorithm Optimization for Spoken
Word Recognition." *IEEE ^{®} Transactions on Acoustics, Speech, and Signal Processing*.
Vol. ASSP-26, No. 1, 1978, pp. 43–49.

`alignsignals`

| `edr`

| `finddelay`

| `findsignal`

| `xcorr`