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Dyadic upsampling

`Y = dyadup(X,EVENODD)`

Y = dyadup(* X*)

Y = dyadup(

`X`

`EVENODD`

`'type'`

Y = dyadup(

`X`

`'type'`

`EVENODD`

Y = dyadup(

`X`

Y = dyaddown(X,1,'c')

Y = dyadup(

`X`

`'type'`

Y = dyadup(

`X`

`'type'`

Y = dyadup(

`X`

`EVENODD`

Y = dyadup(

`X`

`EVENODD`

`dyadup`

implements a simple zero-padding scheme very useful in the wavelet
reconstruction algorithm.

`Y = dyadup(X,EVENODD)`

, where * X* is
a

`X`

`Y`

`EVENODD`

:If

is even, then`EVENODD`

`Y(2k–1) = X(k), Y(2k) = 0`

.If

is odd, then`EVENODD`

`Y(2k–1) = 0, Y(2k) = X(k)`

.

`Y = dyadup(`

is
equivalent to * X*)

`Y = dyadup(``X`

,1)

(odd-indexed
samples).`Y = dyadup(`

or * X*,

`EVENODD`

`'type'`

```
Y
= dyadup(
````X`

,`'type'`

,`EVENODD`

)

,
where `X`

`X`

Columns in | If |

Rows in | If |

Rows and columns in | If |

according to the parameter * EVENODD*,
which is as above.

If you omit the * EVENODD* or

`'type'`

`dyadup`

defaults to `EVENODD = 1`

(zeros
in odd-indexed positions) and `'type'`

`= 'c'`

(insert columns).`Y = dyadup(`

is
equivalent to * X*)

`Y = dyaddown(X,1,'c')`

.`Y = dyadup(`

is
equivalent to * X*,

`'type'`

`Y = dyadup(``X`

,1,`'type'`

)

. `Y = dyadup(``X`

,`EVENODD`

)

is
equivalent to `Y = dyadup(``X`

,`EVENODD`

,'c')

.% For a vector. s = 1:5 s = 1 2 3 4 5 dse = dyadup(s) % Upsample elements at odd indices. dse = 0 1 0 2 0 3 0 4 0 5 0 % or equivalently dse = dyadup(s,1) dse = 0 1 0 2 0 3 0 4 0 5 0 dso = dyadup(s,0) % Upsample elements at even indices. dso = 1 0 2 0 3 0 4 0 5 % For a matrix. s = (1:2)'*(1:3) s = 1 2 3 2 4 6 der = dyadup(s,1,'r') % Upsample rows at even indices. der = 0 0 0 1 2 3 0 0 0 2 4 6 0 0 0 doc = dyadup(s,0,'c') % Upsample columns at odd indices. doc = 1 0 2 0 3 2 0 4 0 6 dem = dyadup(s,1,'m') % Upsample rows and columns % at even indices. dem = 0 0 0 0 0 0 0 0 1 0 2 0 3 0 0 0 0 0 0 0 0 0 2 0 4 0 6 0 0 0 0 0 0 0 0 % Using default values for dyadup and dyaddown, we have: % dyaddown(dyadup(s)) = s. s = 1:5 s = 1 2 3 4 5 uds = dyaddown(dyadup(s)) uds = 1 2 3 4 5 % In general reversed identity is false.

Strang, G.; T. Nguyen (1996), *Wavelets and Filter
Banks*, Wellesley-Cambridge Press.