dyadup (Wavelet Toolbox)

Dyadic upsampling.

Y = dyadup(X,evenodd)
Y = dyadup(X)
Y = dyadup(X,evenodd,'type')
Y = dyadup(X,'type',evenodd)

Description

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

Y = dyadup(X,evenodd), where X is a vector, returns an extended copy of vector X obtained by inserting zeros. Whether the zeros are inserted as even- or odd-indexed elements of Y depends on the value of positive integer evenodd:

If evenodd is even, then Y(2k-1) = X(k), Y(2k) = 0.
If evenodd is odd, then Y(2k-1) = 0, Y(2k) = X(k).

If you omit the evenodd argument, dyadup(X) defaults to evenodd = 1 (zeros in odd-indexed positions).

Y = dyadup(X,evenodd,'type') or Y = dyadup(X,'type',evenodd), where X is a matrix, return extended copies of X obtained by inserting:


Columns in `X`	If `'type'` = `'c'`
Rows in `X`	If `'type'` = `'r'`
Rows and columns in `X`	If `'type'` = `'m'`

If you omit the evenodd or 'type' arguments, dyadup defaults to evenodd = 1 (zeros in odd-indexed positions) and 'type' = 'c' (insert columns).

Examples

% 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

% 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.