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,1,'type')
Y = dyadup(X,EVENODD)
Y = dyadup(X,EVENODD,'c')
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).
Y = dyadup( is
equivalent to X)Y = dyadup( (odd-indexed
samples).X,1)
Y = dyadup( or X,EVENODD,'type')Y
= dyadup(,
where X,'type',EVENODD)X is a matrix,
returns extended copies of X obtained by
inserting
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'
arguments, 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( is
equivalent to X,EVENODD)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.