Wavelet Toolbox

dyadup

Dyadic upsampling

Syntax

• 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).

Y = dyadup(X) is equivalent to Y = dyadup(X,1) (odd-indexed samples).

Y = dyadup(X,EVENODD,'type') or Y = dyadup(X,'type',EVENODD), where X is a matrix, returns 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'

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(X) is equivalent to Y = dyaddown(X,1,'c').

Y = dyadup(X,'type') is equivalent to Y = dyadup(X,1,'type'). Y = dyadup(X,EVENODD) is equivalent to Y = dyadup(X,EVENODD,'c').

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
  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.
  

See Also
dyaddown

References

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

dyaddown

entrupd