Wavelet Toolbox

dyaddown

Dyadic downsampling.

Syntax

Y = dyaddown(X,EVENODD)
Y = dyaddown(X)
Y = dyaddown(X,EVENODD,'type')
Y = dyaddown(X,'type',EVENODD)

Description

Y = dyaddown(X,EVENODD) where X is a vector, returns a version of X that has been downsampled by 2. Whether Y contains the even- or odd-indexed samples of X depends on the value of positive integer EVENODD:

• If EVENODD is even, then Y(k) = X(2k).
• If EVENODD is odd,   then Y(k) = X(2k+1).

Y = dyaddown(X) is equivalent to Y = dyaddown(X,0) (even-indexed samples).

Y = dyaddown(X,EVENODD,'type') or Y = dyaddown(X,'type',EVENODD), where X is a matrix, returns a version of X obtained by suppressing one out of two:

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

according to the parameter EVENODD, which is as above.

If you omit the EVENODD or 'type' arguments, dyaddown defaults to EVENODD = 0 (even-indexed samples) and 'type' = 'c' (columns).

Y = dyaddown(X) is equivalent to Y = dyaddown(X,0,'c'). Y = dyaddown(X,'type') is equivalent to Y = dyaddown(X,0,'type'). Y = dyaddown(X,EVENODD) is equivalent to Y = dyaddown(X,EVENODD,'c').

Examples

% For a vector.
s = 1:10 
s =
   1   2   3   4   5   6   7   8   9  10

dse = dyaddown(s)   % Downsample elements with even indices.
dse =
   2   4   6   8  10
% or equivalently 
dse = dyaddown(s,0)
dse =
   2   4   6   8  10

dso = dyaddown(s,1) % Downsample elements with odd indices.
dso =
   1   3   5   7   9

% For a matrix.
s = (1:3)'*(1:4)
s =
   1   2   3   4
   2   4   6   8
   3   6   9  12

dec = dyaddown(s,0,'c') % Downsample columns with even indices.
dec =
   2   4
   4   8
   6  12

der = dyaddown(s,1,'r') % Downsample rows with odd indices.
der =
 1   2   3   4
 3   6   9  12

dem = dyaddown(s,1,'m') % Downsample rows and columns
                        % with odd indices.
dem =
     1     3
     3     9

See Also
dyadup

References

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

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dyadup