Transform description

This function realizes direct or inverse 1-D or N-D Discrete Sine Transforms with shift depending on the option parameter value:

• For "dst1" the function computes the unnormalized DST-I transform. The 1-D transform of a vector of length n is:

  

• For "dst2" the function computes the unnormalized DST-II transform. the 1-D transform of a vector of length n is:

  

• For "dst3" the function computes the unnormalized DST-III transform. The 1-D transform of a vector of length n is:

  

• For "dst4" the function computes the unnormalized DST-IV transform. the 1-D transform of a vector of length n is:

  

• For "dst" the function computes the normalized DST-I transform. The 1-D transform of a vector of length n is:

  

• For "idst" the function computes the normalized DST-I transform. The 1-D transform of a vector of length n is:

  

The multi-dimensional DST transforms , in general, are the separable product of the given 1d transform along each dimension of the array. For unnormalized transforms , computing the forward followed by the backward/inverse multi-dimensional transform will result in the original array scaled by the product of the dimension sizes.

Syntax description

Short syntax

direct

X=dst(A,-1 [,option]) or X=dst(A [,option]) gives a direct transform according to the option value. The default is normalized DST-I direct transform.

If A is a vector (only one dimension greater than 1) a 1-d transform is performed and in the other cases a n-dimensional transform is done.

(the -1 argument refers to the sign of the exponent..., NOT to "inverse"),

inverse

X=dst(A,1 [,option]) or X=idst(A [,option])performs the inverse transform.

If A is a vector (only one dimension greater than 1) a 1-d transform is performed and in the other cases a n-dimensional transform is done.

Long syntax for DST along specified dimensions

• X=dst(A,sign,selection [,option]) allows to perform efficiently all direct or inverse dst of the "slices" of A along selected dimensions.

  For example, if A is a 3-D array X=dst(A,-1,2) is equivalent to:

  for i1=1:size(A,1),
    for i3=1:size(A,3),
      X(i1,:,i3)=dst(A(i1,:,i3),-1);
    end
  end

  and X=dst(A,-1,[1 3]) is equivalent to:

  for i2=1:size(A,2),
    X(:,i2,:)=dst(A(:,i2,:),-1);
  end

• X=dst(A,sign,dims,incr) is an old syntax that also allows to perform all direct or inverse dst of the slices of A along selected dimensions.

  For example, if A is an array with n1*n2*n3 elements X=dst(A,-1,n1,1) is equivalent to X=dst(matrix(A,[n1,n2,n3]),-1,1). and X=dst(A,-1,[n1 n3],[1 n1*n2]) is equivalent to X=dst(matrix(A,[n1,n2,n3]),-1,[1,3]).

Optimizing dst

Remark: fftw function automatically stores his last parameters in memory to re-use it in a second time. This improves greatly the time computation when consecutives calls (with same parameters) are performed.

It is possible to go further in dst optimization using get_fftw_wisdom, set_fftw_wisdom functions.