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# dst

Discrete sine transform.

# idst

Inverse discrete sine transform.

### Syntax

X=dst(A [,sign] [,option]) X=dst(A,sign,selection [,option]) X=dst(A,sign,dims,incr [,option]) X=idst(A [,option]) X=idst(A,selection [,option]) X=idst(A,dims,incr [,option])

### Arguments

- A
a real or complex vector or real or complex array (vector, matrix or N-D array.

- X
- a real or complex array with same shape as
`A`

. - sign
- an integer. with possible values
`1`

or`-1`

. Select direct or inverse transform. The default value is`-1`

(direct transform). - selection
- a vector containing index on
`A`

array dimensions. See the Description part for details. - dims
- a vector of positive numbers with integer values, or a
vector of positive integers. See the Description part for details.
Each element must be a divisor of the total number of elements of

`A`

.The product of the elements must be less than the total number of elements of

`A`

. - incr
- a vector of positive numbers with integer values, or a
vector of positive integers. See the Description part for
details.
`incr`

must have the same number of elements than`dims`

.Each element must be a divisor of the total number of elements of

`A`

.The

`incr`

elements must be in strictly increasing order. - option
- a character string. with possible values
`"dst1"`

,`"dst2"`

,`"dst4"`

or`"dst"`

for direct transform and`"dst1"`

,`"dst3"`

,`"dst4"`

or`"idst"`

for inverse transform. The default value is`"dst"`

for direct transform and`"idst"`

for inverse transform. See the Description part for details.

### Description

### 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 is:For

`"dst2"`

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

`"dst3"`

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

`"dst4"`

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

`"dst"`

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

`"idst"`

the function computes the normalized DST-I transform. The 1-D transform of a vector of length 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:and

`X=dst(A,-1,[1 3])`

is equivalent to:`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.

### Algorithms

This function is based on the fftw3 library.

### See also

- fft — fast Fourier transform.
- dct — Discrete cosine transform.
- fftw_flags — set method for fft planner algorithm selection
- get_fftw_wisdom — return fftw wisdom
- set_fftw_wisdom — set fftw wisdom
- fftw_forget_wisdom — Reset fftw wisdom

### Bibliography

Matteo Frigo and Steven G. Johnson, "FFTW Documentation" http://www.fftw.org/#documentation

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