`scipy.fftpack._realtransforms:dst`

source: /scipy/fftpack/_realtransforms.py :443

Signature

   def     dst (    x    ,    type    =  2   ,    n    =  None   ,    axis    =  -1   ,    norm    =  None   ,    overwrite_x    =  False     )

Summary

Return the Discrete Sine Transform of arbitrary type sequence x.

Parameters

x : array_like: The input array.
type : {1, 2, 3, 4}, optional: Type of the DST (see Notes). Default type is 2.
n : int, optional: Length of the transform. If n < x.shape[axis], x is truncated. If n > x.shape[axis], x is zero-padded. The default results in n = x.shape[axis].
axis : int, optional: Axis along which the dst is computed; the default is over the last axis (i.e., axis=-1).
norm : {None, 'ortho'}, optional: Normalization mode (see Notes). Default is None.
overwrite_x : bool, optional: If True, the contents of x can be destroyed; the default is False.

Returns

dst : ndarray of reals: The transformed input array.

Notes

For a single dimension array x.

There are, theoretically, 8 types of the DST for different combinations of even/odd boundary conditions and boundary off sets ^[1], only the first 4 types are implemented in scipy.

Type I

There are several definitions of the DST-I; we use the following for norm=None. DST-I assumes the input is odd around n=-1 and n=N.

y_{k} = 2 n = 0 \sum N - 1 x_{n} sin (\frac{π ( k + 1 ) ( n + 1 )}{N + 1})

Note that the DST-I is only supported for input size > 1. The (unnormalized) DST-I is its own inverse, up to a factor 2(N+1). The orthonormalized DST-I is exactly its own inverse.

Type II

There are several definitions of the DST-II; we use the following for norm=None. DST-II assumes the input is odd around n=-1/2 and n=N-1/2; the output is odd around $k = - 1$ and even around k=N-1

y_{k} = 2 n = 0 \sum N - 1 x_{n} sin (\frac{π ( k + 1 ) ( 2 n + 1 )}{2 N})

if norm='ortho', y[k] is multiplied by a scaling factor f

f = ⎩ ⎨ ⎧ \frac{1}{4 N} \frac{1}{2 N} if k = 0, otherwise

Type III

There are several definitions of the DST-III, we use the following (for norm=None). DST-III assumes the input is odd around n=-1 and even around n=N-1

y_{k} = (- 1)^{k} x_{N - 1} + 2 n = 0 \sum N - 2 x_{n} sin (\frac{π ( 2 k + 1 ) ( n + 1 )}{2 N})

The (unnormalized) DST-III is the inverse of the (unnormalized) DST-II, up to a factor 2N. The orthonormalized DST-III is exactly the inverse of the orthonormalized DST-II.

Type IV

There are several definitions of the DST-IV, we use the following (for norm=None). DST-IV assumes the input is odd around n=-0.5 and even around n=N-0.5

y_{k} = 2 n = 0 \sum N - 1 x_{n} sin (\frac{π ( 2 k + 1 ) ( 2 n + 1 )}{4 N})

The (unnormalized) DST-IV is its own inverse, up to a factor 2N. The orthonormalized DST-IV is exactly its own inverse.

Aliases

scipy.fftpack.dst

Signature

Summary

Parameters

Returns

Notes

See also

Aliases