scipy.fftpack.

dst#

scipy.fftpack.dst(x, type=2, n=None, axis=-1, norm=None, overwrite_x=False)[source]#

Return the Discrete Sine Transform of arbitrary type sequence x.

Parameters:
xarray_like

The input array.

type{1, 2, 3, 4}, optional

Type of the DST (see Notes). Default type is 2.

nint, 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].

axisint, 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_xbool, optional

If True, the contents of x can be destroyed; the default is False.

Returns:
dstndarray of reals

The transformed input array.

See also

idst

Inverse DST

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.

yk=2n=0N1xnsin(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

yk=2n=0N1xnsin(π(k+1)(2n+1)2N)

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

f={14Nif k=0,12Notherwise

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

yk=(1)kxN1+2n=0N2xnsin(π(2k+1)(n+1)2N)

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.

Added in version 0.11.0.

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

yk=2n=0N1xnsin(π(2k+1)(2n+1)4N)

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

Added in version 1.2.0: Support for DST-IV.

References

[1]

Wikipedia, “Discrete sine transform”, https://en.wikipedia.org/wiki/Discrete_sine_transform