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: x : array_like
The input array.
type : {1, 2, 3}, optional
Type of the DST (see Notes). Default type is 2.
n : int, optional
Length of the transform.
axis : int, optional
Axis over which to compute the transform.
norm : {None, ‘ortho’}, optional
Normalization mode (see Notes). Default is None.
overwrite_x : bool, optional
If True the contents of x can be destroyed. (default=False)
Returns: dst : ndarray 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 [R35], only the first 3 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.
N-1 y[k] = 2 * sum x[n]*sin(pi*(k+1)*(n+1)/(N+1)) n=0
Only None is supported as normalization mode for DCT-I. Note also that the DCT-I is only supported for input size > 1 The (unnormalized) DCT-I is its own inverse, up to a factor 2(N+1).
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
N-1 y[k] = 2* sum x[n]*sin(pi*(k+1)*(n+0.5)/N), 0 <= k < N. n=0
if norm='ortho', y[k] is multiplied by a scaling factor f
f = sqrt(1/(4*N)) if k == 0 f = sqrt(1/(2*N)) 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
N-2 y[k] = x[N-1]*(-1)**k + 2* sum x[n]*sin(pi*(k+0.5)*(n+1)/N), 0 <= k < N. n=0
The (unnormalized) DCT-III is the inverse of the (unnormalized) DCT-II, up to a factor 2N. The orthonormalized DST-III is exactly the inverse of the orthonormalized DST-II.
New in version 0.11.0.
References
[R35] (1, 2) Wikipedia, “Discrete sine transform”, http://en.wikipedia.org/wiki/Discrete_sine_transform