Discrete sine transform

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the discrete sine transform (DST) is a <a href="/facts/List_of_Fourier-related_transforms/omM5lS1k">Fourier-related transform</a> similar to the <a href="/facts/Discrete_Fourier_transform/uK9Tjsbl">discrete Fourier transform</a> (DFT), but using a purely <a href="/facts/Real_number/R02gw5Pb">real</a> <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a>. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data with <a href="/facts/Even_and_odd_functions/tGHWJqAa">odd</a> <a href="/facts/Symmetry/hpu7DK8p">symmetry</a> (since the Fourier transform of a real and odd function is imaginary and odd), where in some variants the input and/or output data are shifted by half a sample.
The DST is related to the <a href="/facts/Discrete_cosine_transform/gPpDhPwP">discrete cosine transform</a> (DCT), which is equivalent to a DFT of real and even functions. See the DCT article for a general discussion of how the boundary conditions relate the various DCT and DST types. Generally, the DST is derived from the DCT by replacing the <a href="/facts/Neumann_boundary_condition/0e0YBW4G">Neumann condition</a> at x=0 with a <a href="/facts/Dirichlet_condition/m9wsgG89">Dirichlet condition</a>. Both the DCT and the DST were described by <a href="/facts/Nasir_Ahmed_(engineer)/LImldyWe">Nasir Ahmed</a>, T. Natarajan, and <a href="/facts/K.R._Rao/DwrVrQ6u">K.R. Rao</a> in 1974. The type-I DST (DST-I) was later described by <a href="/facts/Anil_K._Jain_(electrical_engineer%2c_born_1946)/8CQ7Sh3J">Anil K. Jain</a> in 1976, and the type-II DST (DST-II) was then described by H.B. Kekra and J.K. Solanka in 1978.

Discrete sine transform open-in-new

Discrete sine transform