File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Direct methods for computing discrete sinusoidal transforms

TitleDirect methods for computing discrete sinusoidal transforms
Authors
Issue Date1990
Citation
Iee Proceedings, Part F: Radar And Signal Processing, 1990, v. 137 n. 6, p. 433-442 How to Cite?
AbstractAccording to Wang, there are four different types of DCT (discrete cosine transform) and DST (discrete sine transform) and the computation of these sinusoidal transforms can be reduced to the computation of the type-IV DCT. As the algorithms involve different sizes of transforms at different stages they are not so regular in structure. Lee has developed a fast cosine transform (FCT) algorithm for DCT-III similar to the decimation-in-time (DIT) Cooley-Tukey fast Fourier transform (FFT) with a regular structure. A disadvantage of this algorithm is that it involves the division of the trigonometric coefficients and may be numerically unstable. Recently, Hou has developed an algorithm for DCT-II which is similar to a decimation-in-frequency (DIF) algorithm and is numerically stable. However, an index mapping is needed to transform the DCT to a phase-modulated discrete Fourier transform (DFT), which may not be performed in-place. In the paper, a variant of Hou's algorithm is presented which is both in-place and numerically stable. The method is then generalised to compute the entire class of discrete sinusoidal transforms. By making use of the DIT and DIF concepts and the orthogonal properties of the DCTs, it is shown that simple algebraic formulations of these algorithms can readily be obtained. The resulting algorithms are regular in structure and are more stable than and have fewer arithmetic operations than similar algorithms proposed by Yip and Rao. By means of the Kronecker matrix product representation, the 1-D algorithms introduced in the paper can readily be generalised to compute transforms of higher dimensions. These algorithms, which can be viewed as the vector-radix generalisation of the present algorithms, share the in-place and regular structure of their 1-D counterparts.
Persistent Identifierhttp://hdl.handle.net/10722/154926
ISSN

 

DC FieldValueLanguage
dc.contributor.authorChan, SCen_US
dc.contributor.authorHo, KLen_US
dc.date.accessioned2012-08-08T08:31:10Z-
dc.date.available2012-08-08T08:31:10Z-
dc.date.issued1990en_US
dc.identifier.citationIee Proceedings, Part F: Radar And Signal Processing, 1990, v. 137 n. 6, p. 433-442en_US
dc.identifier.issn0956-375Xen_US
dc.identifier.urihttp://hdl.handle.net/10722/154926-
dc.description.abstractAccording to Wang, there are four different types of DCT (discrete cosine transform) and DST (discrete sine transform) and the computation of these sinusoidal transforms can be reduced to the computation of the type-IV DCT. As the algorithms involve different sizes of transforms at different stages they are not so regular in structure. Lee has developed a fast cosine transform (FCT) algorithm for DCT-III similar to the decimation-in-time (DIT) Cooley-Tukey fast Fourier transform (FFT) with a regular structure. A disadvantage of this algorithm is that it involves the division of the trigonometric coefficients and may be numerically unstable. Recently, Hou has developed an algorithm for DCT-II which is similar to a decimation-in-frequency (DIF) algorithm and is numerically stable. However, an index mapping is needed to transform the DCT to a phase-modulated discrete Fourier transform (DFT), which may not be performed in-place. In the paper, a variant of Hou's algorithm is presented which is both in-place and numerically stable. The method is then generalised to compute the entire class of discrete sinusoidal transforms. By making use of the DIT and DIF concepts and the orthogonal properties of the DCTs, it is shown that simple algebraic formulations of these algorithms can readily be obtained. The resulting algorithms are regular in structure and are more stable than and have fewer arithmetic operations than similar algorithms proposed by Yip and Rao. By means of the Kronecker matrix product representation, the 1-D algorithms introduced in the paper can readily be generalised to compute transforms of higher dimensions. These algorithms, which can be viewed as the vector-radix generalisation of the present algorithms, share the in-place and regular structure of their 1-D counterparts.en_US
dc.languageengen_US
dc.relation.ispartofIEE Proceedings, Part F: Radar and Signal Processingen_US
dc.titleDirect methods for computing discrete sinusoidal transformsen_US
dc.typeArticleen_US
dc.identifier.emailChan, SC:scchan@eee.hku.hken_US
dc.identifier.emailHo, KL:klho@eee.hku.hken_US
dc.identifier.authorityChan, SC=rp00094en_US
dc.identifier.authorityHo, KL=rp00117en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.scopuseid_2-s2.0-0025530239en_US
dc.identifier.volume137en_US
dc.identifier.issue6en_US
dc.identifier.spage433en_US
dc.identifier.epage442en_US
dc.identifier.scopusauthoridChan, SC=13310287100en_US
dc.identifier.scopusauthoridHo, KL=7403581592en_US

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats