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Article: Direct methods for computing discrete sinusoidal transforms
Title  Direct methods for computing discrete sinusoidal transforms 

Authors  
Issue Date  1990 
Citation  Iee Proceedings, Part F: Radar And Signal Processing, 1990, v. 137 n. 6, p. 433442 How to Cite? 
Abstract  According 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 typeIV 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 DCTIII similar to the decimationintime (DIT) CooleyTukey 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 DCTII which is similar to a decimationinfrequency (DIF) algorithm and is numerically stable. However, an index mapping is needed to transform the DCT to a phasemodulated discrete Fourier transform (DFT), which may not be performed inplace. In the paper, a variant of Hou's algorithm is presented which is both inplace 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 1D algorithms introduced in the paper can readily be generalised to compute transforms of higher dimensions. These algorithms, which can be viewed as the vectorradix generalisation of the present algorithms, share the inplace and regular structure of their 1D counterparts. 
Persistent Identifier  http://hdl.handle.net/10722/154926 
ISSN 
DC Field  Value  Language 

dc.contributor.author  Chan, SC  en_US 
dc.contributor.author  Ho, KL  en_US 
dc.date.accessioned  20120808T08:31:10Z   
dc.date.available  20120808T08:31:10Z   
dc.date.issued  1990  en_US 
dc.identifier.citation  Iee Proceedings, Part F: Radar And Signal Processing, 1990, v. 137 n. 6, p. 433442  en_US 
dc.identifier.issn  0956375X  en_US 
dc.identifier.uri  http://hdl.handle.net/10722/154926   
dc.description.abstract  According 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 typeIV 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 DCTIII similar to the decimationintime (DIT) CooleyTukey 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 DCTII which is similar to a decimationinfrequency (DIF) algorithm and is numerically stable. However, an index mapping is needed to transform the DCT to a phasemodulated discrete Fourier transform (DFT), which may not be performed inplace. In the paper, a variant of Hou's algorithm is presented which is both inplace 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 1D algorithms introduced in the paper can readily be generalised to compute transforms of higher dimensions. These algorithms, which can be viewed as the vectorradix generalisation of the present algorithms, share the inplace and regular structure of their 1D counterparts.  en_US 
dc.language  eng  en_US 
dc.relation.ispartof  IEE Proceedings, Part F: Radar and Signal Processing  en_US 
dc.title  Direct methods for computing discrete sinusoidal transforms  en_US 
dc.type  Article  en_US 
dc.identifier.email  Chan, SC:scchan@eee.hku.hk  en_US 
dc.identifier.email  Ho, KL:klho@eee.hku.hk  en_US 
dc.identifier.authority  Chan, SC=rp00094  en_US 
dc.identifier.authority  Ho, KL=rp00117  en_US 
dc.description.nature  link_to_subscribed_fulltext  en_US 
dc.identifier.scopus  eid_2s2.00025530239  en_US 
dc.identifier.volume  137  en_US 
dc.identifier.issue  6  en_US 
dc.identifier.spage  433  en_US 
dc.identifier.epage  442  en_US 
dc.identifier.scopusauthorid  Chan, SC=13310287100  en_US 
dc.identifier.scopusauthorid  Ho, KL=7403581592  en_US 