a modified split radix fft with fewer arithmetic operations recent results by van buskirk have broken the record set by yavne in 1968 for the lowest exact count of real additions and multiplications to compute a power of two discrete fourier transform dft here we present a simple recursive modification of the split radix algorithm that computes the dft with asymptotically about 6 fewer operations than yavne matching the count achieved by van buskirk s program generation framework we also discuss the application of our algorithm to real data and real symmetric discrete cosine transforms where we are again able to achieve lower arithmetic counts than previously published algorithms

recursive generation of the dif fft algorithm for 1 d dft it is shown by using the walsh hadamard matrix and a conversion matrix a dif fft algorithm can be developed for the radix 2 discrete fourier transform dft the recursive generation of the dft matrix leads to its sparse matrix factorization the flowgraph based on these sparse matrices is identical to that of the dft fft algorithm

chow rings of fine quiver moduli are tautologically presented a result of a king and c walter asserts that the chow ring of a fine quiver moduli space is generated by the chern classes of universal bundles if the quiver is acyclic we will show that defining relations between these chern classes arise geometrically as degeneracy loci associated to the universal representation

transforming real valued sequences fast fourier versus fast hartley transform algorithms five programs for efficient computation of dft of real valued data are analyzed with respect to their operation counts vis a vis run times on weak and powerful floating point processors the results help dispose of the claims of superiority of fht over corresponding real valued fft the bruun 1978 algorithm turns out to be a best performer

input and or output pruning of composite length ffts using a dif dit transform decomposition pruned fast fourier transforms ffts can be efficient alternatives to compute dfts when the input vector is zero padded and or several output elements are not required in this correspondence a new method to prune composite length ffts is proposed the proposed pruning method uses decimation in frequency dif and decimation in time dit to decompose a dft into stages of smaller dfts the pruning process is carried out on the input stage and the output stage of the decomposed transform the proposed pruning method is flexible since it can perform input and or output pruning over any composite length fft action that no other pruning method reported in the literature can carry out additionally no restriction exists with the number of consecutive inputs and consecutive outputs that can be used finally it is shown that the proposed pruning method generates efficient pruned power of three and power of two length ffts

on computing the split radix fft this paper presents an efficient fortran program that computes the duhamel hollmann split radix fft an indexing scheme is used that gives a three loop structure for the split radix fft that is very similar to the conventional cooley tukey fft both a decimation in frequency and a decimation in time program are presented an arithmetic analysis is made to compare the operation count of the cooley tukey fft fo several different radixes to that of the split radix fft the split radix fft seems to require the least total arithmetic of any power of two dft algorithm

efficient computation of the dft with only a subset of input or output points ways of efficiently computing the discrete fourier transform dft when the number of input and output data points differ are discussed the two problems of determining whether the length of the input sequence or the length of the output sequence is reduced can be found to be duals of each other and the same methods can to a large extent be used to solve both the algorithms utilize the redundancy in the input or output to reduce the number of operations below those of the fast fourier transform fft algorithms the usual pruning method is discussed and an efficient algorithm called transform decomposition is introduced it is based on a mixture of a standard fft algorithm and the horner polynomial evaluation scheme equivalent to the one in goertzel s algorithms it requires fewer operations and is more flexible than pruning the algorithm works for power of two and prime factor algorithms as well as for real input data

comments on split manageable efficient algorithm for fourier and hadamard transforms the paper split manageable efficient algorithm for fourier and hadamard transforms in ieee transactions on signal processing vol 48 no 1 pp 172 183 january 2000 presents a novel paired transform fast fourier transform fft algorithm that is claimed to require fewer total real additions and multiplications than previous algorithms we show this claim to be false although the algorithm correctly computes the discrete fourier transform an accurate count shows that it requires more real arithmetic operations than pre existing ffts

recursive fast algorithm and the role of the tensor product the use of the tensor product for modeling and designing fft algorithms is addressed the benefit of the tensor product approach lies in the strong connection between certain tensor product constructs and important computer architectures the scope of the tensor product approach is generalized to include a much larger class of fast recursive algorithms this greatly enhances the versatility of the tensor product technique and brings many different algorithms to the level of understanding and flexibility enjoyed by the fft

cohomologie des varietes de modules de hauteur nulle soient r c1 c2 des entiers avec r 1 m r c 1 c 2 la variete de modules des faisceaux algebriques semi stables sur 2 de rang r et de classes de chern c 1 c 2 et m s r c 1 c 2 l ouvert de m r c 1 c 2 correspondant aux faisceaux stables on note la pente et le discriminant des faisceaux de rang r et de classes de chern c 1 c 2 il existe une unique fonction telle que pour tout choix de r c 1 c 2 m r c 1 c 2 est de dimension positive si et seulement si si on dit que la variete de modules m r c 1 c 2 est de hauteur nulle soit la caracteristique d euler poincare des faisceaux coherents de rang r et de classes de chern c 1 c 2 on suppose que les entiers r c 1 et sont premiers entre eux cette condition signifie que m r c 1 c 2 m s r c 1 c 2 c est une variete projective lisse irreductible on etudie dans cet article la cohomologie entiere de m r c 1 c 2 pour cela on utilise une description particuliere de m r c 1 c 2 soient q m n des entiers avec q 2 m 0 n 0 les applications lineaires m q n sont appelees q modules de kronecker l espace projectif des droites de w l m q n est muni d une action evidente du groupe reductif g sl m sl n qui se prolonge a o 1 on note ss resp s l ouvert de des points semi stables resp stables pour cette action soit n q m n resp ns q m n le quotient algebrique de ss resp s par g il existe des entiers q m n tels que m r c 1 c 2 soit isomorphe a n q m n la condition r c 1 et sont premiers entre eux est equivalente a m et n sont premiers entre eux pour etudier la cohomologie de n q m n on utilise deux methodes la seconde uniquement dans un cas particulier la premiere methode est celle d atiyah bott qui a servi a etudier la cohomologie entiere des varietes de modules de fibres stables sur une courbe projective lisse le principal resultat obtenu est que la cohomologie entiere de m r c 1 c 2 est nulle en degre impair et sans torsion on trouve aussi des generateurs naturels de cette cohomologie la methode permet en outre de calculer les nombres de betti de n q m n le seconde methode utilise des resultats de bialynicki birula on ne traite que le cas de n 3 2 3 elle revient a etudier une action naturelle d un tore sur n 3 2 3 et a determiner ses points fixes on en deduit que n 3 2 3 possede une decomposition cellulaire

a split radix partial input output fast fourier transform algorithm a fast discrete fourier transform dft computing algorithm used in situations where part of the data is zero and only the first transform elements are to be calculated is proposed the method is based on the pruning of a split radix decimation time dit fast fourier transform fft diagram it has the advantage of providing gains as a result of pruning computation and the use of a split radix

recursive cyclotomic factorization a new algorithm for calculating the discrete fourier transform in this paper a new recursive algorithm for calculating the discrete fourier transformation is presented this new so called recursive cyclotomic factorization algorithm rcfa is more efficient than the fast fourier transformation fft algorithm moreover due to its recursive nature the rcfa can also be easily implemented using only a limited number of different computation cells

a robust sequential quadratic programming method the sequential quadratic programming method developed by wilson han and powell may fail if the quadratic programming subproblems become infeasible or if the associated sequence of search directions is unbounded this paper considers techniques which circumvent these difficulties by modifying the structure of the constraint region in the quadratic programming subproblems furthermore questions concerning the occurrence of an unbounded sequence of multipliers and problem feasibility are also addressed

the vector split radix algorithm for 2d dht a decimation in frequency vector split radix algorithm is proposed to decompose an n n 2d discrete hartley transform dht into one n 2 n 2 dht and twelve n 4 dhts the proposed algorithm possesses the in place property and needs no matrix transpose its computational structure is very regular and is simpler than those of all existing nonseparable 2d dhts

fast discrete transforms by means of eigenpolynomials abstract let a a ij be an n n matrix consider the discrete transform u a u and associate with the j th column of a the eigenpolynomial a j x n 1 i 0 a ij x j the properties of eigenpolynomials play an important role in the case where a is a matrix of eigenvectors of a toeplitz matrix 1 2 here we consider the cases where a is the matrix defining the discrete fourier transform dft the discrete hartley transform dht the discrete sine transform dst and the discrete cosine transform dct in its two versions of 3 and 4 for each eigenpolynomial of each transform we explicitly determine all its zeros we use eigenpolynomials as a unifying tool for describing the decimation in frequency dif versions of the main known algorithms for dft moreover by using the information about the zeros of the eigenpolynomials we devise new algorithms for dft dht dst and dct which reach or improve in the case of dst and dct the record complexity bounds without requiring the use of the algorithm for complex multiplication with three multiplications and three additions 5 and of the implicit preconditioning

some feasibility issues in mathematical programs with equilibrium constraints this paper is concerned with some feasibility issues in mathematical programs with equilibrium constraints mpecs where additional joint constraints are present that must be satisfied by the state and design variables of the problems we introduce sufficient conditions that guarantee the feasibility of these mpecs it turns out that these conditions also guarantee the feasibility of the quadratic programming qp subproblems arising from the penalty interior point algorithm pipa and the sequential quadratic programming sqp algorithm for solving mpecs thus the same conditions ensure that these algorithms are applicable for solving this class of jointly constrained mpecs

scaled radix 2 8 algorithm for efficient computation of length n 2 m dfts this paper presents a scaled radix 2 8 fast fourier transform fft sr28fft algorithm for computing length n 2m discrete fourier transforms dfts scaled by complex number rotating factors the idea of the sr28fft algorithm is from the modified split radix fft msrfft algorithm and its purpose is to furnish other algorithms with high efficiency but without shortcomings of the msrfft algorithm a novel radix 2 4 fft nr24fft algorithm and a novel radix 2 8 fft nr28fft algorithm are proposed these two algorithms use sr28fft to calculate their sub dfts of odd indexed terms several aspects of the two algorithms such as computational complexity computation accuracy and coefficient evaluations or accesses to the lookup table all are improved the bit reverse method can be used for their order permutation and no extra memory is required to store their extra coefficients by the two novel algorithms which contribute significantly to the performance of the fft algorithms the sr28fft algorithm can also be applied to other algorithms whose decomposition contains sub dfts of powers of two the appendix presents an algorithm named sr28fft 2 for further reducing the number of arithmetic operations and nr24fft and nr28fft algorithms based on sr28fft 2 requires fewer real operations than that required by the msrfft algorithm

improved fourier and hartley transform algorithms application to cyclic convolution of real data this paper highlights the possible tradeoffs between arithmetic and structural complexity when computing cyclic convolution of real data in the transform domain both fourier and hartley based schemes are first explained in their usual form and then improved either from the structural point of view or in the number of operations involved namely we first present an algorithm for the in place computation of the discrete fourier transform on real data a decimation in time split radix algorithm more compact than the previously published one second we present a new fast hartley transform algorithm with a reduced number of operations a more regular convolution scheme based on fft s is also proposed finally we show that hartley transforms belong to a larger class of algorithms characterized by their generalized convolution property

implementation of split radix fft algorithms for complex real and real symmetric data a new algorithm is presented for the fast computation of the discrete fourier transform this algorithm belongs to that class of recently proposed 2n fft s which present the same arithmetic complexity the lowest among any previously published one moreover this algorithm has the advantage of being performed in place by repetitive use of a butterfly type structure without any data reordering inside the algorithm furthermore it can easily be applied to real and real symmetric data with reduced arithmetic complexity by removing all redundancy in the algorithm

guaranteed stable sliding dft algorithm with minimal computational requirements the discrete fourier transform dft is the most widely used technique for determining the frequency spectra of digital signals however in the sliding transform scenario where the transform window is shifted one sample at a time and the transform process is repeated the use of dft becomes difficult due to its heavy computational burden this paper proposes an optimal sliding dft osdft algorithm that achieves both the lowest computational requirement and the highest computational accuracy among existing sliding dft algorithms the proposed osdft algorithm directly computes the dft bins of the shifted window by simply adding or subtracting the bins of a previous window and an updating vector we show that the updating vector can be efficiently computed with a low complexity in the sliding transform scenario our simulations demonstrate that the proposed algorithm outperforms the existing sliding dft algorithms in terms of computational accuracy and processing time

a subspace limited memory quasi newton algorithm for large scale nonlinear bound constrained optimization in this paper we propose a subspace limited memory quasi newton method for solving large scale optimization with simple bounds on the variables the limited memory quasi newton method is used to update the variables with indices outside of the active set while the projected gradient method is used to update the active variables the search direction consists of three parts a subspace quasi newton direction and two subspace gradient and modified gradient directions our algorithm can be applied to large scale problems as there is no need to solve any subproblems the global convergence of the method is proved and some numerical results are also given

newton s method for large bound constrained optimization problems we analyze a trust region version of newton s method for bound constrained problems our approach relies on the geometry of the feasible set not on the particular representation in terms of constraints the convergence theory holds for linearly constrained problems and yields global and superlinear convergence without assuming either strict complementarity or linear independence of the active constraints we also show that the convergence theory leads to an efficient implementation for large bound constrained problems

on computing the discrete hartley transform the discrete hartley transform dht is a real valued transform closely related to the dft of a real valued sequence bracewell has recently demonstrated a radix 2 decimation in time fast hartley transform fht algorithm in this paper a complete set of fast algorithms for computing the dht is developed including decimation in frequency radix 4 split radix prime factor and winograd transform algorithms the philosophies of all common fft algorithms are shown to be equally applicable to the computation of the dht and the fht algorithms closely resemble their fft counterparts the operation counts for the fht algorithms are determined and compared to the counts for corresponding real valued fft algorithms the fht algorithms are shown to always require the same number of multiplications the same storage and a few more additions than the real valued fft algorithms even though computation of the fht takes more operations in some situations the inherently real valued nature of the discrete hartley transform may justify this extra cost

extended overlap add and save methods for multirate signal processing the overlap add method ola and overlap save method ols are well known as efficient schemes for high order fir filtering in this correspondence new sampling rate conversion methods are proposed by extending the ola and ols and eliminating the redundancy caused by the conversion first for finite duration sequences a rate conversion with the dft domain approach is discussed then using the result the extended ola and ols are proposed for infinite duration sequences last the computational complexities of our proposed methods are shown

on the fixed point accuracy analysis of fft algorithms in this paper we investigate the effect of fixed point arithmetics with limited precision for different fast fourier transform fft algorithms a matrix representation of error propagation model is proposed to analyze the rounding effect an analytic expression of overall quantization loss due to the arithmetic quantization errors is derived to compare the performance with decimation in time dit and decimation in frequency dif configurations from the simulation results the radix 2 dit fft algorithm has better accuracy in term of signal to quantization noise ratio sqnr based on the results a simple criterion of wordlength optimization is proposed to yield comparable accuracy with fewer bit budget

number theoretic transforms over the golden section quadratic field a new number theoretic transform ntt over the real quadratic field q spl radic 5 is suggested and analyzed conventional ntts are used for fast convolution of integer sequences a new approach for computing number theoretic transforms ntts is proposed allowing real signals to be processed as well the method is based on a diophantine approximation of the input real signal before the ntt the choice of the three parameters characterizing any ntt modulus transform length and primitive element is discussed in detail from a practical point of view the suggested ntts offer attractive combinations of these parameters much care has been exercised to reduce the computational complexity the practical usefulness of an irrational number system is demonstrated extensions and open problems are discussed

split radix algorithms for length p sup m dft s the split radix algorithm for the discrete fourier transform dft of length 2 sup m is considered first the reason why the split radix algorithm is better than any single radix algorithm on length 2 sup m dfts is given then the split radix approach is generalized to length p sup m dfts it is shown that whenever a radix p sup 2 outperforms a radix p algorithm then a radix p p sup 2 algorithm will outperform both of them as an example a radix 3 9 algorithm is developed for length 3 sup m dfts

mechanical derivation of fused multiply add algorithms for linear transforms several computer architectures offer fused multiply add fma also called multiply and accumulate mac instructions that are as fast as a single addition or multiplication for the efficient implementation of linear transforms such as the discrete fourier transform or discrete cosine transforms this poses a challenge to algorithm developers as standard transform algorithms have to be manipulated into fma algorithms that make optimal use of fma instructions we present a general method to convert any transform algorithm into an fma algorithm the method works with both algorithms given as directed acyclic graphs dags and algorithms given as structured matrix factorizations we prove bounds on the efficiency of the method in particular we show that it removes all single multiplications except at most as many as the transform has outputs we implemented the dag based version of the method and show that we can generate many of the best known hand derived fma algorithms from the literature as well as a few novel fma algorithms

wiener hopf and spectral factorization of real polynomials by newton s method abstract we present a new method for factoring a real polynomial into the product of two polynomials which have their zeros inside and outside the unit circle respectively the approach is based on solving a nonlinear system by newton s method the jacobi matrix is a polynomial of a companion matrix and thus a bezoutian times the inverse of a triangular toeplitz matrix after getting deeper understanding of the displacement structure of the bezoutian each newton step can be reduced to a few applications of discrete fourier or cosine transforms and the lu decomposition of a conceived linear system with a cauchy like matrix these structural features are employed to design a fast algorithm which shows excellent numerical behavior for example in the case of the extremely ill conditioned test polynomial 2 z n k 0 n 1 z k 2 k 1 n z k of the degree 2 n 20000 we obtain the factorization after 22 newton steps with an error of 3 4 10 8 in the euclidean norm the execution time on a laptop being a couple of minutes the local quadratic convergence of our newton method is proved and explicit convergence balls are given on the basis of estimates for the lipschitz constant which occurs in kantorovich s theorem we also design and test two superfast versions of our method which for polynomials of degree 20000 typically need about half a minute to produce an initial coefficient vector and then perform the newton iteration within 1 s

on the accurate identification of active constraints we consider nonlinear programs with inequality constraints and we focus on the problem of identifying those constraints which will be active at an isolated local solution the correct identification of active constraints is important from both a theoretical and a practical point of view such an identification removes the combinatorial aspect of the problem and locally reduces the inequality constrained minimization problem to an equality constrained problem which can be more easily dealt with we present a new technique which identifies active constraints in a neighborhood of a solution and which requires neither complementary slackness nor uniqueness of the multipliers we also present extensions to variational inequalities and numerical examples illustrating the identification technique

2 d and 1 d multipaired transforms frequency time type wavelets a concept of multipaired unitary transforms is introduced these kinds of transforms reveal the mathematical structure of fourier transforms and can be considered intermediate unitary transforms when transferring processed data from the original real space of signals to the complex or frequency space of their images considering paired transforms we analyze simultaneously the splitting of the multidimensional fourier transform as well as the presentation of the processed multidimensional signal in the form of the short one dimensional 1 d signals that determine such splitting the main properties of the orthogonal system of paired functions are described and the matrix decompositions of the fourier and hadamard transforms via the paired transforms are given the multiplicative complexity of the two dimensional 2 d 2 sup r spl times 2 sup r point discrete fourier transform by the paired transforms is 4 sup r 2 r 7 3 8 3 12 r 3 which shows the maximum splitting of the 5 d fourier transform into the number of the short 1 d fourier transforms the 2 d paired transforms are not separable and represent themselves as frequency time type wavelets for which two parameters are united frequency and time the decomposition of the signal is performed in a way that is different from the traditional haar system of functions

convergence of the bfgs method for lc 1 convex constrained optimization this paper proposes a bfgs sqp method for linearly constrained optimization where the objective function f is required only to have a lipschitz gradient the karush kuhn tucker system of the problem is equivalent to a system of nonsmooth equations f v 0 at every step a quasi newton matrix is updated if f v k satisfies a rule this method converges globally and the rate of convergence is superlinear when f is twice strongly differentiable at a solution of the optimization problem no assumptions on the constraints are required this generalizes the classical convergence theory of the bfgs method which requires a twice continuous differentiability assumption on the objective function applications to stochastic programs with recourse on a cm5 parallel computer are discussed

quantization errors in the computation of the discrete hartley transform the principal objective of this paper is the study of the arithmetic roundoff error characteristics of several discrete hartley transform dht algorithms we first summarize a variety of efficient dht algorithms including bracewell s original decimation in time radix 2 algorithm statistical models for fixed and floating point arithmetic roundoff errors are then used as the basis for a theoretical study of roundoff noise characteristics of a number of the dht algorithms the results of a detailed experimental study of roundoff noise are compared to the theoretical predictions in fixed point implementation of the decimation in time and frequency radix 2 algorithms it is found that the noise to signal ratio increases approximately 1 1 bits per stage for the floating point implementation the number of bits of rms noise to signal ratio for all the algorithms increase as sqrt log 2 n so that doubling the number of points produced a mild increase in the output noise

fixed point analysis and parameter selections of msr cordic with applications to fft designs mixed scaling rotation msr coordinate rotation digital computer cordic is an attractive approach to synthesizing complex rotators this paper presents the fixed point error analysis and parameter selections of msr cordic with applications to the fast fourier transform fft first the fixed point mean squared error of the msr cordic is analyzed by considering both the angle approximation error and signal round off error incurred in the finite precision arithmetic the signal to quantization noise ratio sqnr of the output of the fft synthesized using msr cordic is thereafter estimated based on these analyses two different parameter selection algorithms of msr cordic are proposed for general and dedicated msr cordic structures the proposed algorithms minimize the number of adders and word length when the sqnr of the fft output is constrained design examples show that the fft designed by the proposed method exhibits a lower hardware complexity than existing methods

comments on fast computation of the discrete cosine transform and the discrete hartley transform by h s malvar the commenter shows that the algorithm presented in the above paper ibid vol assp 35 no 10 p 1484 5 oct 1987 requires exactly the same number of multiplications as but more additions than prevalent methods for the computation of the dht discrete hartley transform by existing methods contrary to the author s claim

the harder narasimhan system in quantum groups and cohomology of quiver moduli methods of harder and narasimhan from the theory of moduli of vector bundles are applied to moduli of quiver representations using the hall algebra approach to quantum groups an analog of the harder narasimhan recursion is constructed inside the quantized enveloping algebra of a kac moody algebra this leads to a canonical orthogonal system the hn system in this algebra using a resolution of the recursion an explicit formula for the hn system is given as an application explicit formulas for betti numbers of the cohomology of quiver moduli are derived generalizing several results on the cohomology of quotients in linear algebra type situations

split vector radix fast fourier transform the split radix approach for computing the discrete fourier transform dft is extended for the vector radix fast fourier transform fft to two and higher dimensions it is obtained by further splitting the n 2 n 2 transforms with twiddle factors in the radix 2 2 fft algorithm the generalization of this split vector radix fft algorithm to higher radices and higher dimensions is also presented by introducing a general approach for constructing the fast hartley transform fht from the corresponding fft new vector and split vector radix fht algorithms with the same desirable properties as their fft counterparts are obtained

globally and superlinearly convergent algorithms for the solution of box constrained optimization abstract based on the identification technique of active constraints we propose a newton like algorithm and a quasi newton algorithm for solving the box constrained optimization problem the two algorithms require only the solution of a lower dimensional system of linear equations at each iteration in the proposed quasi newton algorithm we make use of an approximate direction derivative of the multiplier functions so that only first order derivatives of the objective function are needed to evaluate under mild assumptions global convergence of the two algorithms is established in particular locally quadratic convergence for the newton like algorithm and locally superlinear convergence for the quasi newton algorithm are obtained without assuming that the strict complementarity condition holds at the solution

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

a general class of split radix fft algorithms for the computation of the dft of length 2 m in this paper a general class of split radix fast fourier transform fft algorithms for computing the length 2m dft is proposed by introducing a new recursive approach coupled with an efficient method for combining the twiddle factors this enables the development of higher split radix fft algorithms from lower split radix fft algorithms without any increase in the arithmetic complexity specifically an arbitrary radix 2 2s fft algorithm for any value of s 4les sles m is proposed and its arithmetic complexity analyzed it is shown that the number of arithmetic operations multiplications plus additions required by the proposed radix 2 2s fft algorithm is independent of s and is 2m 3 2m 1 8 regardless of whether a complex multiplication is carried out using four multiplications and two additions or three multiplications and three additions this paper thus provides a variety of choices and ways for computing the length 2m dft with the same arithmetic complexity

on the odd dft and its applications to dct idct computation in this correspondence efficient algorithms are presented for simultaneous calculation of the odd discrete fourier transform odd dft and the real dft these algorithms are used to derive a new algorithm to calculate the discrete cosine transform dct that is computationally equivalent to the classical fast fourier transform fft based algorithm for dct calculation in addition odd dft properties are exploited to develop a novel algorithm for an inverse discrete cosine transform idct calculation that outperforms previous fft based solutions for idct calculation

discrete fourier transform algorithms for real valued sequences it is well known that the discrete fourier transformation dft of a real valued sequence contains some redundancies more precisely approximately half of the dft coefficients suffice to completely determine the dft in this paper it is shown that the choice of the set of nonredundant dft coefficients to be calculated affects the efficiency of the resulting algorithm one especially interesting choice is discussed in detail for the case of mixed radix 2 3 dft algorithms algorithms for the dft calculation of both one and more dimensional real valued arrays are discussed