Meghanad D. Wagh

Robot path planning using intersecting convex shapes: Analysis and simulation

An automated path planning algorithm for a mobile robot in a structured environment is presented. An algorithm based on the Quine-McCluskey method of finding prime implicants in a logical expression is used to isolate all the largest rectangular free convex areas in a specified environment. The free convex areas are represented as nodes in a graph, and a graph traversal strategy that dynamically allocates costs to graph paths is used. Complexity of the algorithm and a strategy to trade optimality for smaller computation time are discussed.

A class of translation invariant transforms

A class of translation invariant transforms containing the R-transform is defined, and it is shown that a particular member of this class is superior to the R-transform for pattern recognition applications.

Mapping Cycles and Trees on Wrap-Around Butterfly Graphs

We give a new algebraic representation for the wrap-around butterfly interconnection network. This new representation is based on the direct product of groups and finite fields and allows an algebraic expression of the network connectivity. The abstract algebraic tools may then be employed to explore the structural properties of the butterfly. In this paper we exploit this model to map guest graphs on the butterfly. In particular, we provide designs of unit dilation mappings of all possible length cycles on butterflies. We also map the largest possible binary trees on butterfly networks with a dilation 2 if the network degree is less than 16, 3 if it is less than 32, and 4 if it is less than 64. This is a great improvement over previous results.

A new structured design method for convolutions over finite fields, Part I

The structure of bilinear cyclic convolution algorithms is explored over finite fields. The algorithms derived are valid for any length not divisible by the field characteristic and are based upon the small length polynomial multiplication algorithms. The multiplicative complexity of these algorithms is small and depends on the field of constants. The linear transformation matrices A, B (premultiplication), and C (postmultiplication) defining the algorithm have block structures which are related to one another. The rows of A and B and the columns of C are maximal length recurrent sequences. Because of the highly regular structure of A, B , and C , the algorithms can be very easily designed even for large lengths. The application of these algorithms to the decoding of Reed-Solomon codes is also examined.

Robot path planning using intersecting convex shapes

This paper deals with an automated path planning algorithm for a mobile robot in a structured enviornment. The algorithm is based upon finding all the largest (prime) free convex areas in the environment and representing this information in the form of a graph. A graph traversal algorithm which exploits back-tracking as well as dynamic cost allocation to graph arcs is presented and simulated. A strategy to trade of the optimality of the results for a smaller computation time is described.

Composite Cyclotomic Fourier Transforms With Reduced Complexities

Discrete Fourier transforms (DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic fast Fourier transforms (CFFTs) are promising due to their low multiplicative complexities. Unfortunately, there are two issues with CFFTs: (1) they rely on efficient short cyclic convolution algorithms, which have not been sufficiently investigated in the literature and (2) they have very high additive complexities when directly implemented. To address both issues, we make three main contributions in this paper. First, for any odd prime p, we reformulate a p -point cyclic convolution as the product of a (p-1) × (p-1) Toeplitz matrix and a vector, which has well-known efficient algorithms, leading to efficient bilinear algorithms for p-point cyclic convolutions. Second, to address the high additive complexities of CFFTs, we propose composite cyclotomic Fourier transforms (CCFTs). In comparison to previously proposed fast Fourier transforms, our CCFTs achieve lower overall complexities for moderate to long lengths and the improvement significantly increases as the length grows. Third, our efficient algorithms for p-point cyclic convolutions and CCFTs allow us to obtain longer DFTs over larger fields, e.g., the 2047-point DFT over GF(211) and 4095-point DFT over GF(212) , which are first efficient DFTs of such lengths to the best of our knowledge. Finally, our CCFTs are also advantageous for hardware implementations due to their modular structure.

Fast Algorithm for Modulated Complex Lapped Transform

A new algorithm for the modulated complex lapped transform (MCLT) with a sine windowing function is presented. It is shown that by merging the windowing operation with the main computation, both the real and the imaginary parts of the MCLT with 2N inputs can be obtained from two N-point discrete cosine transforms of type II (DCTs-II) of appropriate inputs. The resulting algorithm is computationally very efficient. In general, the value of N is an even number. When N is a power of 2, the proposed algorithm uses only N log N + 2 real multiplications (including the scaling factors in the DCT computation), with none of those being outside the DCT blocks.

Hamilton cycles in trivalent Cayley graphs

Abstract It is shown that the Trivalent Cayley graphs, TC n , are near recursive . In particular, TC n is a union of four copies of TC n − 2 with additional well placed nodes. This allows one to recursively build the Hamilton cycle in TC n .

An MDCT Hardware Accelerator for MP3 Audio

With the increasing popularity of MP3 audio, there is a need to develop cost and power efficient architectures for the MP3 encoder and decoder. This paper describes dedicated architectures for computing the modified discrete cosine transform (MDCT) and its inverse (IMDCT). Recent profiling studies have shown that these operations represent about 30% of the total MP3 computations. MP3 format defines two frame sizes that can occur in the same data stream. We have developed the most efficient algorithms for MDCT and IMDCT suitable for both sizes. Unlike previous algorithms, our computations can be unified in a single ASIC architecture. This unified architecture implemented in 90 nm TSMC library is still 25% smaller and 25% faster than any previous single frame size architectures designed in the same technology. In addition, at 128 Kbits/sec data rates, our algorithms save nearly 1800 multiplications per second (18%) which can help reduce the power consumption.

A multiplexing theorem and generalisation of R-transform

Analytical properties of Rapid transform are investigated. Transforms of multiplexed patterns are resolved into the transforms of constituent patterns. It is shown that periodicity in pattern domain corresponds to a null subspace in transform domain and a null subspace in pattern domain gives a periodic transform. Further, the nontrivial portion of the transform is related to the transform of the nontrivial portion of the pattern. Based on these properties of R-transform, a generalised R-transformation for rectangular patterns is defined. It displays the translation invariant property of R-transform and reduces to R-transform in case of square and column patterns.