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The perceptual relevance of balance, evenness, and entropy in musical rhythms

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Parallel FFT-hashing

Serge Vaudenay

We propose two families of scalable hash functions for collision-resistant hashing that are highly parallel and based on the generalized fast Fourier transform (FFT). FFT-hashing is based on multipermutations. This is a basic cryptographic primitive for pe ...

1993

Computing m DFT's over GF(q) with one DFT over GF(q^m)

Martin Vetterli

Over the field of complex numbers, it is well-known that if the input is real then it is possible to compute 2 real DFT's with one complex DFT. We extend the result to finite fields and show how to compute m DFT's over GF(q) with one DFT over GF(qm) ...

1993

Split-radix algorithms for length-p^m DFT's

Martin Vetterli

The split-radix algorithm for the discrete Fourier transform of length-2^m is by now fairly popular. First, we give the reason why the split-radix algorithm is better tant any single-radix algorithm on length 2^m DFT's. Then, the split-radix approach is ge ...

1989

Improved Fourier and Hartley transform algorithms: application to cyclic convolution of real data

Martin Vetterli

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 improv ...

1987

Fundamental relations between the LMS algorithm and the DFT

Martin Vetterli

The digital Fourier transform (DFT) and the adaptive least mean square (LMS) algorithm have existed for some time. This paper establishes a connection between them. The result is the "LMS spectrum analyzer," a new means for the calculation of the DFT. The ...

1987

Simple FFT and DCT algorithms with reduced number of operations

Martin Vetterli

A simple algorithm for the evaluation of discrete Fourier transforms (DFT) and discrete cosine transforms (DCT) is presented. This approach, based on the divide and conquer technique, achieves a substantial decrease in the number of additions when compared ...

1984