Showing papers on "Circulant matrix published in 1969"
TL;DR: In this article, the operation of convolution is explored-starting with discrete rather than continuous convolution because of the relative ease of comprehension involved and a proof of the convolution theorem will show that convolution and transform analysis are closely related.
Abstract: Few mathematical operations are more important to the engineer than convolution and transform analysis. In this article, the operation of convolution is explored?starting with discrete rather than continuous convolution because of the relative ease of comprehension involved. With this foundation, the study is extended to continuous convolution. A proof of the convolution theorem will show that convolution and transform analysis are closely related. Of much more interest, however, is an intuitive explanation of why convolution and transform analysis techniques lead to exactly the same solution of a given problem. Perhaps the two most important applications of convolution deal with the analysis of linear systems and the sums of independent random variables?the latter problem being used to introduce discrete convolution.
12 citations
11 citations
TL;DR: For a quasi-skew Hadamard matrix of order 4m and (4n−1, k, m−n+k) configurations with circulant incidence matrices, there exists an HadAMard matrix (4m(4n − 1).
10 citations
TL;DR: The main results of this paper deal with obtaining necessary and sufficient conditions on A in order to ensure the existence of P and P' so that A is equivalent to the canonical matrix with parameters (K, n), where A need not be circulant.
4 citations
01 Sep 1969
TL;DR: The paper demonstrates that since the modal matrix of a permutation matrix contains only one bit of information, the evaluation of the discrete Fourier Transform involves considerably fewer than N multiplications where N is the number of samples involved and is also the order of the matrices involved.
Abstract: This paper provides a description of the Fast Fourier Transform and its connection with the circulant and permutation matrices. It is written for the case where the number of discrete time samples is equal to the number of discrete frequency samples but is otherwise not restricted. The paper demonstrates that since the modal matrix of a permutation matrix contains only one bit of information, the evaluation of the discrete Fourier Transform involves considerably fewer than N multiplications where N is the number of samples involved and is also the order of the matrices involved.
TL;DR: In this article, the mixed cyclotomic numbers (i, j){$ modulo p and exhibit a large class of circulant matrices based upon these constants whose determinants (up to sign) are powers of p. The results in this direction for the special cases e twice an o&prime and e four times an odd prime have been previously discussed in [2] and [3] for additional results.