Abstracts
This paper proposes a new way of tidal spectral analysis based on the Cooley-Tukey algorithm, known as the Fast Fourier Transform. The Fast Fourier Transform analysis is used to compute both the harmonic constants of the tide and the power spectrum.The latter is obtained by means of a weighted sum. A new way is also derived to obtain the formula giving the number of the degrees of freedom,on which is based the confi dence interval corresponding to the noise spectrum.
Este trabalho propõe um novo caminho para a analise espectral da maré baseada no algoritmo de Cooley-Tukey. A análise através da "Transformação Rápida de Fourier" (Fast Fourier Transform - FFT) é empregada tanto para calcular as constantes harmônicas da maré quanto para a obtenção do espectro de energia. Este é calculado por meio de uma soma ponderada. Também é dada uma nova dedução da fórmula que exprime o número de graus de liberdade em que se baseia o intervalo de confiança correspondente ao espectro do ruído. O trabalho foi redigido em inglês a fim de facilitar o intercâmbio de informações.
The Fast Fourier Transform and its application to tidal oscillations* * This is the reprint with minor corrections and improved programs. The former reprint is obsolete.
A. dos Santos Franco; Norman J. Rock** ** Visiting Professor at the Instituto Oceanográfico da Universidade de São Paulo on a Ford Foundation and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) grants.
Instituto Oceanográfico da Universidade de São Paulo
SYNOPSIS
This paper proposes a new way of tidal spectral analysis based on the Cooley-Tukey algorithm, known as the Fast Fourier Transform. The Fast Fourier Transform analysis is used to compute both the harmonic constants of the tide and the power spectrum.The latter is obtained by means of a weighted sum. A new way is also derived to obtain the formula giving the number of the degrees of freedom,on which is based the confi dence interval corresponding to the noise spectrum.
RESUMO
Este trabalho propõe um novo caminho para a analise espectral da maré baseada no algoritmo de Cooley-Tukey. A análise através da "Transformação Rápida de Fourier" (Fast Fourier Transform - FFT) é empregada tanto para calcular as constantes harmônicas da maré quanto para a obtenção do espectro de energia. Este é calculado por meio de uma soma ponderada. Também é dada uma nova dedução da fórmula que exprime o número de graus de liberdade em que se baseia o intervalo de confiança correspondente ao espectro do ruído. O trabalho foi redigido em inglês a fim de facilitar o intercâmbio de informações.
Full text available only in PDF format.
Texto completo disponível apenas em PDF.
ACKNOWLEDGEMENTS
Grateful appreciation is extended to the "Instituto de Física", USP, for allowing unrestricted use of the IBM 360 computer installation.
Also sincere thanks are due to the "Instituto de Comunicações Elétricas" for the free use of the IBM 1130 for high speed plotting of spectra.
A special thank you to Mr. Sylvio José Correa for his valuable collaboration in the preparation of computer programs in Appendices V, VI.
LIST OF SYMBOLS USED
(Received 10/15/1970)
APPENDICES
SET OF PROGRAMS FOR TIDAL ANALYSIS
by the
"Instituto Oceanográfico" Method
N.B. The programs are presented separately to provide greater flexibility to the user. In practice, however, programs in Appendices I, II, III, IV, are inter-linked and executed sequentially by the computer.
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APPENDIX I
FAST FOURIER TRANSFORM
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APPENDIX II
MATRIX GENERATION
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APPENDIX III
CALCULATION OF TIDAL COMPONENTES aj AND bj., HARMONIC CONSTANTS H&g AND CORRECTION OF FOURIER COEFFICIENTS FOR TIDAL EFFECTS TO OBTAIN RESIDUALS ξn AND ηn
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APPENDIX IV
POWER SPECTRAL ANALYSIS
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Publication Dates
-
Publication in this collection
12 June 2012 -
Date of issue
1971
History
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Received
15 Oct 1970