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ASL Basic Functions Vol.3 (for Fortran)

Contents
INTRODUCTION FOURIER TRANSFORMS AND THEIR APPLICATIONS

Chapter 1 INTRODUCTION

1.1
OVERVIEW

1.1.1
Introduction to The Advanced Scientific Library ASL

1.1.2
Distinctive Characteristics of ASL

1.2
KINDS OF LIBRARIES

1.3
ORGANIZATION

1.3.1
Introduction

1.3.2
Organization of Subroutine Description

1.3.3
Contents of Each Item

1.4
SUBROUTINE NAMES

1.5
NOTES

Chapter 2 FOURIER TRANSFORMS AND THEIR APPLICATIONS

2.1
INTRODUCTION

2.1.1
Notes

2.1.2
Algorithms Used

2.1.2.1
One-Dimensional (Continuous) Fourier Transforms

2.1.2.2
Multidimensional (Continuous) Fourier Transforms

2.1.2.3
One-Dimensional Fourier Transform

2.1.2.4
Multidimensional Fourier Transforms

2.1.2.5
Fast Fourier transform

2.1.2.6
One-Dimensional (Continuous) Convolutions and One-Dimensional (Continuous) Correlations

2.1.2.7
One-Dimensional Discrete Convolution and One-Dimensional Discrete Correlation

2.1.2.8
Multidimensional (Continuous) Convolution and Multidimensional (Continuous) Correlation

2.1.2.9
Power Spectrum

2.1.2.10
Laplace Transform

2.1.2.11
Wavelet transform

2.1.3
Reference Bibliography

2.2
ONE-DIMENSIONAL COMPLEX FOURIER TRANSFORM (REAL ARGUMENT TYPE)

2.2.1
[DEPRECATED]DFC1FB, RFC1FB
One-Dimensional Complex Fourier Transforms (Including Initialization)

2.2.2
[DEPRECATED]DFC1BF, RFC1BF
One-Dimensional Complex Fourier Transforms (After Initialization)

2.3
ONE-DIMENSIONAL COMPLEX FOURIER TRANSFORM (COMPLEX ARGUMENT TYPE)

2.3.1
[DEPRECATED]ZFC1FB, CFC1FB
One-Dimensional Complex Fourier Transforms (Including Initialization)

2.3.2
[DEPRECATED]ZFC1BF, CFC1BF
One-Dimensional Complex Fourier Transforms (After Initialization)

2.4
ONE-DIMENSIONAL REAL FOURIER TRANSFORM

2.4.1
[DEPRECATED]DFR1FB, RFR1FB
One-Dimensional Real Fourier Transforms (Including Initialization)

2.4.2
[DEPRECATED]DFR1BF, RFR1BF
One-Dimensional Real Fourier Transforms (After Initialization)

2.5
MULTIPLE ONE-DIMENSIONAL COMPLEX FOURIER TRANSFORM (REAL ARGUMENT TYPE)

2.5.1
[DEPRECATED]DFCMFB, RFCMFB
Multiple One-Dimensional Complex Fourier Transforms (Include Initialization)

2.5.2
[DEPRECATED]DFCMBF, RFCMBF
Multiple One-Dimensional Complex Fourier Transforms (After Initialization)

2.6
MULTIPLE ONE-DIMENSIONAL COMPLEX FOURIER TRANSFORM (COMPLEX ARGUMENT TYPE)

2.6.1
[DEPRECATED]ZFCMFB, CFCMFB
Multiple One-Dimensional Complex Fourier Transforms (Include Initialization)

2.6.2
[DEPRECATED]ZFCMBF, CFCMBF
Multiple One-Dimensional Complex Fourier Transforms (After Initialization)

2.7
MULTIPLE ONE-DIMENSIONAL REAL FOURIER TRANSFORM

2.7.1
[DEPRECATED]DFRMFB, RFRMFB
Multiple One-Dimensional Real Fourier Transforms (Including Initialization)

2.7.2
[DEPRECATED]DFRMBF, RFRMBF
Multiple One-Dimensional Real Fourier Transforms (After Initialization)

2.8
TWO-DIMENSIONAL COMPLEX FOURIER TRANSFORM (REAL ARGUMENT TYPE)

2.8.1
[DEPRECATED]DFC2FB, RFC2FB
Two-Dimensional Complex Fourier Transform (Including Initialization)

2.8.2
[DEPRECATED]DFC2BF, RFC2BF
Two-Dimensional Complex Fourier Transform (After Initialization)

2.9
TWO-DIMENSIONAL COMPLEX FOURIER TRANSFORM (COMPLEX ARGUMENT TYPE)

2.9.1
[DEPRECATED]ZFC2FB, CFC2FB
Two-Dimensional Complex Fourier Transform (Including Initialization)

2.9.2
[DEPRECATED]ZFC2BF, CFC2BF
Two-Dimensional Complex Fourier Transform (After Initialization)

2.10
TWO-DIMENSIONAL REAL FOURIER TRANSFORM

2.10.1
[DEPRECATED]DFR2FB, RFR2FB
Two-Dimensional Real Fourier Transform (Including Initialization)

2.10.2
[DEPRECATED]DFR2BF, RFR2BF
Two-Dimensional Real Fourier Transform (After Initialization)

2.11
THREE-DIMENSIONAL COMPLEX FOURIER TRANSFORM (REAL ARGUMENT TYPE)

2.11.1
[DEPRECATED]DFC3FB, RFC3FB
Three-Dimensional Complex Fourier Transform (Including Initialization)

2.11.2
[DEPRECATED]DFC3BF, RFC3BF
Three-Dimensional Complex Fourier Transform (After Initialization)

2.12
THREE-DIMENSIONAL COMPLEX FOURIER TRANSFORM (COMPLEX ARGUMENT TYPE)

2.12.1
[DEPRECATED]ZFC3FB, CFC3FB
Three-Dimensional Complex Fourier Transform (Including Initialization)

2.12.2
[DEPRECATED]ZFC3BF, CFC3BF
Three-Dimensional Complex Fourier Transform (After Initialization)

2.13
THREE-DIMENSIONAL REAL FOURIER TRANSFORM

2.13.1
[DEPRECATED]DFR3FB, RFR3FB
Three-Dimensional Real Fourier Transform (Including Initialization)

2.13.2
[DEPRECATED]DFR3BF, RFR3BF
Three-Dimensional Real Fourier Transform (After Initialization)

2.14
CONVOLUTIONS

2.14.1
DFCN1D, RFCN1D
One-Dimensional Convolutions

2.14.2
DFCN2D, RFCN2D
Two-Dimensional Convolutions

2.14.3
DFCN3D, RFCN3D
Three-Dimensional Convolutions

2.15
CORRELATIONS

2.15.1
DFCR1D, RFCR1D
One-Dimensional Correlations

2.15.2
DFCR2D, RFCR2D
Two-Dimensional Correlations

2.15.3
DFCR3D, RFCR3D
Three-Dimensional Correlations

2.16
POWER SPECTRUM ANALYSIS

2.16.1
DFPS1D, RFPS1D
One-Dimensional Fourier Periodograms

2.16.2
DFPS2D, RFPS2D
Two-Dimensional Fourier Periodograms

2.16.3
DFPS3D, RFPS3D
Three-Dimensional Fourier Periodograms

2.17
LAPLACE TRANSFORM

2.17.1
DFLARA, RFLARA
Inverse Laplace Transform (Rational Function)

2.17.2
DFLAGE, RFLAGE
Inverse Laplace Transform (General Function)

2.18
WAVELET TRANSFORM

2.18.1
DFWTH1, RFWTH1
Haar Function Generation

2.18.2
DFWTHR, RFWTHR
Wavelet Transform According to Haar Functions

2.18.3
DFWTHS, RFWTHS
Inverse Wavelet Transform According to Haar Functions

2.18.4
DFWTH2, RFWTH2
Haar Function Generation (Equally Spaced Sampling Data)

2.18.5
DFWTHT, RFWTHT
Wavelet Transform According to Haar Functions (Equally Spaced Sampling Data)

2.18.6
DFWTHI, RFWTHI
Inverse Wavelet Transform According to Haar Functions (Equally Spaced Sampling Data)

2.18.7
DFWTMF, RFWTMF
Mexican Hut Function Computation

2.18.8
DFWTMT, RFWTMT
Wavelet Transform According to Mexican Hut Functions

2.18.9
DFWTFF, RFWTFF
French Hut Function Computation

2.18.10
DFWTFT, RFWTFT
Wavelet Transform According to French Hut Function

Appendix

Appendix A
MACHINE CONSTANTS USED IN ASL

A.1
Units for Determining Error

A.2
Maximum and Minimum Values of Floating Point Data