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ASL Basic Functions Vol.3 (for C)

Chapter 1  INTRODUCTION

1.1

OVERVIEW

1.1.1

Introduction to The Advanced Scientific Library ASL C interface

1.1.2

Distinctive Characteristics of ASL C interface

1.2

KINDS OF LIBRARIES

1.3

ORGANIZATION

1.3.1

Introduction

1.3.2

Organization of Function Description

1.3.3

Contents of Each Item

1.4

FUNCTION 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]ASL_dfc1fb, ASL_rfc1fb
One-Dimensional Complex Fourier Transforms (Including Initialization)

2.2.2

[DEPRECATED]ASL_dfc1bf, ASL_rfc1bf
One-Dimensional Complex Fourier Transforms (After Initialization)

2.3

ONE-DIMENSIONAL COMPLEX FOURIER TRANSFORM (COMPLEX ARGUMENT TYPE)

2.3.1

[DEPRECATED]ASL_zfc1fb, ASL_cfc1fb
One-Dimensional Complex Fourier Transforms (Including Initialization)

2.3.2

[DEPRECATED]ASL_zfc1bf, ASL_cfc1bf
One-Dimensional Complex Fourier Transforms (After Initialization)

2.4

ONE-DIMENSIONAL REAL FOURIER TRANSFORM

2.4.1

[DEPRECATED]ASL_dfr1fb, ASL_rfr1fb
One-Dimensional Real Fourier Transforms (Including Initialization)

2.4.2

[DEPRECATED]ASL_dfr1bf, ASL_rfr1bf
One-Dimensional Real Fourier Transforms (After Initialization)

2.5

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

2.5.1

[DEPRECATED]ASL_dfcmfb, ASL_rfcmfb
Multiple One-Dimensional Complex Fourier Transforms (Include Initialization)

2.5.2

[DEPRECATED]ASL_dfcmbf, ASL_rfcmbf
Multiple One-Dimensional Complex Fourier Transforms (After Initialization)

2.6

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

2.6.1

[DEPRECATED]ASL_zfcmfb, ASL_cfcmfb
Multiple One-Dimensional Complex Fourier Transforms (Include Initialization)

2.6.2

[DEPRECATED]ASL_zfcmbf, ASL_cfcmbf
Multiple One-Dimensional Complex Fourier Transforms (After Initialization)

2.7

MULTIPLE ONE-DIMENSIONAL REAL FOURIER TRANSFORM

2.7.1

[DEPRECATED]ASL_dfrmfb, ASL_rfrmfb
Multiple One-Dimensional Real Fourier Transforms (Including Initialization)

2.7.2

[DEPRECATED]ASL_dfrmbf, ASL_rfrmbf
Multiple One-Dimensional Real Fourier Transforms (After Initialization)

2.8

TWO-DIMENSIONAL COMPLEX FOURIER TRANSFORM (REAL ARGUMENT TYPE)

2.8.1

[DEPRECATED]ASL_dfc2fb, ASL_rfc2fb
Two-Dimensional Complex Fourier Transform (Including Initialization)

2.8.2

[DEPRECATED]ASL_dfc2bf, ASL_rfc2bf
Two-Dimensional Complex Fourier Transform (After Initialization)

2.9

TWO-DIMENSIONAL COMPLEX FOURIER TRANSFORM (COMPLEX ARGUMENT TYPE)

2.9.1

[DEPRECATED]ASL_zfc2fb, ASL_cfc2fb
Two-Dimensional Complex Fourier Transform (Including Initialization)

2.9.2

[DEPRECATED]ASL_zfc2bf, ASL_cfc2bf
Two-Dimensional Complex Fourier Transform (After Initialization)

2.10

TWO-DIMENSIONAL REAL FOURIER TRANSFORM

2.10.1

[DEPRECATED]ASL_dfr2fb, ASL_rfr2fb
Two-Dimensional Real Fourier Transform (Including Initialization)

2.10.2

[DEPRECATED]ASL_dfr2bf, ASL_rfr2bf
Two-Dimensional Real Fourier Transform (After Initialization)

2.11

THREE-DIMENSIONAL COMPLEX FOURIER TRANSFORM (REAL ARGUMENT TYPE)

2.11.1

[DEPRECATED]ASL_dfc3fb, ASL_rfc3fb
Three-Dimensional Complex Fourier Transform (Including Initialization)

2.11.2

[DEPRECATED]ASL_dfc3bf, ASL_rfc3bf
Three-Dimensional Complex Fourier Transform (After Initialization)

2.12

THREE-DIMENSIONAL COMPLEX FOURIER TRANSFORM (COMPLEX ARGUMENT TYPE)

2.12.1

[DEPRECATED]ASL_zfc3fb, ASL_cfc3fb
Three-Dimensional Complex Fourier Transform (Including Initialization)

2.12.2

[DEPRECATED]ASL_zfc3bf, ASL_cfc3bf
Three-Dimensional Complex Fourier Transform (After Initialization)

2.13

THREE-DIMENSIONAL REAL FOURIER TRANSFORM

2.13.1

[DEPRECATED]ASL_dfr3fb, ASL_rfr3fb
Three-Dimensional Real Fourier Transform (Including Initialization)

2.13.2

[DEPRECATED]ASL_dfr3bf, ASL_rfr3bf
Three-Dimensional Real Fourier Transform (After Initialization)

2.14

CONVOLUTIONS

2.14.1

ASL_dfcn1d, ASL_rfcn1d
One-Dimensional Convolutions

2.14.2

ASL_dfcn2d, ASL_rfcn2d
Two-Dimensional Convolutions

2.14.3

ASL_dfcn3d, ASL_rfcn3d
Three-Dimensional Convolutions

2.15

CORRELATIONS

2.15.1

ASL_dfcr1d, ASL_rfcr1d
One-Dimensional Correlations

2.15.2

ASL_dfcr2d, ASL_rfcr2d
Two-Dimensional Correlations

2.15.3

ASL_dfcr3d, ASL_rfcr3d
Three-Dimensional Correlations

2.16

POWER SPECTRUM ANALYSIS

2.16.1

ASL_dfps1d, ASL_rfps1d
One-Dimensional Fourier Periodograms

2.16.2

ASL_dfps2d, ASL_rfps2d
Two-Dimensional Fourier Periodograms

2.16.3

ASL_dfps3d, ASL_rfps3d
Three-Dimensional Fourier Periodograms

2.17

LAPLACE TRANSFORM

2.17.1

ASL_dflara, ASL_rflara
Inverse Laplace Transform (Rational Function)

2.17.2

ASL_dflage, ASL_rflage
Inverse Laplace Transform (General Function)

2.18

WAVELET TRANSFORM

2.18.1

ASL_dfwth1, ASL_rfwth1
Haar Function Generation

2.18.2

ASL_dfwthr, ASL_rfwthr
Wavelet Transform According to Haar Functions

2.18.3

ASL_dfwths, ASL_rfwths
Inverse Wavelet Transform According to Haar Functions

2.18.4

ASL_dfwth2, ASL_rfwth2
Haar Function Generation (Equally Spaced Sampling Data)

2.18.5

ASL_dfwtht, ASL_rfwtht
Wavelet Transform According to Haar Functions (Equally Spaced Sampling Data)

2.18.6

ASL_dfwthi, ASL_rfwthi
Inverse Wavelet Transform According to Haar Functions (Equally Spaced Sampling Data)

2.18.7

ASL_dfwtmf, ASL_rfwtmf
Mexican Hut Function Computation

2.18.8

ASL_dfwtmt, ASL_rfwtmt
Wavelet Transform According to Mexican Hut Functions

2.18.9

ASL_dfwtff, ASL_rfwtff
French Hut Function Computation

2.18.10

ASL_dfwtft, ASL_rfwtft
Wavelet Transform According to French Hut Function

Appendix

Appendix A

MACHINE CONSTANTS USED IN ASL C INTERFACE

A.1

Units for Determining Error

A.2

Maximum and Minimum Values of Floating Point Data