### Abstract

An intimate mathematical relation between Hartley and Hilbert transforms is given here in contrast with the well known Fourier and Hilbert transform relations. It is interesting to note that the Fourier-Hilbert and Hartley-Hilbert transforms while possessing the same magnitude differ in phase by 270°. The inverse Hartley-Hilbert transform returns the original function unlike the Fourier-Hilbert transform which results the negative of the original function. Further, it may be realized that the envelope defined here of the analytic signal in both Fourier-Hilbert and Hartley-Hilbert domains numerically remain the same while differing in polarity. The feasibility of Hartley-Hilbert transform for a straight forward interpretation, total magnetic anomaly due to a thin plate from Tejpur, India and self potential data of the Sulleymonkey anomaly in the Ergani Copper district, Turkey are illustrated in contrast with the Fourier-Hilbert transform. This pair of transforms have innumerable geophysical applications.

Original language | English |
---|---|

Pages (from-to) | 157-161 |

Number of pages | 5 |

Journal | Journal of Applied Geophysics |

Volume | 71 |

Issue number | 4 |

DOIs | |

Publication status | Published - Aug 2010 |

### Fingerprint

### Keywords

- Amplitude
- Analytic signal
- Hartley Hilbert transform
- Interpretation

### ASJC Scopus subject areas

- Geophysics

### Cite this

*Journal of Applied Geophysics*,

*71*(4), 157-161. https://doi.org/10.1016/j.jappgeo.2010.06.005

**Fourier-Hilbert versus Hartley-Hilbert transforms with some geophysical applications.** / Sundararajan, N.; Srinivas, Y.

Research output: Contribution to journal › Article

*Journal of Applied Geophysics*, vol. 71, no. 4, pp. 157-161. https://doi.org/10.1016/j.jappgeo.2010.06.005

}

TY - JOUR

T1 - Fourier-Hilbert versus Hartley-Hilbert transforms with some geophysical applications

AU - Sundararajan, N.

AU - Srinivas, Y.

PY - 2010/8

Y1 - 2010/8

N2 - An intimate mathematical relation between Hartley and Hilbert transforms is given here in contrast with the well known Fourier and Hilbert transform relations. It is interesting to note that the Fourier-Hilbert and Hartley-Hilbert transforms while possessing the same magnitude differ in phase by 270°. The inverse Hartley-Hilbert transform returns the original function unlike the Fourier-Hilbert transform which results the negative of the original function. Further, it may be realized that the envelope defined here of the analytic signal in both Fourier-Hilbert and Hartley-Hilbert domains numerically remain the same while differing in polarity. The feasibility of Hartley-Hilbert transform for a straight forward interpretation, total magnetic anomaly due to a thin plate from Tejpur, India and self potential data of the Sulleymonkey anomaly in the Ergani Copper district, Turkey are illustrated in contrast with the Fourier-Hilbert transform. This pair of transforms have innumerable geophysical applications.

AB - An intimate mathematical relation between Hartley and Hilbert transforms is given here in contrast with the well known Fourier and Hilbert transform relations. It is interesting to note that the Fourier-Hilbert and Hartley-Hilbert transforms while possessing the same magnitude differ in phase by 270°. The inverse Hartley-Hilbert transform returns the original function unlike the Fourier-Hilbert transform which results the negative of the original function. Further, it may be realized that the envelope defined here of the analytic signal in both Fourier-Hilbert and Hartley-Hilbert domains numerically remain the same while differing in polarity. The feasibility of Hartley-Hilbert transform for a straight forward interpretation, total magnetic anomaly due to a thin plate from Tejpur, India and self potential data of the Sulleymonkey anomaly in the Ergani Copper district, Turkey are illustrated in contrast with the Fourier-Hilbert transform. This pair of transforms have innumerable geophysical applications.

KW - Amplitude

KW - Analytic signal

KW - Hartley Hilbert transform

KW - Interpretation

UR - http://www.scopus.com/inward/record.url?scp=77955276302&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955276302&partnerID=8YFLogxK

U2 - 10.1016/j.jappgeo.2010.06.005

DO - 10.1016/j.jappgeo.2010.06.005

M3 - Article

AN - SCOPUS:77955276302

VL - 71

SP - 157

EP - 161

JO - Journal of Applied Geophysics

JF - Journal of Applied Geophysics

SN - 0926-9851

IS - 4

ER -