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.
|Number of pages||5|
|Journal||Journal of Applied Geophysics|
|Publication status||Published - Aug 2010|
- Analytic signal
- Hartley Hilbert transform
ASJC Scopus subject areas