SUMMARY

Applies a Hilbert transform.

SYNTAX

HILBERT

DESCRIPTION

Each data file, y(n), in the data file list is replaced by its Hilbert transform, x(n). The transform is found by convolving y(n) (in the time domain) with a 201 point FIR filter: The filter impulse response is obtained by windowing an ideal Hilbert transformer impulse response with a Hamming window: In the frequency domain, this filter approximates the transfer function: The phase criterion is met exactly (90 degree phase shift at each frequency), and the magnitude response is (ideally) unity.

Note that the operation is inexact in small regions about DC and the folding frequency. If transforms are to be taken of very low frequency data, such as long period surface waves, the signals should first be decimated. Since the transformation is performed in the time domain, computations are done in-place using the overlap-save algorithm. There are no restrictions on the length of data file.

Added in 2013 Hilbert transforms can be used to calculate the minimum-delay phase from (the log of) the spectral amplitude. Such amplitudes are effectively low-pass filters, which are not band-limited, and the procedure used here does not work very well for such functions.

HEADER CHANGES

DEPMIN, DEPMAX, DEPMEN

ACKNOWLEDGEMENT

The subroutines used to perform the Hilbert transform were designed and developed by Dave Harris.

LATEST REVISION

April 21, 1989 (Version 10.4c)

Amplitude Response of Hilbert Transform.