Next: hist, Previous: hfk5z, Up: Internal Routines [Contents][Index]

`hilbert(`

`data` [, `axes`, `direction`, /back, /all,
/avgkeep, /highkeep])

Returns a discrete Hilbert transform of the

along the
indicated `data`

in the indicated `axes`

.
The Hilbert transform changes the phases of the Fourier components in
the data by 90 degrees, replacing sines by cosines and cosines by sines
(with appropriate signs). By default, the phases are shifted forward in
the first dimension.
`direction`

If

(after transformation to an integer) is
negative, then the phases are shifted back. If `direction`

is zero or positive, then the phases are shifted forward. If
`direction`

is not specified, then `direction``/back`

implies the
backward shift.

If

is specified, then it is taken to contain the axes
along which transformation is to be done. No axis may appear more than
once. The axes need not be in any specific order. If `axes`

is not specified, then if `axes``/all`

is specified, all axes are
treated. If neither

nor `axes``/all`

are specified,
then the first axis is assumed.

By default, the forward and backward transforms are almost each other’s
inverse: If you apply the one and the equivalent other in succession,
then you get the original data back, except that the Hilbert transform
sets averages to zero and also removes the very highest frequency from
the data (which by definition always has its sine component equal to
zero). However, keyword `/avgkeep`

retains the average, and
keyword `/highkeep`

retains the highest frequency.

The power spectrum of the default Hilbert transform of `x`

is equal
to the power spectrum of `x`

itself, except at zero frequency
(corresponding to the average) and at the very highest frequency.

• hilbert Details: |

Next: hist, Previous: hfk5z, Up: Internal Routines [Contents][Index]