hilbert.filter: Select a Hilbert Wavelet Pair

In waveslim: Basic Wavelet Routines for One-, Two- and Three-dimensional Signal Processing

Description

Converts name of Hilbert wavelet pair to filter coefficients.

Usage

hilbert.filter(name)

Arguments

name	Character string of Hilbert wavelet pair, see acceptable names below (e.g., "k3l3").

Details

Simple switch statement selects the appropriate HWP. There are two parameters that define a Hilbert wavelet pair using the notation of Selesnick (2001,2002), K and L. Currently, the only implemented combinations (K,L) are (3,3), (3,5), (4,2) and (4,4).

Value

List containing the following items:

L	length of the wavelet filter
h0,g0	low-pass filter coefficients
h1,g1	high-pass filter coefficients

Author(s)

B. Whitcher

References

Selesnick, I.W. (2001). Hilbert transform pairs of wavelet bases. IEEE Signal Processing Letters\/~8(6), 170–173.

Selesnick, I.W. (2002). The design of approximate Hilbert transform pairs of wavelet bases. IEEE Transactions on Signal Processing\/~50(5), 1144–1152.

See Also

wave.filter

Examples

hilbert.filter("k3l3")
hilbert.filter("k3l5")
hilbert.filter("k4l2")
hilbert.filter("k4l4")

Example output

waveslim: Wavelet Method for 1/2/3D Signals (version = 1.7.5)

$length
[1] 12

$hpf
$hpf[[1]]
 [1] -0.0022260892  0.0426791770  0.0248291600 -0.4982782400  0.7997265200
 [6] -0.2867863600 -0.1564275500  0.0331898960  0.0434276420  0.0022046914
[11] -0.0022229002 -0.0001159435

$hpf[[2]]
 [1] -1.558262e-02  4.943225e-02  2.167541e-01 -7.458501e-01  6.133371e-01
 [6]  1.550640e-02 -1.270504e-01 -3.236969e-02  1.970114e-02  6.190912e-03
[11] -5.254341e-05 -1.656336e-05


$lpf
$lpf[[1]]
 [1]  0.0001159435 -0.0022229002 -0.0022046914  0.0434276420 -0.0331898960
 [6] -0.1564275500  0.2867863600  0.7997265200  0.4982782400  0.0248291600
[11] -0.0426791770 -0.0022260892

$lpf[[2]]
 [1]  1.656336e-05 -5.254341e-05 -6.190912e-03  1.970114e-02  3.236969e-02
 [6] -1.270504e-01 -1.550640e-02  6.133371e-01  7.458501e-01  2.167541e-01
[11] -4.943225e-02 -1.558262e-02


$length
[1] 12

$hpf
$hpf[[1]]
 [1] -5.854176e-06  2.299268e-04  2.864101e-03 -1.273398e-02 -5.957379e-02
 [6]  1.300891e-01  2.653746e-01 -7.875716e-01  5.340248e-01 -3.981034e-03
[11] -4.557677e-02 -3.574788e-02  1.021288e-02  2.614091e-03 -2.131052e-04
[16] -5.425879e-06

$hpf[[2]]
 [1] -6.439594e-05 -4.664223e-05  9.547891e-03  6.282690e-03 -1.233684e-01
 [6]  4.621801e-03  5.832856e-01 -7.650914e-01  2.292948e-01  7.456225e-02
[11]  9.250975e-03 -2.860147e-02 -8.400312e-04  1.166470e-03  3.572714e-07
[16] -4.932617e-07


$lpf
$lpf[[1]]
 [1]  5.425879e-06 -2.131052e-04 -2.614091e-03  1.021288e-02  3.574788e-02
 [6] -4.557677e-02  3.981034e-03  5.340248e-01  7.875716e-01  2.653746e-01
[11] -1.300891e-01 -5.957379e-02  1.273398e-02  2.864101e-03 -2.299268e-04
[16] -5.854176e-06

$lpf[[2]]
 [1]  4.932617e-07  3.572714e-07 -1.166470e-03 -8.400312e-04  2.860147e-02
 [6]  9.250975e-03 -7.456225e-02  2.292948e-01  7.650914e-01  5.832856e-01
[11] -4.621801e-03 -1.233684e-01 -6.282690e-03  9.547891e-03  4.664223e-05
[16] -6.439594e-05


$length
[1] 12

$hpf
$hpf[[1]]
 [1]  0.002285229 -0.017099408 -0.061694251  0.160409270  0.227520750
 [6] -0.774586170  0.560358370 -0.041525062 -0.034722190 -0.036090743
[11]  0.013358873  0.001785330

$hpf[[2]]
 [1]  0.0114261460  0.0059121296 -0.1332013800  0.0403150080  0.5409737900
 [6] -0.7795662200  0.2746430800  0.0584667250  0.0134499020 -0.0325914860
[11] -0.0001847535  0.0003570660


$lpf
$lpf[[1]]
 [1] -0.001785330  0.013358873  0.036090743 -0.034722190  0.041525062
 [6]  0.560358370  0.774586170  0.227520750 -0.160409270 -0.061694251
[11]  0.017099408  0.002285229

$lpf[[2]]
 [1] -0.0003570660 -0.0001847535  0.0325914860  0.0134499020 -0.0584667250
 [6]  0.2746430800  0.7795662200  0.5409737900 -0.0403150080 -0.1332013800
[11] -0.0059121296  0.0114261460


$length
[1] 16

$hpf
$hpf[[1]]
 [1] -2.593319e-05  6.742522e-04  5.732357e-03 -1.697939e-02 -6.975951e-02
 [6]  1.337267e-01  2.790955e-01 -7.833091e-01  5.302173e-01 -8.136445e-03
[11] -5.068726e-02 -3.860533e-02  1.320347e-02  5.548244e-03 -6.690907e-04
[16] -2.573467e-05

$hpf[[2]]
 [1] -2.333987e-04 -1.556956e-04  1.548964e-02  9.196125e-03 -1.352010e-01
 [6] -5.170879e-03  5.883470e-01 -7.574938e-01  2.329811e-01  7.708457e-02
[11]  7.702384e-03 -3.355466e-02 -1.980900e-03  2.990384e-03  1.907454e-06
[16] -2.859407e-06


$lpf
$lpf[[1]]
 [1]  2.573467e-05 -6.690907e-04 -5.548244e-03  1.320347e-02  3.860533e-02
 [6] -5.068726e-02  8.136445e-03  5.302173e-01  7.833091e-01  2.790955e-01
[11] -1.337267e-01 -6.975951e-02  1.697939e-02  5.732357e-03 -6.742522e-04
[16] -2.593319e-05

$lpf[[2]]
 [1]  2.859407e-06  1.907454e-06 -2.990384e-03 -1.980900e-03  3.355466e-02
 [6]  7.702384e-03 -7.708457e-02  2.329811e-01  7.574938e-01  5.883470e-01
[11]  5.170879e-03 -1.352010e-01 -9.196125e-03  1.548964e-02  1.556956e-04
[16] -2.333987e-04

waveslim documentation built on May 2, 2019, 4:41 p.m.