Select a Hilbert Wavelet Pair — hilbert.filter • waveslim

Converts name of Hilbert wavelet pair to filter coefficients.

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

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

Author

B. Whitcher

Examples

hilbert.filter("k3l3")
#> $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
#> 
#> 
hilbert.filter("k3l5")
#> $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
#> 
#> 
hilbert.filter("k4l2")
#> $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
#> 
#> 
hilbert.filter("k4l4")
#> $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
#> 
#>