Multiresolution Analysis#
The functions in this module can be used to project a signal onto wavelet subspaces and an approximation subspace. This is an additive decomposition such that the sum of the coefficients equals the original signal. The projected signal coefficients remains temporally aligned with the original, regardless of the symmetry of the wavelet used for the analysis.
Multilevel 1D mra
#
- pywt.mra(data, wavelet, level=None, axis=-1, transform='swt', mode='periodization')#
Forward 1D multiresolution analysis.
It is a projection onto the wavelet subspaces.
- Parameters
- data: array_like
Input data
- waveletWavelet object or name string
Wavelet to use
- levelint, optional
Decomposition level (must be >= 0). If level is None (default) then it will be calculated using the dwt_max_level function.
- axis: int, optional
Axis over which to compute the DWT. If not given, the last axis is used. Currently only available when
transform='dwt'
.- transform{‘dwt’, ‘swt’}
Whether to use the DWT or SWT for the transforms.
- modestr, optional
Signal extension mode, see Modes (default: ‘symmetric’). This option is only used when transform=’dwt’.
- Returns
- [cAn, {details_level_n}, … {details_level_1}]list
For more information, see the detailed description in wavedec
Notes
This is sometimes referred to as an additive decomposition because the inverse transform (
imra
) is just the sum of the coefficient arrays [1]. The decomposition usingtransform='dwt'
corresponds to section 2.2 while that using an undecimated transform (transform='swt'
) is described in section 3.2 and appendix A.This transform does not share the variance partition property of
swt
with norm=True. It does however, result in coefficients that are temporally aligned regardless of the symmetry of the wavelet used.The redundancy of this transform is
(level + 1)
.References
- 1
Donald B. Percival and Harold O. Mofjeld. Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets. Journal of the American Statistical Association Vol. 92, No. 439 (Sep., 1997), pp. 868-880. https://doi.org/10.2307/2965551
Multilevel 2D mra2
#
- pywt.mra2(data, wavelet, level=None, axes=(-2, -1), transform='swt2', mode='periodization')#
Forward 2D multiresolution analysis.
It is a projection onto wavelet subspaces.
- Parameters
- data: array_like
Input data
- waveletWavelet object or name string, or 2-tuple of wavelets
Wavelet to use. This can also be a tuple containing a wavelet to apply along each axis in axes.
- levelint, optional
Decomposition level (must be >= 0). If level is None (default) then it will be calculated using the dwt_max_level function.
- axes2-tuple of ints, optional
Axes over which to compute the DWT. Repeated elements are not allowed. Currently only available when
transform='dwt2'
.- transform{‘dwt2’, ‘swt2’}
Whether to use the DWT or SWT for the transforms.
- modestr or 2-tuple of str, optional
Signal extension mode, see Modes (default: ‘symmetric’). This option is only used when transform=’dwt2’.
- Returns
- coeffslist
For more information, see the detailed description in wavedec2
Notes
This is sometimes referred to as an additive decomposition because the inverse transform (
imra2
) is just the sum of the coefficient arrays [1]. The decomposition usingtransform='dwt'
corresponds to section 2.2 while that using an undecimated transform (transform='swt'
) is described in section 3.2 and appendix A.This transform does not share the variance partition property of
swt2
with norm=True. It does however, result in coefficients that are temporally aligned regardless of the symmetry of the wavelet used.The redundancy of this transform is
3 * level + 1
.References
- 1
Donald B. Percival and Harold O. Mofjeld. Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets. Journal of the American Statistical Association Vol. 92, No. 439 (Sep., 1997), pp. 868-880. https://doi.org/10.2307/2965551
Multilevel n-dimensional mran
#
- pywt.mran(data, wavelet, level=None, axes=None, transform='swtn', mode='periodization')#
Forward nD multiresolution analysis.
It is a projection onto the wavelet subspaces.
- Parameters
- data: array_like
Input data
- waveletWavelet object or name string, or tuple of wavelets
Wavelet to use. This can also be a tuple containing a wavelet to apply along each axis in axes.
- levelint, optional
Decomposition level (must be >= 0). If level is None (default) then it will be calculated using the dwt_max_level function.
- axestuple of ints, optional
Axes over which to compute the DWT. Repeated elements are not allowed.
- transform{‘dwtn’, ‘swtn’}
Whether to use the DWT or SWT for the transforms.
- modestr or tuple of str, optional
Signal extension mode, see Modes (default: ‘symmetric’). This option is only used when transform=’dwtn’.
- Returns
- coeffslist
For more information, see the detailed description in wavedecn.
Notes
This is sometimes referred to as an additive decomposition because the inverse transform (
imran
) is just the sum of the coefficient arrays [1]. The decomposition usingtransform='dwt'
corresponds to section 2.2 while that using an undecimated transform (transform='swt'
) is described in section 3.2 and appendix A.This transform does not share the variance partition property of
swtn
with norm=True. It does however, result in coefficients that are temporally aligned regardless of the symmetry of the wavelet used.The redundancy of this transform is
(2**n - 1) * level + 1
wheren
corresponds to the number of axes transformed.References
- 1
Donald B. Percival and Harold O. Mofjeld. Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets. Journal of the American Statistical Association Vol. 92, No. 439 (Sep., 1997), pp. 868-880. https://doi.org/10.2307/2965551
Inverse Multilevel 1D imra
#
- pywt.imra(mra_coeffs)#
Inverse 1D multiresolution analysis via summation.
- Parameters
- mra_coeffslist of ndarray
Multiresolution analysis coefficients as returned by mra.
- Returns
- recndarray
The reconstructed signal.
See also
References
- 1
Donald B. Percival and Harold O. Mofjeld. Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets. Journal of the American Statistical Association Vol. 92, No. 439 (Sep., 1997), pp. 868-880. https://doi.org/10.2307/2965551
Inverse Multilevel 2D imra2
#
- pywt.imra2(mra_coeffs)#
Inverse 2D multiresolution analysis via summation.
- Parameters
- mra_coeffslist
Multiresolution analysis coefficients as returned by mra2.
- Returns
- recndarray
The reconstructed signal.
See also
References
- 1
Donald B. Percival and Harold O. Mofjeld. Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets. Journal of the American Statistical Association Vol. 92, No. 439 (Sep., 1997), pp. 868-880. https://doi.org/10.2307/2965551
Inverse Multilevel n-dimensional imran
#
- pywt.imran(mra_coeffs)#
Inverse nD multiresolution analysis via summation.
- Parameters
- mra_coeffslist
Multiresolution analysis coefficients as returned by mra2.
- Returns
- recndarray
The reconstructed signal.
See also
References
- 1
Donald B. Percival and Harold O. Mofjeld. Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets. Journal of the American Statistical Association Vol. 92, No. 439 (Sep., 1997), pp. 868-880. https://doi.org/10.2307/2965551