Inverse Discrete Wavelet Transform (IDWT)

Single level idwt

pywt.idwt(cA, cD, wavelet, mode='symmetric', axis=-1)

Single level Inverse Discrete Wavelet Transform.

Parameters:
cA : array_like or None

Approximation coefficients. If None, will be set to array of zeros with same shape as cD.

cD : array_like or None

Detail coefficients. If None, will be set to array of zeros with same shape as cA.

wavelet : Wavelet object or name

Wavelet to use

mode : str, optional (default: ‘symmetric’)

Signal extension mode, see Modes.

axis: int, optional

Axis over which to compute the inverse DWT. If not given, the last axis is used.
Returns:
rec: array_like

Single level reconstruction of signal from given coefficients.

Examples

>>> import pywt
>>> (cA, cD) = pywt.dwt([1,2,3,4,5,6], 'db2', 'smooth')
>>> pywt.idwt(cA, cD, 'db2', 'smooth')
array([ 1.,  2.,  3.,  4.,  5.,  6.])

One of the neat features of idwt is that one of the cA and cD arguments can be set to None. In that situation the reconstruction will be performed using only the other one. Mathematically speaking, this is equivalent to passing a zero-filled array as one of the arguments.

>>> (cA, cD) = pywt.dwt([1,2,3,4,5,6], 'db2', 'smooth')
>>> A = pywt.idwt(cA, None, 'db2', 'smooth')
>>> D = pywt.idwt(None, cD, 'db2', 'smooth')
>>> A + D
array([ 1.,  2.,  3.,  4.,  5.,  6.])

Multilevel reconstruction using waverec

pywt.waverec(coeffs, wavelet, mode='symmetric', axis=-1)

Multilevel 1D Inverse Discrete Wavelet Transform.

Parameters:
coeffs : array_like

Coefficients list [cAn, cDn, cDn-1, …, cD2, cD1]

wavelet : Wavelet object or name string

Wavelet to use

mode : str, optional

Signal extension mode, see Modes.

axis: int, optional

Axis over which to compute the inverse DWT. If not given, the last axis is used.

Notes

It may sometimes be desired to run waverec with some sets of coefficients omitted. This can best be done by setting the corresponding arrays to zero arrays of matching shape and dtype. Explicitly removing list entries or setting them to None is not supported.

Specifically, to ignore detail coefficients at level 2, one could do:

coeffs[-2] == np.zeros_like(coeffs[-2])

Examples

>>> import pywt
>>> coeffs = pywt.wavedec([1,2,3,4,5,6,7,8], 'db1', level=2)
>>> pywt.waverec(coeffs, 'db1')
array([ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.])

Direct reconstruction with upcoef

pywt.upcoef(part, coeffs, wavelet, level=1, take=0)

Direct reconstruction from coefficients.

Parameters:
part : str

Coefficients type: * ‘a’ - approximations reconstruction is performed * ‘d’ - details reconstruction is performed

coeffs : array_like

Coefficients array to recontruct

wavelet : Wavelet object or name

Wavelet to use

level : int, optional

Multilevel reconstruction level. Default is 1.

take : int, optional

Take central part of length equal to ‘take’ from the result. Default is 0.
Returns:
rec : ndarray

1-D array with reconstructed data from coefficients.

See also

downcoef

Examples

>>> import pywt
>>> data = [1,2,3,4,5,6]
>>> (cA, cD) = pywt.dwt(data, 'db2', 'smooth')
>>> pywt.upcoef('a', cA, 'db2') + pywt.upcoef('d', cD, 'db2')
array([-0.25      , -0.4330127 ,  1.        ,  2.        ,  3.        ,
        4.        ,  5.        ,  6.        ,  1.78589838, -1.03108891])
>>> n = len(data)
>>> pywt.upcoef('a', cA, 'db2', take=n) + pywt.upcoef('d', cD, 'db2', take=n)
array([ 1.,  2.,  3.,  4.,  5.,  6.])