# 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. 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. rec : ndarray 1-D array with reconstructed data from coefficients.

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.])