Performs single-level n-dimensional Discrete Wavelet Transform.
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Results are arranged in a dictionary, where key specifies the transform type on each dimension and value is a n-dimensional coefficients array.
For example, for a 2D case the result will look something like this:
{
'aa': <coeffs> # A(LL) - approx. on 1st dim, approx. on 2nd dim
'ad': <coeffs> # H(LH) - approx. on 1st dim, det. on 2nd dim
'da': <coeffs> # V(HL) - det. on 1st dim, approx. on 2nd dim
'dd': <coeffs> # D(HH) - det. on 1st dim, det. on 2nd dim
}
Integration of wavelet function approximations as well as any other signals can be performed using the pywt.intwave() function.
The result of the call depends on the wavelet argument:
for orthogonal wavelets - an integral of the wavelet function specified on an x-grid:
[int_psi, x] = intwave(wavelet, precision)
for other wavelets - integrals of decomposition and reconstruction wavelet functions and a corresponding x-grid:
[int_psi_d, int_psi_r, x] = intwave(wavelet, precision)
for a tuple of coefficients data and a x-grid - an integral of function and the given x-grid is returned (the x-grid is used for computations).:
[int_function, x] = intwave((data, x), precision)
Example:
>>> import pywt
>>> wavelet1 = pywt.Wavelet('db2')
>>> [int_psi, x] = pywt.intwave(wavelet1, precision=5)
>>> wavelet2 = pywt.Wavelet('bior1.3')
>>> [int_psi_d, int_psi_r, x] = pywt.intwave(wavelet2, precision=5)
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