Wavelet packet transforms are also related to the discrete wavelet transform. Wavelet&colon; formula 36 where formula 37 is a single mother wavelet function. For details, see comparison of the discrete wavelet transform with the discrete Fourier transform. This is accomplished using an inverse wavelet transform. Wavelet compression can be either lossless or lossy. This decomposition is done using wavelet filtering. The motivation for development of the Wavelet transform was the Short-time Fourier transform. The multidimensional generalization of this wavelet is called the Laplacian of Gaussian function. Both pairs of identities form the basis for the algorithm of the fast wavelet transform. The quantized sub-bands are split further into "precincts", rectangular regions in the wavelet domain. This implies that an orthonormal wavelet is self-dual. The Haar transform is the simplest of the wavelet transforms. Complex wavelet transform is another form. The Morlet wavelet transform method is applied to music transcription. One of the most popular applications of wavelet transform is image compression.