The DWT function implements Mallat's algorithm (an iterate algorithm in the Discrete Wavelet Transform field) and applies wavelet transform on multiple sequences simultaneously.
The input is typically a set of time series sequences. You specify the wavelet name or wavelet filter table, transform level, and (optionally) extension mode. The function returns the transformed sequences in Hilbert space with the corresponding component identifiers and indices. (The transformation is also called the decomposition.)
The wavelet filter table does not appear in the preceding diagram because it is seldom used.
You can filter the result to reduce the lengths of the transformed sequences and then use the function IDWT to reconstruct them; therefore, the DWT and IDWT functions are useful for compression and removing noise.