Function max_modwt_level 

pub fn max_modwt_level(signal_length: usize, filter_length: usize) -> usize

Calculate maximum decomposition level for MODWT

The maximum level J is constrained by: 2^J * (L-1) < N where:

• J is the decomposition level
• L is the filter length (number of wavelet coefficients)
• N is the signal length

This constraint ensures that the dilated filter at level J doesn’t exceed the signal length. At level J, the filter is dilated by a factor of 2^J, creating gaps between filter coefficients.

Why this constraint exists:

Unlike DWT which downsamples by 2 at each level, MODWT keeps all coefficients but dilates (upsamples) the filters. At level J:

• The filter spans (2^J * (L-1) + 1) samples due to dilation
• This span must fit within the signal length N for valid convolution

Examples

• Signal length 1024, Haar wavelet (L=2): max level = 9

  • 2^9 * (2-1) = 512 < 1024 ✓
  • 2^10 * (2-1) = 1024 ≥ 1024 ✗

• Signal length 1024, DB4 wavelet (L=8): max level = 7

  • 2^7 * (8-1) = 896 < 1024 ✓
  • 2^8 * (8-1) = 1792 ≥ 1024 ✗

Financial Time Series Note

For financial applications with long time series (e.g., years of tick data), this usually isn’t a limitation. However, for short windows (e.g., analyzing just a few minutes of data), the maximum level may be restricted, especially with longer wavelets.