split subbands

class description

split_subbands.split_subbands(settings: Dict[str, Any], msap_in: numpy.ndarray) → numpy.ndarray

Compute subfrequency bands for a given 1/3rd octave frequency spectrum.

Parameters

• settings (Dict[str, Any]) – pyna settings

• msap_in (np.ndarray [settings.N_f']]) – mean-square acoustic pressure of the source (re. rho_0,^2c_0^2) [-]

Returns

mean-square acoustic pressure of the source, split into sub-frequency bands (re. rho_0,^2c_0^2) [-]

Return type

msap_sb [settings.N_f’]*settings.N_b’]]

theory

The atmospheric absorption and ground absorption and reflections are applied to a sub-band frequency spectrum. Each frequency, \(f_i\), within the one-third octave frequency spectrum (i.e. \(i \in [1, N_f]\)) is divided into \(N_b = 2m+1\) sub-bands, where \(m\) is a strictly positive integer. The ratio of sub-band center frequencies is:

\[\frac{f_{sb, j+1}}{f_{sb, j}} = w = 2^{1/(3N_b)}\]

where \(j = (i-1)N_b + h\) is the index of the sub-band center frequency and \(h \in [1,N_b]\). Thus, the j-th sub-band center frequency is computed from the i-th original frequency using:

\[f_j = w^{h-m-1} f_i \quad \textrm{with} h \in [1, N_b] \ \textrm{and}\ i \in [1, N_f]\]

The mean-square acoustic pressure of each original one-third frequency band, \(<p^2>^*_i\), is also divided into sub-bands. Firstly, the slopes of the mean-square acoustic pressure in the lower (\(u\)) and upper (\(v\)) half of the band are computed using:

\[\begin{split}\begin{cases} u_i = \frac{<p^2>^*[i]}{<p^2>^*[i-1]}; v = \frac{<p^2>^*[i+1]}{<p^2>^*[i]}\quad & \textrm{if} \quad i \in [2, N_f]\\ u_i = v_i = \frac{<p^2>^*[1]}{<p^2>^*[0]} \quad & \textrm{if} \quad i = 1 \\ u_i = v_i = \frac{<p^2>^*[N_f]}{<p^2>^*[N_f-1]} \quad & \textrm{if} \quad i = N_f \\ \end{cases}\end{split}\]

The sub-band adjusting factor, \(A_i\), is computed using:

\[A_i = 1 + \sum_{h = 1}^{m} \left( u_i^{(h-m-1)/N_b} + v_i^{1/N_b} \right)\]

Finally, the mean-square acoustic pressure of each sub-band frequency is given by:

\[\begin{split}<p^2>^*_j = \begin{cases} (<p^2>^*_i / A_i)u_i^{h-m-1} \quad & \textrm{if} \quad h \in [1, m] \\ (<p^2>^*_i / A_i) \quad & \textrm{if} \quad h = m + 1\\ (<p^2>^*_i / A_i)v_i^{h-m-1} \quad & \textrm{if} \quad h \in [m+2, N_b]\\ \end{cases}\end{split}\]