Filters - Hilbert Transform and Absolute Value of Magnitude Response
Neb, i dunno where you got that frequency response expression from, but it's flawed.  from the description (of parameters like $W$ in "octaves"), it should be like this:

$$ Gain(f) = \begin{cases}
10^{Boost/20} \times \frac{1}{2}\left\{1 + \cos\left(\pi \frac{\log_2(f/F_c)}{W} \right) \right\}, &amp; \text{if }|\log_2(f/F_c)|&lt;W \\
0, &amp; \text{otherwise } \end{cases} $$