Shelf Filter

Figure 18: First-order shelf filter where $H(\omega ) = 0$ at $\omega =\pi$ and $H(\omega )=1$ at $\omega =0$. The cutoff frequency is given by $\omega _T$ and $H(\omega _T)$ is given by $\sigma _T$.

• The first-order shelf is characterized by
  1. Unity gain at DC
  2. A band edge gain $g_{\pi}>0$
  3. A gain $\sqrt{g_{\pi}}$ at the transition frequency $f_t$.